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in an election between two candidates , the winner has a margin of 20 % of the votes polled . if 1000 people change their mind and vote for the loser , the loser would have won by a margin of 20 % of the votes polled . find the total number of votes polled in the election ? | winner - looser 60 % - 40 % if 1000 people change their mind and vote for the loser : winner - looser 40 % - 60 % thus 1,000 people compose 20 % of all voters , which means that the total number of votes is 5,000 . answer : b | a ) 10000 , b ) 5000 , c ) 15000 , d ) 20000 , e ) 6000 | b | divide(1000, divide(20, const_100)) | divide(n0,const_100)|divide(n1,#0) | gain | allenai/math_qa |
a cube is divided into 343 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ? | "each side of the cube has 7 x 7 = 49 cubelets . only the interior cubelets are painted one colour . on each side , 5 x 5 = 25 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 25 = 150 the answer is b ." | a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225 | b | divide(subtract(343, multiply(multiply(const_4, const_2), const_3)), const_2) | multiply(const_2,const_4)|multiply(#0,const_3)|subtract(n0,#1)|divide(#2,const_2)| | geometry | allenai/math_qa |
if log 2 = 0.3010 and log 3 = 0.4771 , the values of log 5 512 is | "ans : log 5512 = { \ color { black } \ frac { \ log 512 } { \ log 5 } } = { \ color { black } \ frac { \ log 2 ^ { 9 } } { \ log ( \ frac { 10 } { 2 } ) } } = { \ color { black } \ frac { 9 \ log 2 } { \ log 10 - \ log 2 } } = { \ color { black } \ frac { ( 9 \ times 0.3010 ) } { 1 - 0.3010 } } = { \ color { black } \ frac { 2.709 } { 0.699 } } = { \ color { black } \ frac { 2709 } { 699 } } = 3.876 answer : b ) 3.875" | a ) 3.879 , b ) 3.875 , c ) 3.872 , d ) 3.828 , e ) 3.192 | b | multiply(0.3010, divide(0.3010, 0.4771)) | divide(n1,n3)|multiply(n1,#0)| | other | allenai/math_qa |
in one hour , a boat goes 15 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is : | "sol . speed in still water = 1 / 2 ( 15 + 5 ) kmph = 10 kmph . answer c" | a ) 2 , b ) 4 , c ) 10 , d ) 12 , e ) 15 | c | divide(add(15, 5), const_2) | add(n0,n1)|divide(#0,const_2)| | physics | allenai/math_qa |
a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12200 after a year ? | "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12200 = 3660 . answer : a" | a ) 3660 , b ) 2881 , c ) 2887 , d ) 9977 , e ) 2212 | a | multiply(divide(6300, add(add(6300, 4200), 10500)), 12200) | add(n0,n1)|add(n2,#0)|divide(n0,#1)|multiply(n3,#2)| | gain | allenai/math_qa |
carol spends 1 / 4 of her savings on a stereo and 2 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ? | total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 2 / 3 ) ( 1 / 4 ) s = ( 1 / 3 ) * ( 1 / 4 ) * s = ( 1 / 12 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 12 ) / s = 1 / 4 answer : a | a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12 | a | divide(1, 4) | divide(n0,n1) | general | allenai/math_qa |
10 ^ 222 ÷ 10 ^ 220 = ? | 10 ^ 222 ÷ 10 ^ 220 = 10 ^ ( 222 - 220 ) = 10 ^ 2 = 100 answer is c | a ) 10 , b ) 1000 , c ) 100 , d ) 10000 , e ) 100000 | c | divide(power(10, 222), power(10, 220)) | power(n0,n1)|power(n0,n3)|divide(#0,#1) | general | allenai/math_qa |
ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1000 then loss of pyarelal ? | "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1000 , loss of pyarelal = 1000 * 9 x / 10 x = 900 answer : d" | a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000 | d | divide(multiply(9, 1000), add(1, 9)) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0)| | gain | allenai/math_qa |
a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 65 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . ) | for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.65 * 12000 = 12000 - 7800 x = 4200 earning becomes 9360 + 3 x = 9360 + 3 * 4200 = 21960 ans : d | a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,960 , e ) $ 27,360 | d | add(multiply(const_100, const_3), const_60) | multiply(const_100,const_3)|add(#0,const_60) | general | allenai/math_qa |
if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ? | we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > ( 2 x 9 ) % of x = ( 1 x 9 ) % of y thus , 18 % of x = 9 % of y . answer : b | a ) 7 % , b ) 9 % , c ) 11 % , d ) 12 % , e ) none of these | b | divide(multiply(6, 18), 12) | multiply(n1,n2)|divide(#0,n0) | general | allenai/math_qa |
what is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1 ? | since 500 = 2 ^ 2 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 250 odd numbers from 1 to 500 . we then need to eliminate the 50 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 495 . there are a total of 250 - 50 = 200 such numbers between 1 and 500 . the answer is c . | a ) 50 , b ) 100 , c ) 200 , d ) 300 , e ) 400 | c | subtract(subtract(500, const_1), subtract(add(add(divide(subtract(subtract(500, const_2), const_2), const_2), const_1), add(divide(subtract(subtract(500, divide(500, const_100)), divide(500, const_100)), divide(500, const_100)), const_1)), add(divide(subtract(subtract(500, const_10), const_10), const_10), 1))) | divide(n0,const_100)|subtract(n0,const_1)|subtract(n0,const_2)|subtract(n0,const_10)|subtract(#2,const_2)|subtract(n0,#0)|subtract(#3,const_10)|divide(#4,const_2)|divide(#6,const_10)|subtract(#5,#0)|add(#7,const_1)|add(n2,#8)|divide(#9,#0)|add(#12,const_1)|add(#10,#13)|subtract(#14,#11)|subtract(#1,#15) | general | allenai/math_qa |
thomas worked in the factory @ 4550 / - per week . owner told him to give the amount after one month . then how much amount will be paid to thomas ? | total salary paid to thomas in one week : 4550 / - salary for one day : 4550 / 7 = 650 / - total for one month = 650 / - * 30 days = 19500 / - answer is option ( d ) | a ) 9500 , b ) 17500 , c ) 18200 , d ) 19500 , e ) 6750 | d | add(add(multiply(multiply(const_100, const_10), const_10), multiply(4550, const_2)), multiply(const_100, const_4)) | multiply(const_10,const_100)|multiply(n0,const_2)|multiply(const_100,const_4)|multiply(#0,const_10)|add(#3,#1)|add(#4,#2) | general | allenai/math_qa |
he total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ? | "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c" | a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95 | c | divide(150, const_2) | divide(n0,const_2)| | general | allenai/math_qa |
the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.3 years , the ratio of the number of boys to the number of girls in the class is | "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) < = > k = 0.5 / 0.6 = 5 / 6 . required ratio = 5 / 6 : 1 = 5 : 6 . answer : e" | a ) 7 : 3 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 5 : 6 | e | divide(subtract(15.8, 15.3), subtract(16.4, 15.8)) | subtract(n0,n2)|subtract(n1,n0)|divide(#0,#1)| | general | allenai/math_qa |
on selling 20 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is : | "( c . p . of 20 balls ) - ( s . p . of 20 balls ) = ( c . p . of 5 balls ) c . p . of 15 balls = s . p . of 20 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 15 = rs . 48 . answer : option a" | a ) s . 48 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 70 | a | divide(720, subtract(20, 5)) | subtract(n0,n2)|divide(n1,#0)| | gain | allenai/math_qa |
a pipe takes a hours to fill the tank . but because of a leakage it took 4 times of its original time . find the time taken by the leakage to empty the tank | "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 240 x = 80 min answer : d" | a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min | d | multiply(const_10, multiply(const_1, 4)) | multiply(n0,const_1)|multiply(#0,const_10)| | physics | allenai/math_qa |
shop offered 30 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ? | "sp * ( 70 / 100 ) = 560 sp = 8 * 100 = > cp = 800 answer : b" | a ) 500 , b ) 800 , c ) 600 , d ) 700 , e ) 750 | b | divide(560, subtract(const_1, divide(30, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | gain | allenai/math_qa |
if 17 ^ 4 * 13 ^ 4 * 9 ^ 4 * 8 ^ 4 = x , what is the units digit of x ? | "17 ^ 4 * 13 ^ 4 * 9 ^ 4 * 8 ^ 4 = x units digit of x will be 7 ^ 4 * 3 ^ 4 * 9 ^ 4 * 8 ^ 4 = 1 * 1 * 1 * 6 = 6 therefore , units digit of x = 6 answer c" | a ) 8 , b ) 3 , c ) 6 , d ) 7 , e ) 9 | c | divide(multiply(4, 4), const_10) | multiply(n1,n7)|divide(#0,const_10)| | general | allenai/math_qa |
find the simple interest on rs . 68,000 at 16 2 / 3 % per year for 9 months . | "p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is c ." | a ) 7500 , b ) 6500 , c ) 8500 , d ) 9500 , e ) none of them | c | multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100)) | add(n2,n3)|divide(const_1,const_100)|multiply(n3,n3)|multiply(n2,n3)|multiply(n1,n3)|add(n2,#4)|multiply(n2,#3)|multiply(#3,const_100)|multiply(#2,const_100)|multiply(#0,n2)|divide(#2,#6)|divide(#5,n3)|multiply(#7,const_100)|multiply(#8,#9)|add(#12,#13)|multiply(#14,#11)|multiply(#10,#15)|multiply(#1,#16)| | gain | allenai/math_qa |
if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 65 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ? | "0.1 x = 0.08 ( 2000 - x ) + 65 0.18 x = 225 x = 1250 then the amount invested at 8 % is $ 2000 - $ 1250 = $ 750 the answer is c ." | a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950 | c | subtract(multiply(multiply(const_100, 10), const_2), divide(add(multiply(multiply(10, 8), const_2), 65), add(divide(10, const_100), divide(8, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|multiply(n0,const_100)|multiply(n0,n1)|add(#0,#1)|multiply(#2,const_2)|multiply(#3,const_2)|add(n4,#6)|divide(#7,#4)|subtract(#5,#8)| | general | allenai/math_qa |
the captain of a cricket team of 11 members is 28 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ? | "explanation : let the average age of the whole team by x years . 11 x â € “ ( 28 + 31 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 50 2 x = 50 x = 25 so , average age of the team is 25 years . answer e" | a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 25 years | e | divide(subtract(add(28, add(28, 3)), multiply(3, 3)), const_2) | add(n1,n2)|multiply(n2,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,const_2)| | general | allenai/math_qa |
( 7895632 x 881 ) = ? | 7895632 x 881 = 6956051792 ans e | a ) 6846381250 , b ) 6584638130 , c ) 6584638135 , d ) 6584638140 , e ) 6956051792 | e | multiply(7895632, power(add(const_4, const_1), const_4)) | add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)| | general | allenai/math_qa |
employees of a certain company are each to receive a unique 5 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , and 4 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ? | there are 3 ! ways to make codes starting with 12 . there are 3 ! ways to make codes starting with 24 . the number of codes is 2 * 3 ! = 12 . the answer is b . | a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | b | multiply(multiply(const_2, const_3), 2) | multiply(const_2,const_3)|multiply(n3,#0) | general | allenai/math_qa |
what is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1 ? | "since 200 = 2 ^ 3 * 5 ^ 2 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 100 odd numbers from 1 to 200 . we then need to eliminate the 20 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 195 . there are a total of 100 - 20 = 80 such numbers between 1 and 200 . the answer is c ." | a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100 | c | subtract(subtract(200, 1), subtract(add(add(divide(subtract(subtract(200, const_2), const_2), const_2), 1), add(divide(subtract(subtract(200, divide(200, const_100)), divide(200, const_100)), divide(200, const_100)), 1)), add(divide(subtract(subtract(200, const_10), const_10), const_10), 1))) | divide(n0,const_100)|subtract(n0,n2)|subtract(n0,const_2)|subtract(n0,const_10)|subtract(#2,const_2)|subtract(n0,#0)|subtract(#3,const_10)|divide(#4,const_2)|divide(#6,const_10)|subtract(#5,#0)|add(#7,n2)|add(n2,#8)|divide(#9,#0)|add(#12,n2)|add(#10,#13)|subtract(#14,#11)|subtract(#1,#15)| | general | allenai/math_qa |
in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 9 people all together . how many people can sit in a bus ? | "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 9 total people can seat = 81 + 9 = 90 answer : d" | a ) 52 , b ) 49 , c ) 95 , d ) 90 , e ) 66 | d | add(multiply(add(15, subtract(15, 3)), 3), 9) | subtract(n0,n1)|add(n0,#0)|multiply(n1,#1)|add(n3,#2)| | general | allenai/math_qa |
the ratio of the arithmetic mean of two numbers to one of the numbers is 4 : 7 . what is the ratio of the smaller number to the larger number ? | "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 4 : 7 , thus the smaller number must have a ratio of 1 . the ratio of the smaller number to the larger number is 1 : 7 . the answer is b ." | a ) 1 : 8 , b ) 1 : 7 , c ) 1 : 6 , d ) 1 : 5 , e ) 1 : 4 | b | multiply(subtract(divide(4, 7), divide(const_1, const_2)), const_2) | divide(n0,n1)|divide(const_1,const_2)|subtract(#0,#1)|multiply(#2,const_2)| | other | allenai/math_qa |
when positive integer w is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ? | the equation that can be formed w is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | b | subtract(reminder(multiply(13, add(5, 2)), 8), 2) | add(n1,n3)|multiply(n0,#0)|reminder(#1,n2)|subtract(#2,n1) | general | allenai/math_qa |
a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ? | "explanation we have : l = 30 ft and lb = 720 sq . ft . so , b = 24 ft . length of fencing = ( l + 2 b ) = ( 30 + 48 ) ft = 78 ft . answer a" | a ) 78 , b ) 40 , c ) 68 , d ) 88 , e ) none | a | add(multiply(divide(720, 30), const_2), 30) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | geometry | allenai/math_qa |
the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 700 per sq . metre . | "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 800 ã — 22 ) = rs . 15400 answer : option b" | a ) s . 15,550 , b ) s . 15,400 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900 | b | multiply(700, multiply(5.5, 4)) | multiply(n0,n1)|multiply(n2,#0)| | physics | allenai/math_qa |
y = x ^ 2 + bx + 64 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ? | "as the curve cuts the x - axis at ( h , 0 ) and ( k , 0 ) . therefore h , k are the roots of the quadratic equation . for the quadratic equation is in the form ofax ^ 2 + bx + c = 0 , the product of the roots = c / a = 64 / 1 = 256 and the sum of the roots = - b / a = - b 64 can be expressed as product of two numbers in the following ways : 1 * 64 2 * 32 4 * 16 the sum of the roots is maximum when the roots are 1 and 64 and the maximum sum is 1 + 64 = 65 . the least value possible for b is therefore - 65 . b" | a ) - 65 , b ) - 64 , c ) - 32 , d ) 32 , e ) 64 | b | subtract(negate(64), const_1) | negate(n1)|subtract(#0,const_1)| | general | allenai/math_qa |
if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 7 . | "6 * 15 * 3 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 7 + 1 ) = ( √ 8 * 18 ) / 8 = ( √ 144 ) / 8 = 12 / 8 = 1.5 answer is e" | a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 1.5 | e | divide(sqrt(multiply(add(6, 2), add(15, 3))), add(7, 1)) | add(n0,n3)|add(n1,n4)|add(n2,n5)|multiply(#0,#1)|sqrt(#3)|divide(#4,#2)| | general | allenai/math_qa |
m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 4 ) both lie on the line defined by the equation x = ( y / 2 ) - ( 2 / 5 ) , what is the value of p ? | "( m , n ) m = x n = y m = n / 2 - 2 / 5 10 m = 5 n - 4 ( multiplied by 10 to simplify equation ) ( m + p , n + 4 ) m + p = x n + 4 = y m + p = ( n + 4 ) / 2 - 2 / 5 multiplied by 10 again 10 m + 10 p = 5 n + 20 - 4 use both equations to solve for p and you get 10 p = 20 p = 2 answer : c" | a ) 4 / 5 , b ) 1 , c ) 2 , d ) 5 , e ) 8 | c | divide(4, 2) | divide(n0,n1)| | general | allenai/math_qa |
if a ( a - 6 ) = 27 and b ( b - 6 ) = 27 , where a ≠ b , then a + b = ? | "i . e . if a = - 3 then b = 9 or if a = 9 then b = - 3 but in each case a + b = - 3 + 9 = 6 answer : option d" | a ) − 48 , b ) − 2 , c ) 46 , d ) 6 , e ) 48 | d | subtract(subtract(subtract(subtract(add(add(6, 27), subtract(6, 27)), const_1), const_1), const_1), const_1) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|subtract(#2,const_1)|subtract(#3,const_1)|subtract(#4,const_1)|subtract(#5,const_1)| | general | allenai/math_qa |
what is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square ? | 1008 = 2 ^ 4 x 3 ^ 2 x 7 . therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7 . answer d . | ['a ) 2', 'b ) 3', 'c ) 5', 'd ) 7', 'e ) 11'] | d | add(const_3, const_4) | add(const_3,const_4) | geometry | allenai/math_qa |
two trains , a and b , started simultaneously from opposite ends of a 200 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 200 - mile trip in 10 hours ; train b , traveling at a constant rate , completed the 200 - mile trip in 6 hours . how many miles had train a traveled when it met train b ? | "as the ratio of the rates of a and b is 6 to 10 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 6 / ( 6 + 10 ) = 6 / 16 of 200 miles : 200 * 6 / 16 = 75 miles . answer : b ." | a ) 70 , b ) 75 , c ) 87.5 , d ) 90 , e ) 92.5 | b | multiply(divide(6, add(10, 6)), 200) | add(n2,n4)|divide(n4,#0)|multiply(n0,#1)| | physics | allenai/math_qa |
excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 33 kmph . of how many minutes does the train stop per hour ? | "explanation : t = 12 / 45 * 60 = 16 answer : option c" | a ) 73 , b ) 83 , c ) 16 , d ) 83 , e ) 28 | c | subtract(const_60, multiply(const_60, divide(33, 45))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | physics | allenai/math_qa |
in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate . | "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 × 476000 = 33320000 / 100 = 333200 d )" | a ) 330000 , b ) 340000 , c ) 347000 , d ) 333200 , e ) 357000 | d | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(70, const_100)) | divide(n0,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(n2,#2)|multiply(#0,#3)| | gain | allenai/math_qa |
two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? | t = ( 111 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 6.85 answer : c | a ) 4.85 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.15 | c | divide(add(111, 165), multiply(add(80, 65), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2) | physics | allenai/math_qa |
in the faculty of reverse - engineering , 220 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ? | answer is e : 636 solution : total number of students studying both are 423 + 220 - 134 = 509 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 509 , so 100 % is approx . 636 . | a ) 515 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 636 . | e | add(220, 423) | add(n0,n1) | general | allenai/math_qa |
325.124 x 12.98 ã · 3.001 + 21.21 = ? | "explanation : ? = 325.124 x 12.98 ã · 3.001 + 21.21 = ? â ‰ ˆ ( 325.124 x 13 / 3 ) + 21.21 â ‰ ˆ 1408.87 + 21.21 â ‰ ˆ 1430.080 answer : option a" | a ) 1430.08 , b ) 1420.06 , c ) 781.189 , d ) 656.112 , e ) 456.512 | a | multiply(325.124, power(12.98, 3.001)) | power(n1,n2)|multiply(n0,#0)| | general | allenai/math_qa |
there are 50 students in a class . if 2 % are absent on a particular day , find the number of students present in the class . | "number of students absent on a particular day = 1 % of 50 i . e . , 2 / 100 × 50 = 1 therefore , the number of students present = 50 - 1 = 49 students . answer : d" | a ) 43 , b ) 36 , c ) 28 , d ) 49 , e ) 11 | d | multiply(subtract(const_1, divide(2, 50)), 50) | divide(n1,n0)|subtract(const_1,#0)|multiply(#1,n0)| | gain | allenai/math_qa |
the length of a side of a hexagon is 10 inches . what is the perimeter ? | "hexagon . it means 6 equal sides . p = 6 ( 10 ) = 60 inches answer e" | a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 60 | e | multiply(10, multiply(const_3, const_2)) | multiply(const_2,const_3)|multiply(n0,#0)| | physics | allenai/math_qa |
a man can swim in still water at 15 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ? | "m = 15 s = x ds = 15 + x us = 15 - x 15 + x = ( 15 - x ) 2 15 + x = 30 - 2 x 3 x = 15 x = 5 answer : b" | a ) 3.9 , b ) 5 , c ) 5.3 , d ) 1.5 , e ) 5.2 | b | divide(15, const_3) | divide(n0,const_3)| | general | allenai/math_qa |
if x , y , and z are positive integers , and 2 x = 5 y = 7 z , then the least possible value of x + y + z is | "take lcm of 2,5 and 7 = 70 now 2 x = 70 = > x = 35 5 y = 70 = > y = 14 7 z = 70 = > z = 10 35 + 14 + 10 = 59 . option e ." | a ) 15 , b ) 28 , c ) 37 , d ) 42 , e ) 59 | e | add(add(divide(divide(multiply(multiply(2, 5), 7), const_2), 2), divide(divide(multiply(multiply(2, 5), 7), const_2), 5)), divide(divide(multiply(multiply(2, 5), 7), const_2), 7)) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_2)|divide(#2,n0)|divide(#2,n1)|divide(#2,n2)|add(#3,#4)|add(#6,#5)| | general | allenai/math_qa |
a train requires 10 seconds to pass a pole while it requires 35 seconds to cross a stationary train which is 500 mtrs long . find the speed of the train . | "in 10 s the train crosses the pole and in 35 sec the train crosses one more stationary train in 25 sec the train travels a distance of 500 mtrs speed = 500 / 25 = 20 m / s = 20 ( 3600 / 1000 ) = 20 * 18 / 5 = 72 kmph answer : c" | a ) 68 kmph , b ) 70 kmph , c ) 72 kmph , d ) 60 kmph , e ) 50 kmph | c | multiply(divide(500, subtract(35, 10)), const_3_6) | subtract(n1,n0)|divide(n2,#0)|multiply(#1,const_3_6)| | physics | allenai/math_qa |
sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 170 . if the ratio of his marks in english and maths is 1 : 4 , find his marks in science ? | s : e = 1 : 3 e : m = 1 : 4 - - - - - - - - - - - - s : e : m = 1 : 4 : 12 1 / 17 * 170 = 17 answer : a | a ) 17 , b ) 77 , c ) 66 , d ) 55 , e ) 31 | a | add(add(add(multiply(1, const_3), 1), multiply(multiply(1, const_3), add(multiply(1, const_3), 1))), 1) | multiply(n1,const_3)|add(n1,#0)|multiply(#1,#0)|add(#1,#2)|add(n1,#3) | general | allenai/math_qa |
can c and can в are both right circular cylinders . the radius of can c is twice the radius of can b , while the height of can c is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can c with the same brand of gasoline ? | let x be the radius of b and 2 h be the height of b . therefore , radius of c = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e | a ) $ 1 , b ) $ 2 , c ) $ 4 , d ) $ 8 , e ) $ 16 | e | multiply(multiply(const_2, 4), const_2) | multiply(n0,const_2)|multiply(#0,const_2) | geometry | allenai/math_qa |
rs . 770 were divided among a , b , c in such a way that a had rs . 40 more than b and c had rs 30 more than a . how much was b â € ™ s share ? | let b gets rs x . then we can say a gets rs ( x + 40 ) and c gets rs ( x + 70 ) . x + 40 + x + x + 70 = 770 3 x = 660 x = 220 . b â € ™ s share = rs ( 220 + 70 ) = rs . 290 d | a ) rs . 260 , b ) rs . 270 , c ) rs . 280 , d ) rs . 290 , e ) rs . 300 | d | add(add(divide(subtract(770, add(add(40, 40), 30)), const_3), 30), 40) | add(n1,n1)|add(n2,#0)|subtract(n0,#1)|divide(#2,const_3)|add(n2,#3)|add(n1,#4) | general | allenai/math_qa |
sakshi can do a piece of work in 10 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work : | "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 10 : x ⇒ x = ( 10 x 4 / 5 ) ⇒ x = 8 days . hence , tanya takes 8 days is complete the work . answer a" | a ) 8 , b ) 16 , c ) 18 , d ) 25 , e ) 10 | a | divide(10, add(const_1, divide(25, const_100))) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)| | physics | allenai/math_qa |
an ant walks an average of 500 meters in 12 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ? | "the ant walks an average of 500 meters in 12 minutes or , 500 meters in 1 / 5 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 12 minutes or , 0.425 km in 12 / 60 = 1 / 5 hours speed = 0.425 * 5 = 2.125 km / h ans should be 2.125 answer : a" | a ) 2.215 , b ) 2.5 . , c ) 2.775 , d ) 3.2 , e ) 3.5 | a | multiply(divide(divide(500, 500), divide(12, const_60)), subtract(const_1, divide(15, const_100))) | divide(n0,n0)|divide(n1,const_60)|divide(n2,const_100)|divide(#0,#1)|subtract(const_1,#2)|multiply(#3,#4)| | general | allenai/math_qa |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : d" | a ) 17 years , b ) 19 years , c ) 29 years , d ) 8 years , e ) 12 years | d | divide(multiply(subtract(22, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general | allenai/math_qa |
a can give b 90 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ? | "a runs 1000 m while b runs 910 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 910 = 879.12 m . b can give c = 1000 - 879.12 = 120.88 m . answer : a" | a ) 120.88 , b ) 120.13 , c ) 111.22 , d ) 120.0 , e ) 111.12 | a | subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 90))) | multiply(const_10,const_100)|subtract(#0,n1)|subtract(#0,n0)|multiply(#0,#1)|divide(#3,#2)|subtract(#0,#4)| | physics | allenai/math_qa |
at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 10 on candy , how much did john spend at the supermarket ? | "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 10 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 10 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 300 = 30 t 28 t + 300 = 30 t 300 = 2 t t = 150 john spent $ 90 at the supermarket . answer : e" | a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 150 | e | divide(10, subtract(1, add(add(divide(1, 10), divide(1, 3)), divide(1, 2)))) | divide(n0,n5)|divide(n0,n3)|divide(n0,n1)|add(#0,#1)|add(#3,#2)|subtract(n0,#4)|divide(n6,#5)| | general | allenai/math_qa |
the difference between compound interest and simple interest on a sum for 3 years at 10 % p . a . is rs . 124 find the sum . | "for 3 years , we know c . i - s . i = p ( r / 100 ) ^ 3 + 3 ( r / 100 ) ^ 2 so , putting all values we have , 124 = p ( ( 10 / 100 ) ^ 3 + 3 ( 10 / 100 ) ^ 2 ) = 4000 answer : b" | a ) rs . 5000 , b ) rs . 4000 , c ) rs . 6000 , d ) rs . 8000 , e ) rs . 7000 | b | divide(124, subtract(power(add(const_1, divide(3, const_100)), 10), add(const_1, multiply(10, divide(3, 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 |
find the value for x from below equation : x / 2 = - 2 ? | "1 . multiply both sides by 2 : x * 2 / 2 = - 2 / 2 simplify both sides : x = - 4 e" | a ) - 6 , b ) 1 , c ) - 2 , d ) - 3 , e ) - 4 | e | multiply(subtract(2, const_4), 2) | subtract(n1,const_4)|multiply(#0,n0)| | general | allenai/math_qa |
last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 8 % of her salary . the amount saved this year was what percent of the amount she saved last year ? | "let last year ' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.08 * 1.1 x = 0.088 x 0.088 x / 0.06 x = 88 / 60 = 1.47 = 147 % the answer is b ." | a ) 132 % , b ) 147 % , c ) 158 % , d ) 176 % , e ) 188 % | b | multiply(divide(multiply(divide(8, const_100), add(const_100, 10)), divide(multiply(6, const_100), const_100)), const_100) | add(n1,const_100)|divide(n2,const_100)|multiply(n0,const_100)|divide(#2,const_100)|multiply(#0,#1)|divide(#4,#3)|multiply(#5,const_100)| | gain | allenai/math_qa |
in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 35 , what is the greatest possible value of b x a ? | "i also was confused when i was looking forabove number : d as far as i understood , 35 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 35 x 1 ( a = 3 , b = 5 respectively we have = 15 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 35 x 3 = 105 ( a = 0 b = 5 respectively . hey ! that ' s 0 now . 35 x 5 = 175 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) . this is the greatest possible value of b x a . imo e ." | a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 35 | e | multiply(add(const_3, const_4), add(const_2, const_3)) | add(const_3,const_4)|add(const_2,const_3)|multiply(#0,#1)| | general | allenai/math_qa |
a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 22.5 % . what % discount did the merchant offer ? | let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.225 p x = 1.225 / 1.75 = 0.7 which is a discount of 30 % . the answer is c . | a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 % | c | multiply(divide(subtract(subtract(add(const_1, divide(75, const_100)), const_1), divide(22.5, const_100)), add(const_1, divide(75, const_100))), const_100) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(#2,const_1)|subtract(#3,#1)|divide(#4,#2)|multiply(#5,const_100) | gain | allenai/math_qa |
a total of 320 chocolates were distributed among 100 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ? | "let the number of boys be x . number of girls is 100 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 100 - x ) = 320 = > 300 - x = 320 = > x = 20 . so , the number of boys or girls is 20 . answer : d" | a ) 10,10 , b ) 30,40 , c ) 70 , 50 , d ) 20,20 , e ) 10,15 | d | subtract(multiply(3, 100), divide(320, const_10)) | divide(n0,const_10)|multiply(n1,n3)|subtract(#1,#0)| | general | allenai/math_qa |
in an office , totally there are 800 employees and 25 % of the total employees are males . 40 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ? | "number of male employees = 800 * 25 / 100 = 200 required number of male employees who are less than 50 years old = 200 * ( 100 - 40 ) % = 200 * 60 / 100 = 120 . answer : a" | a ) 120 , b ) 160 , c ) 132 , d ) 130 , e ) none of these | a | multiply(divide(multiply(800, 25), const_100), divide(subtract(const_100, 40), const_100)) | multiply(n0,n1)|subtract(const_100,n2)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)| | general | allenai/math_qa |
convert 1.6 hectares in ares | "1.6 hectares in ares 1 hectare = 100 ares therefore , 1.6 hectares = 1.6 × 100 ares = 160 ares . answer - b" | a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares . | b | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 1.6), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)| | physics | allenai/math_qa |
the ratio of the radius of two circles is 1 : 4 , and then the ratio of their areas is ? | "r 1 : r 2 = 1 : 4 π r 12 : π r 22 r 12 : r 22 = 1 : 16 answer : a" | a ) 1 : 16 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 2 | a | divide(circle_area(1), circle_area(4)) | circle_area(n0)|circle_area(n1)|divide(#0,#1)| | geometry | allenai/math_qa |
each of the three people individually can complete a certain job in 4 , 6 , and 8 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ? | "the two slowest people work at rates of 1 / 6 and 1 / 8 of the job per hour . the sum of these rates is 1 / 6 + 1 / 8 = 7 / 24 of the job per hour . the answer is c ." | a ) 3 / 8 , b ) 5 / 12 , c ) 7 / 24 , d ) 11 / 36 , e ) 13 / 48 | c | add(divide(1, 6), divide(1, 8)) | divide(n3,n1)|divide(n3,n2)|add(#0,#1)| | physics | allenai/math_qa |
a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 1100 . how many workers were part of the latter production run ? | the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1100 . . thus for the current period = 1100 - 500 = 600 ( 5 n + 45 ) k = 600 k = 600 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 600 / 5 n + 45 500 ( 5 n + 45 ) = 600 ( 5 n + 20 ) 2500 n + 22500 = 3000 n + 12000 - 500 n = - 10500 n = 21 thus n + 5 = 26 hence a | a ) 26 , b ) b ) 10 , c ) c ) 11 , d ) d ) 15 , e ) e ) 23.5 | a | add(20, 5) | add(n0,n1) | general | allenai/math_qa |
running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 4 w widgets . | "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 24 days to doing 4 w widgets . answer : e" | a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 24 | e | multiply(multiply(4, 2), 3) | multiply(n0,n4)|multiply(n3,#0)| | general | allenai/math_qa |
john and david work at a hospital with 4 other workers . for an internal review , 2 of the 4 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ? | "probability that john and david will both be chosen out of 8 workers = ( 2 / 4 ) * ( 1 / 3 ) = 1 / 6 answer e" | a ) 1 / 14 , b ) 1 / 20 , c ) 1 / 13 , d ) 1 / 7 , e ) 1 / 6 | e | multiply(2, multiply(divide(const_1, subtract(4, const_1)), divide(const_1, 4))) | divide(const_1,n0)|subtract(n0,const_1)|divide(const_1,#1)|multiply(#2,#0)|multiply(n1,#3)| | physics | allenai/math_qa |
mrs . evans gave a test to her freshmen economics class , which has 50 students enrolled and 25 of them answered question 1 correctly . if 20 answered question 2 correctly and 20 did not take the test then how many answered both questions correctly ? | "total number of enrolled students = 50 number of students who did not take test = 20 hence , number of students who took test = 50 - 20 = 30 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 : d" | a ) 23 , b ) 22 , c ) 21 , d ) 20 , e ) 19 | d | subtract(add(add(25, 20), 20), 50) | add(n1,n3)|add(n5,#0)|subtract(#1,n0)| | other | allenai/math_qa |
a can run 4 times as fast as b and gives b a start of 72 m . how long should the race course be so that a and b might reach in the same time ? | "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 72 m he gains 72 * ( 4 / 3 ) i . e 96 m answer : e" | a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 96 m | e | add(multiply(4, divide(divide(72, 4), subtract(4, const_1))), 72) | divide(n1,n0)|subtract(n0,const_1)|divide(#0,#1)|multiply(n0,#2)|add(n1,#3)| | physics | allenai/math_qa |
karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many w miles will tom drive before karen wins the bet ? | "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him w : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ." | a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27 | d | subtract(divide(add(multiply(divide(45, 60), 4), 4), subtract(divide(60, 60), divide(45, 60))), 4) | divide(n3,n2)|divide(n2,n2)|multiply(n0,#0)|subtract(#1,#0)|add(n0,#2)|divide(#4,#3)|subtract(#5,n0)| | physics | allenai/math_qa |
two - third of a positive number and 25 / 216 of its reciprocal are equal . the number is : | "let the number be x . then , 2 / 3 x = 25 / 216 * 1 / x x 2 = 25 / 216 * 3 / 2 = 25 / 144 x = 5 / 12 answer : a" | a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25 | a | sqrt(divide(multiply(25, const_3), multiply(216, const_2))) | multiply(n0,const_3)|multiply(n1,const_2)|divide(#0,#1)|sqrt(#2)| | general | allenai/math_qa |
if 1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ? | "1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter 1000 microns = 1 , 000,000 angstroms 1 micron = 1 , 000,000 / 1,000 = 1,000 answer : b" | a ) 10 , b ) 1000 , c ) 100 , d ) 0.01 , e ) 0.0001 | b | multiply(divide(1, multiply(const_100, const_100)), multiply(const_100, const_100)) | multiply(const_100,const_100)|divide(n1,#0)|multiply(#1,#0)| | general | allenai/math_qa |
an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4000 , what will be the difference between q and r ' s share ? | "4 - - - 4000 5 - - - ? = > 5000 answer : b" | a ) 2788 , b ) 5000 , c ) 7282 , d ) 2782 , e ) 2729 | b | multiply(subtract(12, 7), divide(4000, subtract(7, 3))) | subtract(n1,n0)|subtract(n2,n1)|divide(n3,#0)|multiply(#2,#1)| | general | allenai/math_qa |
10 ^ ( 65 ) ã · 10 ^ ( 64 ) = ? | "10 ^ ( 65 ) ã · 10 ^ ( 64 ) = 10 ^ ( 65 - 64 ) = 10 ^ 1 = 10 answer : b" | a ) 1 , b ) 10 , c ) 100 , d ) 1000 , e ) 10000 | b | power(10, subtract(65, 64)) | subtract(n1,n3)|power(n0,#0)| | general | allenai/math_qa |
reduce 4128 / 4386 to its lowest terms | explanation : hcf of 4128 and 4386 4128 ) 4386 ( 1 4128 - - - - - 258 ) 4128 ( 16 4128 - - - - 0 hence hcf of 4128 and 4386 is 258 . 4128 / 258 = 16 4386 / 258 = 17 4128 / 4386 = 16 / 17 answer : option c | a ) 14 / 13 , b ) 13 / 17 , c ) 16 / 17 , d ) 13 / 18 , e ) none of these | c | divide(divide(divide(4128, const_2), const_3), divide(divide(4386, const_2), const_3)) | divide(n0,const_2)|divide(n1,const_2)|divide(#0,const_3)|divide(#1,const_3)|divide(#2,#3) | general | allenai/math_qa |
after decreasing 24 % in the price of an article costs rs . 836 . find the actual cost of an article ? | cp * ( 76 / 100 ) = 836 cp = 11 * 100 = > cp = 1100 answer : d | a ) 1667 , b ) 6789 , c ) 1200 , d ) 1100 , e ) 1421 | d | divide(836, subtract(const_1, divide(24, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1) | gain | allenai/math_qa |
kim finds a 5 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ? | "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is d" | a ) 8 / 15 , b ) 1 / 2 , c ) 7 / 5 , d ) 3 / 5 , e ) 7 / 5 | d | subtract(const_1, add(add(divide(5, multiply(add(const_2, 5), 5)), divide(const_2, multiply(add(const_2, 5), 5))), divide(const_1, multiply(add(const_2, 5), 5)))) | add(const_2,n0)|multiply(n0,#0)|divide(n0,#1)|divide(const_2,#1)|divide(const_1,#1)|add(#2,#3)|add(#5,#4)|subtract(const_1,#6)| | physics | allenai/math_qa |
a picture is copied onto a sheet of paper 8.5 inches by 10 inches . a 1.5 inch margin is left all around . what area in square inches does the picture cover ? | area covered by picture = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e | ['a ) 76', 'b ) 65', 'c ) 59.5', 'd ) 49', 'e ) 38.5'] | e | multiply(subtract(8.5, multiply(1.5, const_2)), subtract(10, multiply(1.5, const_2))) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|multiply(#1,#2) | geometry | allenai/math_qa |
seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 30 percent ryegrass , what percent of the weight of this mixture is x ? | "qnty . ( cheaper ) / qty . ( dearer ) = ( dearer - mean ) / ( mean - cheaper ) thus qy / qx = ( 40 - 30 ) / ( 30 - 25 ) = 2 therefore qy = 2 qx and qy + qx = 100 % ( total ) . hence qx = 33.33 % answer : b" | a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.66 % | b | divide(subtract(30, 25), subtract(divide(40, const_100), divide(25, const_100))) | divide(n0,const_100)|divide(n2,const_100)|subtract(n4,n2)|subtract(#0,#1)|divide(#2,#3)| | gain | allenai/math_qa |
x is the product of each integer from 1 to 75 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ? | "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 75 = 50 ! no . of trailing zeros in 75 ! = 75 / 5 + 75 / 5 ^ 2 = 15 + 3 = 18 100 ^ k = 10 ^ 2 k → k = 18 / 2 = 9 d" | a ) 8 , b ) 7 , c ) 6 , d ) 9 , e ) 10 | d | add(divide(75, const_10), 1) | divide(n1,const_10)|add(#0,n0)| | general | allenai/math_qa |
the balance of a trader weighs 8 % less than it should . still the trader marks up his goods to get an overall profit of 20 % . what is the mark up on the cost price ? | "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 92 gms because it weighs 8 % less . say , the cost price is $ 92 ( $ 1 / gm ) . since he gets a profit of 20 % , the selling price must be 92 + ( 20 / 100 ) * 92 = $ 110.4 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 110.4 , the mark up is simply 10.4 % . ans : c" | a ) 40 % , b ) 8 % , c ) 10.4 % , d ) 16.66 % , e ) 9 % | c | subtract(add(multiply(multiply(const_4, 8), divide(20, const_100)), multiply(const_4, 8)), const_100) | divide(n1,const_100)|multiply(n0,const_4)|multiply(#0,#1)|add(#2,#1)|subtract(#3,const_100)| | gain | allenai/math_qa |
a sum of rs . 1190 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is : | explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1190 = > 17 x / 12 = 1190 = > 1190 x 12 / 17 = rs . 840 hence , b ’ s share = rs . ( 840 / 4 ) = rs . 210 . answer b | a ) rs . 120 , b ) rs . 210 , c ) rs . 240 , d ) rs . 300 , e ) none | b | subtract(subtract(multiply(divide(1190, const_10), const_2), const_12), const_12) | divide(n0,const_10)|multiply(#0,const_2)|subtract(#1,const_12)|subtract(#2,const_12) | general | allenai/math_qa |
a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 16000 left with him . find salary . . | "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 16000 , = [ 1 - 9 / 10 ] * total salary = $ 16000 , total salary = $ 16000 * 10 = $ 160000 , correct answer ( c )" | a ) $ 10800 , b ) $ 18000 , c ) $ 160000 , d ) $ 1800 , e ) none | c | divide(16000, subtract(1, add(add(divide(1, 5), divide(1, 10)), divide(3, 5)))) | divide(n0,n1)|divide(n0,n3)|divide(n4,n1)|add(#0,#1)|add(#3,#2)|subtract(n0,#4)|divide(n6,#5)| | general | allenai/math_qa |
the average of 13 numbers is 60 . average of the first 7 of them is 55 and that of the last 7 is 61 . find the 8 th number ? | "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 55 = 385 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 385 - 780 = 32 . answer : a" | a ) 32 , b ) 83 , c ) 45 , d ) 53 , e ) 64 | a | subtract(multiply(8, 61), subtract(multiply(13, 60), multiply(55, 7))) | multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)| | general | allenai/math_qa |
if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 13 ? | "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 13 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 13 is 12 . answer : d ." | a ) 0 , b ) 1 , c ) 2 , d ) 13 , e ) 5 | d | subtract(power(add(3, 2), 2), multiply(13, const_4)) | add(n0,n1)|multiply(n2,const_4)|power(#0,n1)|subtract(#2,#1)| | general | allenai/math_qa |
a 280 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ? | "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 280 ) / 9 = 500 / 9 = > x = 220 . answer : e" | a ) 230 , b ) 288 , c ) 267 , d ) 256 , e ) 220 | e | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 280) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | physics | allenai/math_qa |
if x is real , find the maximum value of the expression - 2 x ^ 2 + 9 x + 11 . | "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 9 x + 11 = ( - 2 x + 11 ) ( x + 1 ) the roots are 11 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 2.25 the maximum value is - 2 ( 2.25 ) ^ 2 + 9 ( 2.25 ) + 11 = 21.125 the answer is d ." | a ) 12.125 , b ) 15.125 , c ) 18.125 , d ) 21.125 , e ) 24.125 | d | subtract(add(multiply(9, divide(multiply(2, 2), 9)), 11), multiply(2, power(divide(multiply(2, 2), 9), 2))) | multiply(n0,n0)|divide(#0,n2)|multiply(n2,#1)|power(#1,n0)|add(n3,#2)|multiply(n0,#3)|subtract(#4,#5)| | general | allenai/math_qa |
what is the probability that company g ' s advertisement will be one of the first two be shown during the first commercial break ? | g 1 / 15 + ( 14 / 15 ) * 1 / 14 = 2 / 15 d | a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15 | d | divide(const_2, multiply(const_3, const_5)) | multiply(const_3,const_5)|divide(const_2,#0) | probability | allenai/math_qa |
the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 50 % profit ? | "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 150 % of rs . 640 = 150 / 100 * 640 = rs . 960 . answer : b" | a ) 277 , b ) 960 , c ) 277 , d ) 266 , e ) 121 | b | multiply(subtract(832, divide(subtract(832, 448), const_2)), add(const_1, divide(50, const_100))) | divide(n2,const_100)|subtract(n0,n1)|add(#0,const_1)|divide(#1,const_2)|subtract(n0,#3)|multiply(#2,#4)| | gain | allenai/math_qa |
evaluate : 50 - 12 ÷ 2 × 2 = | "according to order of operations , 12 ÷ 2 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 2 × 2 = 6 × 2 = 12 hence 50 - 12 ÷ 6 × 2 = 50 - 12 = 38 correct answer is b ) 38" | a ) a ) 36 , b ) b ) 38 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44 | b | subtract(50, multiply(multiply(12, 2), 2)) | multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)| | general | allenai/math_qa |
? % of 360 = 165.6 | "? % of 360 = 165.6 or , ? = 165.6 × 100 / 360 = 46 answer e" | a ) 277 , b ) 36 , c ) 64 , d ) 72 , e ) 46 | e | divide(multiply(165.6, const_100), 360) | multiply(n1,const_100)|divide(#0,n0)| | gain | allenai/math_qa |
the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ? | answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a | a ) 34 , b ) 25 , c ) 48 , d ) 50 , e ) none | a | divide(add(multiply(40, 30), multiply(30, 40)), add(40, 30)) | add(n0,n1)|multiply(n0,n1)|add(#1,#1)|divide(#2,#0) | general | allenai/math_qa |
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 ? | "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" | a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 105 | e | multiply(divide(multiply(divide(1, 12), const_3), divide(divide(1, 30), const_2)), 7) | divide(n0,n1)|divide(n0,n2)|divide(#1,const_2)|multiply(#0,const_3)|divide(#3,#2)|multiply(n3,#4)| | other | allenai/math_qa |
each factor of 230 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 46 ? | "so the # of factors 230 has 8 ( see below ) ; so out of 8 factors only two are multiples of 46 : 46 and 230 , itself ; so , the probability is 2 / 8 = 1 / 4 . answer : e ." | a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4 | e | divide(divide(choose(46, const_1), 46), power(const_3, const_2)) | choose(n1,const_1)|power(const_3,const_2)|divide(#0,n1)|divide(#2,#1)| | other | allenai/math_qa |
how many seconds will a train 200 meters long running at the rate of 36 kmph take to pass a certain telegraph post ? | distance = length of train = 200 meters speed = 36 kmph = 36 * 5 / 18 = 10 m / s required time = 200 / 10 = 20 sec answer is b | a ) 10 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 35 sec | b | divide(200, multiply(const_0_2778, 36)) | multiply(n1,const_0_2778)|divide(n0,#0) | physics | allenai/math_qa |
a man can row downstream at the rate of 16 km / hr and upstream at 8 km / hr . find man ' s rate in still water and the rate of current ? | "explanation : rate of still water = 1 / 2 ( 16 + 8 ) = 12 km / hr rate of current = 1 / 2 ( 16 - 8 ) = 4 km / hr answer : option a" | a ) 12,4 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these | a | divide(subtract(16, 8), const_2) | subtract(n0,n1)|divide(#0,const_2)| | gain | allenai/math_qa |
if 1 / 12 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 3 are from africa , 1 / 6 are from asia and the remaining 35 people are citizens of other continents , then how many passengers are on board the ship ? | 1 / 12 + 1 / 8 + 1 / 3 + 1 / 6 = ( 2 + 3 + 8 + 4 ) / 24 = 17 / 24 let x be the number of passengers on the ship . 35 = ( 7 / 24 ) x x = 120 the answer is c . | a ) 110 , b ) 115 , c ) 120 , d ) 125 , e ) 130 | c | divide(35, subtract(const_1, add(add(add(divide(1, 12), divide(1, 8)), divide(1, 3)), divide(1, 6)))) | divide(n0,n1)|divide(n0,n3)|divide(n0,n5)|divide(n0,n7)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(const_1,#6)|divide(n8,#7) | general | allenai/math_qa |
the guests at a football banquet consumed a total of 406 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ? | "to minimize one quantity maximize other . 162 * 2.5 ( max possible amount of food a guest could consume ) = 405 pounds , so there must be more than 162 guests , next integer is 163 . answer : d ." | a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164 | d | add(floor(divide(406, 2.5)), const_1) | divide(n0,n1)|floor(#0)|add(#1,const_1)| | general | allenai/math_qa |
the ages of two person differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively | "let their ages be x and ( x + 20 ) years . then , 5 ( x - 5 ) = ( x + 20 - 5 ) = > 4 x = 40 = > x = 10 their present ages are 30 years and 10 year . answer : a" | a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10 | a | add(divide(add(multiply(5, 5), subtract(20, 5)), subtract(5, const_1)), 20) | multiply(n1,n2)|subtract(n0,n1)|subtract(n2,const_1)|add(#0,#1)|divide(#3,#2)|add(n0,#4)| | general | allenai/math_qa |
find k if 64 ÷ k = 4 . | "since 64 ÷ k = 4 and 64 ÷ 16 = 4 , then k = 16 correct answer b" | a ) 8 , b ) 16 , c ) 24 , d ) 36 , e ) 40 | b | divide(64, 4) | divide(n0,n1)| | general | allenai/math_qa |
a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be c ' s share of the earnings ? | "explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , c ' s share will be 2 * 2340 / 9 = 520 . correct choice is ( b )" | a ) $ 1100 , b ) $ 520 , c ) $ 1080 , d ) $ 1170 , e ) $ 630 | b | multiply(2340, divide(inverse(8), add(inverse(12), add(inverse(6), inverse(8))))) | inverse(n1)|inverse(n0)|inverse(n2)|add(#1,#0)|add(#3,#2)|divide(#0,#4)|multiply(n3,#5)| | physics | allenai/math_qa |
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