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load_in_math_allenai_math

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set a contains all the even numbers between 4 and 50 inclusive . set b contains all the even numbers between 104 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
"set a contains 4 , 6 . . . 50 set b contains 104 , 106 . . . 150 number of terms in each set = 24 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 24 = 2400 answer a"
a ) 2400 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
a
multiply(subtract(104, 4), add(divide(subtract(50, 4), const_2), const_1))
subtract(n1,n0)|subtract(n2,n0)|divide(#0,const_2)|add(#2,const_1)|multiply(#3,#1)|
general
allenai/math_qa
in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 45 percent of the vote . how many additional votes would james have needed to win the election ?
"james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 45 / 100 ) * total votes + 1 = ( 45 / 100 ) * 2000 + 1 = 901 remaining voted needed to win election = 901 - 10 = 891 answer : option d"
a ) 901 , b ) 989 , c ) 990 , d ) 891 , e ) 1,001
d
subtract(add(const_1000, const_1000), multiply(add(const_1000, const_1000), 0.5))
add(const_1000,const_1000)|multiply(n0,#0)|subtract(#0,#1)|
general
allenai/math_qa
a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 336,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
"number of boxes = total volume / volume of one box = 336,000 / ( 8 * 10 * 12 ) = 350 one box costs 7.50 , so 350 box will cost = 350 * 7.5 = 2625 d is the answer"
a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,625 , e ) $ 2,250
d
divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 7.50), const_1000)
multiply(const_100,const_3)|multiply(n0,n1)|multiply(n0,n1)|add(#0,#1)|multiply(n2,#2)|add(#3,const_4)|multiply(#5,const_1000)|divide(#6,#4)|multiply(n3,#7)|divide(#8,const_1000)|
general
allenai/math_qa
if the average of 8 digits is 20 and the average of 5 of them is 12 , calculate the average of the remaining 3 numbers ?
"explanation : total of the 8 digits - 8 * 20 = 160 total of the 5 digits - 5 * 12 = 60 total of the remaining 3 digits - 160 - 60 = 100 average of the remaining 3 numbers = 100 / 3 = 33.3 answer : e"
a ) 13.3 , b ) 38.3 , c ) 35.3 , d ) 31.3 , e ) 33.3
e
divide(subtract(multiply(8, 20), multiply(5, 12)), 3)
multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)|
general
allenai/math_qa
a collection of books went on sale , and 2 / 3 of them were sold for $ 4 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
"since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 4 ) or $ 288 . the best answer is therefore a . answer : a ."
a ) $ 288 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
a
multiply(const_2.0, divide(multiply(36, divide(2, 3)), divide(const_1, 3)))
divide(n2,n1)|divide(const_1,n1)|multiply(n3,#0)|divide(#2,#1)|multiply(n0,#3)|
general
allenai/math_qa
of the people who responded to a market survey , 360 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 9 to 1 , how many people responded to the survey ?
"ratio = 9 : 1 = > 9 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 360 = > 9 x = 360 = > x = 40 hence total no . of respondents = 360 + 40 = 400 hence e is the answer ."
a ) 80 , b ) 160 , c ) 240 , d ) 360 , e ) 400
e
add(divide(360, 9), 360)
divide(n0,n1)|add(n0,#0)|
other
allenai/math_qa
two motor cycles a & b are started from one point at 4 kmph & 6 kmph ; after 45 min b starts returning , at what time they will meet ?
distance covered by a in 45 mins = 3 kms . distance covered by b in 45 mins = 4.5 kms . distance between and b after 45 mins = 1.5 kms . relative speed when b is returning = 4 + 6 = 10 kmph distance between a and b is covered in 1.5 / 10 = 0.15 hrs = 9 mins so they will meet again after 54 mins from starting time . answer : a
a ) 54 mins , b ) 55 mins , c ) 56 mins , d ) 57 mins , e ) 58 mins
a
add(45, multiply(divide(subtract(multiply(6, divide(45, const_60)), multiply(4, divide(45, const_60))), add(4, 6)), const_60))
add(n0,n1)|divide(n2,const_60)|multiply(n1,#1)|multiply(n0,#1)|subtract(#2,#3)|divide(#4,#0)|multiply(#5,const_60)|add(n2,#6)
physics
allenai/math_qa
what should be the least number to be added to the 3198 number to make it divisible by 8 ?
"answer : 2 option : c"
a ) 12 , b ) 17 , c ) 2 , d ) 77 , e ) 26
c
subtract(8, reminder(3198, 8))
reminder(n0,n1)|subtract(n1,#0)|
general
allenai/math_qa
what no . should be subtracted from x ^ 3 + 4 x 2 βˆ’ 7 x + 12 x ^ 3 + 4 x ^ 2 βˆ’ 7 x + 12 , if it is to be perfectly divisible by x + 3 x + 3 ?
according to remainder theorem when dfracf ( x ) x + adfracf ( x ) x + a , then the remainder is f ( βˆ’ a ) f ( βˆ’ a ) . in this case , as x + 3 x + 3 divides x 3 + 4 x 2 βˆ’ 7 x + 12 – kx 3 + 4 x 2 βˆ’ 7 x + 12 – k perfectly ( kk being the number to be subtracted ) , the remainder is 0 when the value of xx is substituted by - 3 . i . e . , ( βˆ’ 3 ) 3 + 4 ( βˆ’ 3 ) 2 βˆ’ 7 ( βˆ’ 3 ) + 12 βˆ’ k = 0 ( βˆ’ 3 ) 3 + 4 ( βˆ’ 3 ) 2 βˆ’ 7 ( βˆ’ 3 ) + 12 βˆ’ k = 0 or βˆ’ 27 + 36 + 21 + 12 = k βˆ’ 27 + 36 + 21 + 12 = k or k = k = 42 b
a ) 38 , b ) 42 , c ) 46 , d ) 49 , e ) 62
b
add(subtract(add(power(negate(3), 3), multiply(4, power(negate(3), 2))), multiply(7, negate(3))), 12)
negate(n0)|multiply(n3,#0)|power(#0,n2)|power(#0,n0)|multiply(n1,#2)|add(#4,#3)|subtract(#5,#1)|add(n4,#6)
general
allenai/math_qa
the cross - section of a water channel is a trapezium in shape . if the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 700 square meters , what is the depth of the channel ( in meters ) ?
1 / 2 * d * ( 12 + 8 ) = 700 d = 70 the answer is c .
['a ) 50', 'b ) 60', 'c ) 70', 'd ) 80', 'e ) 90']
c
divide(700, divide(add(12, 8), const_2))
add(n0,n1)|divide(#0,const_2)|divide(n2,#1)
physics
allenai/math_qa
amit , sumit and pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations . after breakfast , each of them boards a different tourist vehicle from the nearest bus - depot . after 3 hours , sumit who had gone to a famous beach , calls on the mobile of pramit and claims that he has observed a shark in the waters . pramit learns from the local guide that at that time of the year , only 8 sea - creatures ( including a shark ) are observable and the probability of observing any creature is equal . however , amit and pramit later recall during their discussion that sumit has a reputation for not telling the truth 5 out of 6 times . what is the probability that sumit actually observed a shark in the waters ?
explanation : the probability that sumit actually sees a shark , given that he claimed to have seen one . = > p ( he actually sees the shark and reports truth ) / p ( he claims of seeing a shark ) . = > p ( sees the shark ) p ( reports truth ) / ( p ( he sees a shark ) p ( reports truth ) + p ( does n ' t see ) p ( reports false ) . = > ( 1 / 8 Γ— 1 / 6 ) / ( 1 / 8 Γ— 1.6 + 7 / 8 Γ— 5 / 6 ) = > 1 / 36 . answer : a
a ) 1 / 36 , b ) 1 / 30 , c ) 5 / 36 , d ) 1 / 24 , e ) 1 / 28
a
divide(multiply(divide(const_1, 8), divide(const_1, 6)), add(multiply(divide(const_1, 8), divide(const_1, 6)), multiply(divide(5, 6), divide(add(6, const_1), 8))))
add(n3,const_1)|divide(const_1,n1)|divide(const_1,n3)|divide(n2,n3)|divide(#0,n1)|multiply(#1,#2)|multiply(#3,#4)|add(#5,#6)|divide(#5,#7)
general
allenai/math_qa
if 20 liters of chemical x are added to 80 liters of a mixture that is 20 % chemical x and 80 % chemical y , then what percentage of the resulting mixture is chemical x ?
"the amount of chemical x in the solution is 20 + 0.2 ( 80 ) = 36 liters . 36 liters / 100 liters = 36 % the answer is c ."
a ) 30 % , b ) 33 % , c ) 36 % , d ) 39 % , e ) 42 %
c
add(20, multiply(divide(20, const_100), 80))
divide(n2,const_100)|multiply(n1,#0)|add(n0,#1)|
general
allenai/math_qa
one - third less than 30 % of 180 is equal to :
"lots of ways to tackle this . 30 % of 180 = 54 1 / 3 of 45 = 18 so , 1 / 3 less than 54 is equal to 54 - 18 = 36 answer : c"
a ) 15 , b ) 30 , c ) 36 , d ) 40 , e ) 45
c
subtract(multiply(divide(30, const_100), 180), multiply(divide(const_1, const_3), multiply(divide(30, const_100), 180)))
divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)|
general
allenai/math_qa
a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 45 kmph when will the owner over take the thief from the start ?
"explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 45 40 d = 20 rs = 45 – 40 = 5 t = 20 / 5 = 4 hours answer : option d"
a ) a ) 2 , b ) b ) 5 , c ) c ) 7 , d ) d ) 4 , e ) e ) 8
d
subtract(divide(multiply(divide(const_1, const_2), 40), subtract(45, 40)), divide(const_1, const_2))
divide(const_1,const_2)|subtract(n1,n0)|multiply(n0,#0)|divide(#2,#1)|subtract(#3,#0)|
physics
allenai/math_qa
what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 60 ?
"put in simple words , we need to find the highest power of 2 in 100 ^ 60 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 60 = ( 2 ^ 2 * 5 ^ 2 ) ^ 60 = 2 ^ 120 * 5 ^ 120 answer : c"
a ) 100 , b ) 110 , c ) 120 , d ) 105 , e ) 115
c
subtract(100, subtract(power(2, divide(100, 60)), const_1))
divide(n1,n2)|power(n0,#0)|subtract(#1,const_1)|subtract(n1,#2)|
general
allenai/math_qa
the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 45 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
"20 x + 45 = 21 ( x – 5 ) x = 60 answer : e"
a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 60
e
subtract(multiply(add(20, const_1), 5), 45)
add(n0,const_1)|multiply(n2,#0)|subtract(#1,n1)|
general
allenai/math_qa
find out the square of a number which when doubled exceeds its one nineth by 17 ?
"let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 9 ) + 17 = > 18 p = p + 153 = > p = 9 p ^ 2 = 9 ^ 2 = 81 answer : c"
a ) 16 , b ) 25 , c ) 81 , d ) 26 , e ) 17
c
power(divide(17, subtract(const_2, divide(const_1, add(const_4, const_1)))), const_2)
add(const_1,const_4)|divide(const_1,#0)|subtract(const_2,#1)|divide(n0,#2)|power(#3,const_2)|
general
allenai/math_qa
a reduction of 40 % in the price of bananas would enable a man to obtain 50 more for rs . 40 , what is reduced price per dozen ?
"40 * ( 40 / 100 ) = 16 - - - 50 ? - - - 12 = > rs . 3.84 answer : c"
a ) 1.34 , b ) 2.84 , c ) 3.84 , d ) 4.34 , e ) 5
c
multiply(const_12, divide(multiply(40, divide(40, const_100)), 50))
divide(n0,const_100)|multiply(n0,#0)|divide(#1,n1)|multiply(#2,const_12)|
gain
allenai/math_qa
calculate the l . c . m of 1 / 5 , 6 / 7 , 5 / 6 , 3 / 5 is :
"required l . c . m = l . c . m . of 1 , 6 , 5 , 3 / h . c . f . of 5 , 7 , 6 , 5 = 30 / 1 = 30 answer is b"
a ) 15 , b ) 30 , c ) 20 , d ) 40 , e ) 10
b
multiply(multiply(1, 6), multiply(5, 3))
multiply(n0,n2)|multiply(n4,n6)|multiply(#0,#1)|
physics
allenai/math_qa
the perimeters of 2 squares are 40 cm and 32 cm . find the perimeter of a third square whose area is equal to the difference of the areas of the two squares ?
"side of the 1 st square = 40 / 4 = 10 cm side of the 2 nd square = 32 / 4 = 8 cm area of the 3 rd square = 10 ^ 2 - 8 ^ 2 = 36 cm ^ 2 side of the 3 rd square = 6 cm required perimeter = 6 * 4 = 24 cm answer is b"
a ) 20 cm , b ) 24 cm , c ) 32 cm , d ) 28 cm , e ) 30 cm
b
square_perimeter(sqrt(subtract(square_area(divide(40, const_4)), square_area(divide(32, const_4)))))
divide(n1,const_4)|divide(n2,const_4)|square_area(#0)|square_area(#1)|subtract(#2,#3)|sqrt(#4)|square_perimeter(#5)|
geometry
allenai/math_qa
one - third of rahul ’ s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 2 , 50000 as total savings , how much has he saved in public provident fund ?
explanation let savings in n . s . c and p . p . f . be rs . x and rs . ( 250000 – x ) respectively . then , 1 / 3 x = 1 / 2 ( 250000 - x ) = > x / 3 + x / 2 = 125000 = > 5 x / 6 = 125000 = > x = 125000 x 6 / 5 = 150000 savings in public provident fund = rs . ( 250000 – 150000 ) = rs . 100000 answer d
a ) rs . 30,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 100,000 , e ) none
d
subtract(add(multiply(2, multiply(const_100, const_1000)), 50000), divide(add(multiply(2, multiply(const_100, const_1000)), 50000), add(const_2, const_3)))
add(const_2,const_3)|multiply(const_100,const_1000)|multiply(n0,#1)|add(n1,#2)|divide(#3,#0)|subtract(#3,#4)
general
allenai/math_qa
in a 8 x 8 chess board what is the total number of squares .
ans : the total number of squares in a n x n chess board is equal to ` ` the sum of first n natural number squares ' ' i . e . , n ( n + 1 ) ( 2 n + 1 ) 6 n ( n + 1 ) ( 2 n + 1 ) 6 so substituting 8 in the above formula we get 204 answer : b
a ) 238 , b ) 204 , c ) 678 , d ) 169 , e ) 161
b
divide(multiply(multiply(8, add(8, const_1)), add(multiply(8, const_2), const_1)), subtract(8, const_2))
add(n0,const_1)|multiply(n0,const_2)|subtract(n0,const_2)|add(#1,const_1)|multiply(n0,#0)|multiply(#3,#4)|divide(#5,#2)
general
allenai/math_qa
the average weight of a group of boys is 30 kg . after a boy of weight 33 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
"let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 33 kg joins the group , total weight of boys = 30 x + 33 so 30 x + 33 = 31 ( x + 1 ) = > x = 2 . answer : c"
a ) 4 , b ) 5 , c ) 2 , d ) 7 , e ) 8
c
add(subtract(33, add(30, 1)), 1)
add(n0,n2)|subtract(n1,#0)|add(#1,n2)|
general
allenai/math_qa
integer d is the product of the integers a , b , and c and 1 < a < b < c . if the remainder when 233 is divided by d is 79 , what is the value of a + c ?
79 is the remainder , therefore the number ( a * b * c ) or multiple of the number we need is 79 less than 233 hence 233 - 79 = 154 therefore , 154 is either a number we want or it is a multiple of the number we want but the largest factor of 154 is 77 because 77 * 2 = 154 but 77 is less than 79 hence it can not be a number thus 154 is the number we want a * b * c = 154 now factorize 154 = 1 * 2 * 7 * 11 all are prime also we know 1 < a < b < c thus a = 2 and c = 11 therefore a + c = 2 + 11 = 13 answer : c
a ) 7 , b ) 9 , c ) 13 , d ) 14 , e ) 18
c
add(const_2, divide(divide(subtract(233, 79), const_2), add(const_3, const_4)))
add(const_3,const_4)|subtract(n1,n2)|divide(#1,const_2)|divide(#2,#0)|add(#3,const_2)
general
allenai/math_qa
the average of first six prime numbers which are between 50 and 90 is
"explanation : first six prime numbers which are between 50 and 90 = 53 , 59 , 61 , 67 , 71 , 73 average = ( 53 + 59 + 61 + 67 + 71 + 73 ) / 6 = 64 answer : d"
a ) 35.4 , b ) 42 , c ) 45.7 , d ) 64 , e ) 67
d
add(50, const_1)
add(n0,const_1)|
general
allenai/math_qa
17 times a positive integer is more than its square by 70 , then the positive integer is
"explanation : let the number be x . then , 17 x = x 2 + 70 = > x 2 - 17 x + 70 = 0 = > ( x - 7 ) ( x - 10 ) = 0 = > x = 7 or 10 answer : b"
a ) 13 , b ) 10 , c ) 11 , d ) 12 , e ) 14
b
divide(add(17, subtract(power(17, const_2), multiply(70, const_4))), const_2)
multiply(n1,const_4)|power(n0,const_2)|subtract(#1,#0)|add(n0,#2)|divide(#3,const_2)|
general
allenai/math_qa
how many plants will be there in a circular bed whose outer edge measure 32 cms , allowing 4 cm 2 for each plant ?
"circumference of circular bed = 32 cm area of circular bed = ( 32 ) 2 Γ’  β€ž 4 Γ― € space for each plant = 4 cm 2 Γ’ Λ† Β΄ required number of plants = ( 32 ) 2 Γ’  β€ž 4 Γ― € Γ£ Β· 4 = 20.36 = 20 ( approx ) answer d"
a ) 18 , b ) 750 , c ) 24 , d ) 20 , e ) none of these
d
divide(circle_area(divide(32, multiply(2, const_pi))), 4)
multiply(n2,const_pi)|divide(n0,#0)|circle_area(#1)|divide(#2,n1)|
physics
allenai/math_qa
recipe requires 15 mins to cook . you have 7 mins hourglass and a 11 mins hourglass with you . how will you measure 15 mins using them ?
correct answer : a put up both hour glasses . time starts when 7 min hourglass turns empty . and 11 min hourglass will run for 4 min . now flip 11 min hour glass upside down as soon as it runs empty . it will be empty in another 11 mins . and time is up . so 4 + 11 = 15 mins
a ) 15 mins , b ) 12 mins , c ) 13 mins , d ) 17 mins , e ) 20 mins
a
add(11, subtract(11, 7))
subtract(n2,n1)|add(n2,#0)
physics
allenai/math_qa
what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 21 ?
"when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d ."
a ) 5037 , b ) 5447 , c ) 5867 , d ) 6297 , e ) 6617
d
add(lcm(lcm(18, 70), lcm(100, 21)), 3)
lcm(n1,n2)|lcm(n3,n4)|lcm(#0,#1)|add(n0,#2)|
general
allenai/math_qa
after 2 games , team b had an average of 61.5 points per game . if it got only 47 points in game 3 , how many more points does it need to score to get its total above 500 ?
( 2 * 61.5 ) + 47 + x > 500 123 + 47 + x > 500 170 + x > 500 = > x > 330 option e
a ) 805 , b ) 740 , c ) 670 , d ) 530 , e ) 330
e
subtract(500, add(multiply(2, 61.5), 47))
multiply(n0,n1)|add(n2,#0)|subtract(n4,#1)
general
allenai/math_qa
in an office , totally there are 5200 employees and 45 % of the total employees are males . 50 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
"number of male employees = 5200 * 45 / 100 = 2340 required number of male employees who are less than 50 years old = 4160 * ( 100 - 50 ) % = 2340 * 50 / 100 = 1170 . answer : b"
a ) 1040 , b ) 1170 , c ) 1150 , d ) 4160 , e ) none of these
b
multiply(divide(multiply(5200, 45), const_100), divide(subtract(const_100, 50), const_100))
multiply(n0,n1)|subtract(const_100,n2)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|
general
allenai/math_qa
a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 196 km downstream
"explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 196 km time taken = distance / speed = 196 / 28 = 7 hours answer : option e"
a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
e
divide(196, add(24, 4))
add(n0,n1)|divide(n2,#0)|
physics
allenai/math_qa
the radius of a semi circle is 6.6 cm then its perimeter is ?
"36 / 7 r = 6.6 = 33.9 answer : d"
a ) 32.7 , b ) 32.4 , c ) 22.4 , d ) 33.9 , e ) 32.1
d
add(divide(circumface(6.6), const_2), multiply(6.6, const_2))
circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)|
physics
allenai/math_qa
at what price must an article costing rs . 51.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
"cp = 51.50 sp = 51.50 * ( 125 / 100 ) = 64.375 mp * ( 95 / 100 ) = 64.375 mp = 67.7 answer : d"
a ) 60.5 , b ) 69.5 , c ) 67.5 , d ) 67.7 , e ) 22.5
d
divide(multiply(add(51.50, divide(multiply(51.50, 25), const_100)), const_100), subtract(const_100, 5))
multiply(n0,n2)|subtract(const_100,n1)|divide(#0,const_100)|add(n0,#2)|multiply(#3,const_100)|divide(#4,#1)|
gain
allenai/math_qa
in a certain alphabet , 16 letters contain a dot and a straight line . 30 letters contain a straight line but do not contain a dot . if that alphabet has 50 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 16 + 30 = 46 ; next , we find the total # of letters without line : 50 - 46 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 . answer : a"
a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20
a
subtract(50, add(16, 30))
add(n0,n1)|subtract(n2,#0)|
other
allenai/math_qa
what is the remainder when 1201 Γ— 1202 Γ— 1205 Γ— 1210 is divided by 6 ?
"the remainders when dividing each number by six are : 1 , 2 , 5 , and 4 . the product is 1 * 2 * 5 * 4 = 40 the remainder when dividing 40 by 6 is 4 . the answer is d ."
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
d
reminder(multiply(1202, 1201), 1205)
multiply(n0,n1)|reminder(#0,n2)|
general
allenai/math_qa
a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 50 percent greater than the wholesale price . if the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent ?
answer : d = 5 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 50 % increase makes retail price = 150 . now 30 % decrease - > ( 1 - 30 / 100 ) * 150 = 105 . now compared to the wholesale price of 100 , 5 % increase is what will have the same effect as increasing the wholesale price .
a ) 15 , b ) 20 , c ) 10 , d ) 5 , e ) 8
d
multiply(subtract(multiply(add(const_1, divide(50, const_100)), subtract(const_1, divide(30, const_100))), const_1), const_100)
divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|subtract(#4,const_1)|multiply(#5,const_100)
gain
allenai/math_qa
to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 10 hours a day ?
"man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 10 = 200 therefore number of days = 5760 / 200 = 28.8 days ans = a"
a ) 28.8 , b ) 30 , c ) 32 , d ) 34 , e ) 36
a
divide(multiply(multiply(multiply(30, 12), 8), 2), multiply(20, 10))
multiply(n1,n2)|multiply(n4,n6)|multiply(n3,#0)|multiply(n5,#2)|divide(#3,#1)|
physics
allenai/math_qa
if - 3 / ( a - 3 ) = 3 / ( a + 2 ) , then a = ?
multiply all terms of the given equation by ( a - 3 ) ( a + 2 ) , simplify and solve ( a - 3 ) ( a + 2 ) [ - 3 / ( a - 3 ) ] = ( a - 3 ) ( a + 2 ) [ 3 / ( a + 2 ) ] - 3 ( a + 2 ) = 3 ( a - 3 ) a = 1 / 2 correct answer a
a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
a
divide(3, multiply(3, 2))
multiply(n0,n3)|divide(n0,#0)
general
allenai/math_qa
a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 3000 , then his salary per month in rupees is :
"total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 Γ— salary = 3000 , salary = 20000 rs . answer : a"
a ) 20000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
a
divide(multiply(3000, const_100), 5)
multiply(n4,const_100)|divide(#0,n3)|
gain
allenai/math_qa
in a sports club with 27 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
"let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 27 38 - 2 x + x = 27 38 - x = 27 x = 11 so 8 members play both badminton and tennis . e"
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
e
subtract(add(add(17, 19), 2), 27)
add(n1,n2)|add(n3,#0)|subtract(#1,n0)|
other
allenai/math_qa
a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.05 ?
the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.05 - $ 0.65 = $ 1.40 the charge for the next 1300 grams is $ 1.30 which leaves a charge of $ 0.10 the weight is somewhere between 1550 and 1650 . the answer is d .
a ) 980 , b ) 1130 , c ) 1440 , d ) 1610 , e ) 1820
d
divide(add(subtract(2.05, divide(65, const_100)), multiply(divide(divide(10, 100), 100), 250)), divide(divide(10, 100), 100))
divide(n2,n3)|divide(n0,const_100)|divide(#0,n3)|subtract(n4,#1)|multiply(n1,#2)|add(#4,#3)|divide(#5,#2)
general
allenai/math_qa
a cricket bat is sold for $ 850 , making a profit of $ 230 . the profit percentage would be
"230 / ( 850 - 230 ) = 230 / 620 = 23 / 62 = 37 % answer : d ."
a ) 24 % , b ) 25 % , c ) 30 % , d ) 37 % , e ) 40 %
d
multiply(divide(230, subtract(850, 230)), const_100)
subtract(n0,n1)|divide(n1,#0)|multiply(#1,const_100)|
gain
allenai/math_qa
a man whose bowling average is 12.4 , takes 7 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
12.4 * x + 26 = ( 7 + x ) 12 solve equation x = 145 answer : c
a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147
c
divide(subtract(multiply(floor(12.4), 7), 26), subtract(12.4, floor(12.4)))
floor(n0)|multiply(n1,#0)|subtract(n0,#0)|subtract(#1,n2)|divide(#3,#2)
general
allenai/math_qa
two trains of length 100 m and 160 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
"relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 160 = 260 m . the time required = d / s = 260 / 20 = 13 sec . answer : c"
a ) 18 sec , b ) 70 sec , c ) 13 sec , d ) 20 sec , e ) 19 sec
c
divide(add(100, 160), multiply(add(42, 30), const_0_2778))
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
physics
allenai/math_qa
in a group of houses , 40 had dogs , 30 had cats and 10 houses having both dogs and cats . what is the number of houses ?
make a venn diagram , and enter your data . let the number of houses be x 30 + 10 + 20 = x x = 60 so number of houses were = 60 answer b
a ) 30 , b ) 60 , c ) 40 , d ) 45 , e ) 50
b
subtract(add(40, 30), 10)
add(n0,n1)|subtract(#0,n2)
other
allenai/math_qa
sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 08 : 00 and starts climbing at a constant pace . ken starts climbing only at 10 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
"both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 10 : 00 , in 5 hrs , the time will be 15 : 00 answer ( d )"
a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
d
add(divide(add(700, 50), subtract(500, divide(700, const_2))), 10)
add(n4,n6)|divide(n4,const_2)|subtract(n5,#1)|divide(#0,#2)|add(n2,#3)|
physics
allenai/math_qa
if r is a positive integer , and r / 15 = 8.2 , what is the remainder when r is divided by 15 ?
if r were a multiple of 15 , the quotient r / 15 would be an integer . the fact that it ' s a decimal tells us that 15 goes into r eight whole times and some decimal part of a time . this decimal part , 0.2 is the remainder divided by the divisor . let b be the remainder . b / 15 = 0.2 = 1 / 5 b = ( 15 ) * ( 1 / 5 ) = 3 answer = ( c )
a ) a . 1 , b ) b . 2 , c ) c . 3 , d ) d . 4 , e ) e . 8
c
reminder(multiply(8.2, 15), 15)
multiply(n0,n1)|reminder(#0,n0)
general
allenai/math_qa
the sum of ages of 5 children born 1.5 years different each is 50 years . what is the age of the elder child ?
"let the ages of children be x , ( x + 1.5 ) , ( x + 3 ) , ( x + 4.5 ) and ( x + 6 ) years . then , x + ( x + 1.5 ) + ( x + 3 ) + ( x + 4.5 ) + ( x + 6 ) = 50 5 x = 35 x = 7 . x + 6 = 7 + 6 = 13 answer : e"
a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 13
e
divide(add(add(add(add(1.5, const_4), add(1.5, const_4)), add(const_4, const_4)), 50), 5)
add(n1,const_4)|add(const_4,const_4)|add(#0,#0)|add(#2,#1)|add(n2,#3)|divide(#4,n0)|
general
allenai/math_qa
hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :
2 ( 15 + 12 ) x h = 2 ( 15 x 12 ) h = 180 / 27 m = 20 / 3 m . volume = 15 x 12 x 20 / 3 m 3 answer : option c
['a ) 720', 'b ) 900', 'c ) 1200', 'd ) 1800', 'e ) 2100']
c
multiply(multiply(15, 12), divide(multiply(multiply(15, 12), const_2), multiply(add(15, 12), const_2)))
add(n0,n1)|multiply(n0,n1)|multiply(#1,const_2)|multiply(#0,const_2)|divide(#2,#3)|multiply(#4,#1)
geometry
allenai/math_qa
evaluate : 983 x 207 - 983 x 107
"983 x 207 - 983 x 107 = 983 x ( 207 - 107 ) = 983 x 100 = 98300 . answer is d ."
a ) 93700 , b ) 97300 , c ) 93800 , d ) 98300 , e ) none of them
d
subtract(983, multiply(multiply(207, 983), 107))
multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|
general
allenai/math_qa
in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 15 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
"setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 40 % not job of choice with diploma = . 15 x not job of choice w / o diploma = . 85 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 15 % of 60 % = 9 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 10 % = 30 % ) . 30 % + 9 % = 39 % . therefore 39 % of the people in country z have a diploma . ans a"
a ) 39 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
a
add(divide(multiply(15, subtract(const_100, 40)), const_100), subtract(40, 10))
subtract(const_100,n2)|subtract(n2,n0)|multiply(n1,#0)|divide(#2,const_100)|add(#3,#1)|
gain
allenai/math_qa
a certain company ’ s profit in 1996 was 17 percent greater than its profit in 1995 , and its profit in 1997 was 25 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
"profit in 1995 - 100 profit in 1996 - 117 % increae profit in 1997 in comparison to 1995 = 17 + 117 * 25 % = 46.25 correct option : e"
a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 46.25 %
e
multiply(subtract(multiply(add(divide(25, const_100), const_1), add(const_1, divide(17, const_100))), const_1), const_100)
divide(n4,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#2,#3)|subtract(#4,const_1)|multiply(#5,const_100)|
gain
allenai/math_qa
a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 3 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
"the ratio of economy to luxury cars is 5 : 3 - - > e : l = 5 : 3 = 20 : 12 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 12 : 15 . answer : a ."
a ) 12 : 15 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
a
divide(divide(multiply(const_4, 3), multiply(3, 3)), divide(multiply(3, const_4), multiply(3, const_4)))
multiply(n3,const_4)|multiply(n3,n3)|multiply(n1,const_4)|divide(#0,#1)|divide(#0,#2)|divide(#3,#4)|
other
allenai/math_qa
how many pieces of 85 cm length can be cut from a rod of 38.25 meters long ?
"number of pieces = 3825 / 85 = 45 the answer is c ."
a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
c
divide(multiply(38.25, const_100), 85)
multiply(n1,const_100)|divide(#0,n0)|
physics
allenai/math_qa
a can do a job in 45 days and b can do it in 30 days . a and b working together will finish four times the amount of work in - - - - - - - days ?
"1 / 45 + 1 / 30 = 5 / 90 = 1 / 18 18 / 1 = 18 * 4 = 72 days answer : e"
a ) 30 days , b ) 45 days , c ) 80 days , d ) 72 1 / 2 days , e ) 72 days
e
add(divide(const_1, 45), divide(const_1, 30))
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|
physics
allenai/math_qa
if 5 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 5 c 2 for vertical 8 c 2 total parallelogram is 5 c 2 * 8 c 2 = 10 * 28 = 280 answer : a
a ) 280 , b ) 63 , c ) 120 , d ) 160 , e ) 1260
a
multiply(divide(multiply(5, subtract(5, const_1)), const_2), divide(multiply(8, subtract(8, const_1)), const_2))
subtract(n0,const_1)|subtract(n1,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)|divide(#3,const_2)|multiply(#4,#5)
physics
allenai/math_qa
pipe a can fill a tank in 2 hours . due to a leak at the bottom , it takes 4 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
"let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 4 = > 1 / x = 1 / 2 - 1 / 4 = 1 / 4 = > x = 4 . answer : d"
a ) 2 , b ) 5 , c ) 6 , d ) 4 , e ) 1
d
divide(multiply(4, 2), subtract(4, 2))
multiply(n0,n1)|subtract(n1,n0)|divide(#0,#1)|
physics
allenai/math_qa
amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is
amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } / { 6 } = 4250 answer : a
a ) rs . 4250 , b ) rs . 4228 , c ) rs . 4128 , d ) rs . 4988 , e ) rs . 4192
a
add(4200, divide(subtract(1500, 1200), multiply(const_2, const_3)))
multiply(const_2,const_3)|subtract(n2,n1)|divide(#1,#0)|add(n0,#2)
general
allenai/math_qa
the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 80 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
"let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 80 percent to make square c length of each side of square c = 1.8 * 20 = 36 area of c = 36 ^ 2 = 1296 difference in areas of c and cummulative areas of a and b = 1296 - ( 400 + 100 ) = 796 percent is the area of square c greater than the sum of the areas of squares a and b = ( 796 / 500 ) * 100 % = 159.2 % answer e"
a ) 75 % , b ) 80 % , c ) 100 % , d ) 150 % , e ) 159.2 %
e
multiply(divide(subtract(subtract(square_area(add(add(const_1, divide(100, 100)), divide(multiply(add(const_1, divide(100, 100)), 80), 100))), const_1), const_4), add(const_1, square_area(add(const_1, divide(100, 100))))), 100)
divide(n0,n0)|add(#0,const_1)|multiply(n1,#1)|square_area(#1)|add(#3,const_1)|divide(#2,n0)|add(#1,#5)|square_area(#6)|subtract(#7,const_1)|subtract(#8,const_4)|divide(#9,#4)|multiply(n0,#10)|
geometry
allenai/math_qa
an employee ’ s annual salary was increased $ 15,000 . if her new annual salary now equals $ 90,000 , what was the percent increase ?
"new annual salary = $ 90,000 salary increase = $ 15,000 . original salary = $ 90,000 - $ 15,000 . = $ 75,000 % increase = ( $ 15,000 / $ 75,000 ) * 100 = 20 % hence c ."
a ) 15 % , b ) 16 2 ⁄ 3 % , c ) 20 % , d ) 22 % , e ) 24 %
c
multiply(subtract(divide(multiply(subtract(const_100, const_10), const_1000), subtract(multiply(subtract(const_100, const_10), const_1000), multiply(multiply(const_0_25, const_100), const_1000))), const_1), const_100)
multiply(const_0_25,const_100)|subtract(const_100,const_10)|multiply(#1,const_1000)|multiply(#0,const_1000)|subtract(#2,#3)|divide(#2,#4)|subtract(#5,const_1)|multiply(#6,const_100)|
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 15.5 years . the ration of the number of boys to the number of girls in the class is ?
"let the ratio be k : 1 . then , k * 16.4 + 1 * 15.5 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.5 ) = k = 0.3 / 0.6 = 1 / 2 required ratio = 1 / 2 : 1 = 1 : 2 . answer : e"
a ) 2 : 6 , b ) 2 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 1 : 2
e
divide(subtract(15.8, 15.5), subtract(16.4, 15.8))
subtract(n0,n2)|subtract(n1,n0)|divide(#0,#1)|
general
allenai/math_qa
a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 6 seconds ?
"the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 6 / 30 = 1 / 5 . the probability that he will stay in the dark is 1 - 1 / 5 = 4 / 5 the answer is b ."
a ) 5 / 6 , b ) 4 / 5 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 2
b
subtract(const_1, divide(6, multiply(6, const_3)))
multiply(n1,const_3)|divide(n1,#0)|subtract(const_1,#1)|
physics
allenai/math_qa
following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
"price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 9 / 1.5 = 6 total price = 8 + 6 = 14 d is the answer"
a ) 11 . , b ) 12 . , c ) 13 . , d ) 14 . , e ) 14.5
d
add(divide(multiply(10, const_100), add(const_100, 25)), divide(multiply(9, const_100), add(const_100, 50)))
add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|multiply(n1,const_100)|divide(#2,#0)|divide(#3,#1)|add(#4,#5)|
general
allenai/math_qa
the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 5 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
"5 b = 7 c and so b = 7 c / 5 7 a = 2 b and so a = 2 b / 7 = 2 c / 5 a + b = 2 c / 5 + 7 c / 5 = 9 c / 5 b + c = 7 c / 5 + c = 12 c / 5 the ratio of a + b : b + c = 9 : 12 = 3 : 4 the answer is c ."
a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
c
divide(add(1, divide(7, 2)), add(divide(7, 2), divide(5, 2)))
divide(n0,n1)|divide(n2,n1)|add(n4,#0)|add(#0,#1)|divide(#2,#3)|
general
allenai/math_qa
the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.8 kg . the weight of the new student is ?
answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.8 - 19 x 15 ) kg = 11 kg . correct option : c
a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none
c
subtract(multiply(add(19, const_1), 14.8), multiply(19, 15))
add(n0,const_1)|multiply(n0,n1)|multiply(n2,#0)|subtract(#2,#1)
general
allenai/math_qa
the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 384 square centimeters , what is the length of the rectangle in centimeters ?
"perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 384 2 l ^ 2 / 3 = 384 l ^ 2 = 576 l = 24 cm the answer is e ."
a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
e
divide(384, const_10)
divide(n2,const_10)|
geometry
allenai/math_qa
if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 45000 sheets of xerox paper ?
"30 sec approach - solve it using approximation 45000 sheet at full price , 5 cent = 2250 45000 sheet at max discount price , 4 cent = 2000 your ans got to be between these two . ans e it is ."
a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 2100
e
multiply(subtract(10000, 2000), multiply(subtract(const_1, divide(const_1, 10)), divide(const_1, 10)))
divide(const_1,n1)|subtract(n4,n2)|subtract(const_1,#0)|multiply(#0,#2)|multiply(#3,#1)|
gain
allenai/math_qa
a seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
"ifno caris selected more than once then the number of clients = 10 / 2 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option c"
a ) 8 , b ) 10 , c ) 15 , d ) 14 , e ) 16
c
multiply(divide(10, 2), const_3)
divide(n0,n1)|multiply(#0,const_3)|
general
allenai/math_qa
one day , raviraj left home and cycled 20 km southwards , turned right and cycled 10 km and turned right and cycled 20 km and turned left and cycled 20 km . how many kilometres will he have to cycle to reach his home straight ?
raviraj starts from home at a , moves 20 km in south upto b . then he turns right and moves 10 km upto c , then he turns right and moves 20 km upto d , then he turns lefts and moves 20 km upto e . so from image it is clear that , if he moves straight then he will have to move ad + de , ad = bc = 10 km so , he will have to move 10 + 20 = 30 km answer b
a ) 50 , b ) 30 , c ) 40 , d ) 60 , e ) 80
b
add(20, 10)
add(n0,n1)
physics
allenai/math_qa
a and b can do a piece of work in 6 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
"c = 1 / 5 – 1 / 6 = 1 / 30 = > 30 days answer : b"
a ) 10 days , b ) 20 days , c ) 25 days , d ) 15 days , e ) 45 days
b
inverse(subtract(4, divide(4, 6)))
divide(n1,n0)|subtract(n1,#0)|inverse(#1)|
physics
allenai/math_qa
equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 7 full and other jar 1 / 6 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
"same amount of water made bigger jar 1 / 7 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 7 + 1 / 7 = 2 / 7 full . answer : d ."
a ) 1 / 7 , b ) 7 / 12 , c ) 1 / 2 , d ) 2 / 7 , e ) 2 / 3
d
divide(const_2, 7)
divide(const_2,n1)|
general
allenai/math_qa
a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
"speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 110 * 3 / 55 = 6 sec . answer : b"
a ) 7 sec , b ) 6 sec , c ) 4 sec , d ) 2 sec , e ) 9 sec
b
divide(110, multiply(add(60, 6), const_0_2778))
add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)|
physics
allenai/math_qa
if 5 men undertook a piece of construction work and finished half the job in 15 days . if two men drop out , then the job will be completed in
that is , half the work done = 5 * 15 * 1 / 2 then , 5 * 15 * 1 / 2 = 3 * ? * 1 / 2 i . e . 5 * 15 = 3 * ? = 5 * 15 / 3 = 25 day d
a ) 5 days , b ) 15 days , c ) 10 days , d ) 25 days , e ) 20 days
d
divide(multiply(15, 5), subtract(5, const_2))
multiply(n0,n1)|subtract(n0,const_2)|divide(#0,#1)
physics
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 47 , the 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 = 47 5 x = 45 x = 9 . hence , b ' s age = 2 x = 19 years . d )"
a ) 10 years , b ) 12 years , c ) 14 years , d ) 18 years , e ) 16 years
d
divide(multiply(subtract(47, 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
in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 48 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
working backward from the day it ' s covered : day 48 : fully covered day 47 : half covered so 47 days answer : e
a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
e
subtract(48, const_1)
subtract(n0,const_1)
physics
allenai/math_qa
a train 110 m long is running with a speed of 80 km / hr . in what time will it pass a man who is running at 8 km / hr in the direction opposite to that in which the train is going ?
"speed of train relative to man = 80 + 8 = 88 km / hr . = 88 * 5 / 18 = 220 / 9 m / sec . time taken to pass the men = 110 * 9 / 220 = 4.5 sec . answer : option c"
a ) 5 , b ) 6 , c ) 4.5 , d ) 8 , e ) 9
c
divide(110, multiply(add(80, 8), const_0_2778))
add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)|
physics
allenai/math_qa
a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 60 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
"this is easiest to solve with a bell - curve histogram . m here is equal to Β΅ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 60 % is one st . dev , then on either side of m we have 60 / 2 = 30 % . so , 30 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 30 = 80 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 80 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it a"
a ) 80 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
a
subtract(const_100, divide(subtract(const_100, 60), const_2))
subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)|
general
allenai/math_qa
the average of 45 results is 10 . the average of first 22 of them is 16 and that of last 22 is 20 . find the 23 result ?
"23 th result = sum of 45 results - sum of 44 results 10 * 45 - 16 * 22 + 20 * 22 = 450 - 352 + 440 = 538 answer is c"
a ) 600 , b ) 480 , c ) 538 , d ) 650 , e ) 560
c
subtract(subtract(multiply(45, 10), multiply(22, 20)), multiply(22, 16))
multiply(n0,n1)|multiply(n2,n5)|multiply(n2,n3)|subtract(#0,#1)|subtract(#3,#2)|
general
allenai/math_qa
a can do a piece of work in 3 days of 5 hours each and b alone can do it in 5 days of 3 hours each . how long will they take it to do working together 3 / 4 hours a day ?
a ' s work per hour = 1 / 15 b ' s work per hour = 1 / 15 a & b ' s work per hour together = ( 1 / 15 ) + ( 1 / 15 ) = 2 / 15 so a & b together complete the work in 15 / 2 hours . . . if they work 2 1 / 2 = 5 / 2 hours a day , it will take ( 15 / 2 ) / ( 3 / 4 ) days = 10 days . . . answer : c
a ) 6 days , b ) 5 days , c ) 10 days , d ) 9 days , e ) 8 days
c
divide(divide(const_1, add(divide(const_1, multiply(3, 5)), divide(const_1, multiply(3, 5)))), divide(3, 4))
divide(n0,n5)|multiply(n0,n1)|divide(const_1,#1)|add(#2,#2)|divide(const_1,#3)|divide(#4,#0)
physics
allenai/math_qa
set a consists of all the prime numbers between 2 and 13 . what is the range of set a ?
"the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 11 lowest number = 3 range = highest - lowest = 11 - 3 = 8 option e"
a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 8
e
subtract(subtract(13, const_2), add(add(2, const_4), const_1))
add(n0,const_4)|subtract(n1,const_2)|add(#0,const_1)|subtract(#1,#2)|
general
allenai/math_qa
if ( 27 / 4 ) x - 18 = 3 x + 27 what is the value of x ?
( 27 / 4 ) x - 18 = 3 x + 27 = > 27 x - 72 = 12 x + 108 = > 15 x = 180 = > x = 12 answer : a
a ) 12 , b ) - 12 , c ) 1 / 12 , d ) - 1 / 12 , e ) 3
a
divide(add(27, 18), subtract(divide(27, 4), 3))
add(n0,n2)|divide(n0,n1)|subtract(#1,n3)|divide(#0,#2)
general
allenai/math_qa
if 75 percent of a class answered the first question on a certain test correctly , 35 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
"i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 35 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 110 x = 30 ans : c"
a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
c
subtract(add(add(75, 35), 20), const_100)
add(n0,n1)|add(n2,#0)|subtract(#1,const_100)|
other
allenai/math_qa
a batsman makes a score of 87 runs in the 17 th inning and thus increases his avg by 3 . find his average after 17 th inning .
"let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) . : . 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . ans : b"
a ) 12 , b ) 39 , c ) 43 , d ) 52 , e ) 34
b
add(subtract(87, multiply(17, 3)), 3)
multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)|
general
allenai/math_qa
a man can row upstream at 26 kmph and downstream at 30 kmph , and then find the speed of the man in still water ?
"us = 26 ds = 30 m = ( 30 + 26 ) / 2 = 28 answer : b"
a ) 29 , b ) 28 , c ) 30 , d ) 32 , e ) 23
b
divide(add(26, 30), const_2)
add(n0,n1)|divide(#0,const_2)|
physics
allenai/math_qa
if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
"since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
a
multiply(multiply(5000, const_2), const_2)
multiply(n1,const_2)|multiply(#0,const_2)|
general
allenai/math_qa
a train 160 m long is running at 30 kmph . in how much time will it pass a platform 120 m long ?
distance travelled = 160 + 120 m = 280 m speed = 30 * 5 / 8 = 75 / 4 m time = 280 * 4 / 75 = 14.93 seconds answer : d .
a ) 15.89 seconds , b ) 24.36 seconds , c ) 15.96 seconds , d ) 14.93 seconds , e ) 22.23 seconds
d
divide(add(160, 120), multiply(30, const_0_2778))
add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)|
physics
allenai/math_qa
a present value of a machine is $ 2000 . its value depletiation rate is 20 % per annum then find the machine value before 2 years ?
"p = $ 2000 r = 20 % t = 2 years machine value before 2 years = p / [ ( 1 - r / 100 ) ^ t ] = 2000 * 5 / 4 * 5 / 4 = $ 3125 answer is a"
a ) $ 3125 , b ) $ 2945 , c ) $ 3012 , d ) $ 2545 , e ) $ 3150
a
multiply(2000, power(subtract(const_1, divide(20, const_100)), 2))
divide(n1,const_100)|subtract(const_1,#0)|power(#1,n2)|multiply(n0,#2)|
gain
allenai/math_qa
a can finish a piece of work in 4 days . b can do it in 8 days . they work together for two days and then a goes away . in how many days will b finish the work ?
"2 / 4 + ( 2 + x ) / 8 = 1 = > x = 2 days answer : d"
a ) 4 , b ) 5 , c ) 6 , d ) 2 , e ) 8
d
divide(subtract(const_1, add(multiply(divide(const_1, 4), const_2), multiply(divide(const_1, 8), const_2))), divide(const_1, 8))
divide(const_1,n0)|divide(const_1,n1)|multiply(#0,const_2)|multiply(#1,const_2)|add(#2,#3)|subtract(const_1,#4)|divide(#5,#1)|
physics
allenai/math_qa
1704 x 1704 = ?
"1704 x 1704 = ( 1704 ) 2 = ( 1700 + 4 ) 2 = ( 1700 ) 2 + ( 4 ) 2 + ( 2 x 1700 x 4 ) = 2890000 + 16 + 13600 . = 2903616 . b )"
a ) a ) 3623216 , b ) b ) 2903616 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
b
multiply(divide(1704, 1704), const_100)
divide(n0,n1)|multiply(#0,const_100)|
general
allenai/math_qa
the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 5 is :
required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 5 = 540 + 5 = 545 . answer : a
a ) 545 , b ) 488 , c ) 542 , d ) 548 , e ) 560
a
multiply(54, const_10)
multiply(n3,const_10)
general
allenai/math_qa
mohit sold an article for $ 27000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
"let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 27000 - 10 / 100 ( 27000 ) = 27000 - 2700 = $ 22500 = > 1.08 x = 22500 = > x = 22500 b"
a ) 16000 , b ) 22500 , c ) 15000 , d ) 18000 , e ) 17000
b
multiply(divide(subtract(27000, divide(multiply(27000, 10), const_100)), add(const_100, 8)), const_100)
add(n2,const_100)|multiply(n0,n1)|divide(#1,const_100)|subtract(n0,#2)|divide(#3,#0)|multiply(#4,const_100)|
gain
allenai/math_qa
a rectangular grass field is 75 m * 55 m , it has a path of 3.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
"area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.5 * 2 ) 2 * 3.5 = > 959 959 * 2 = rs . 1918 answer : e"
a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1918
e
multiply(subtract(rectangle_area(add(75, multiply(3.5, 2)), add(55, multiply(3.5, 2))), rectangle_area(75, 55)), 2)
multiply(n2,n3)|rectangle_area(n0,n1)|add(n0,#0)|add(n1,#0)|rectangle_area(#2,#3)|subtract(#4,#1)|multiply(n3,#5)|
geometry
allenai/math_qa
the average weight of 8 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
"total weight increases = 8 Γ— 1.5 = 12 kg so the weight of new person = 65 + 12 = 77 kg answer b"
a ) 76 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
b
add(65, multiply(8, 1.5))
multiply(n0,n1)|add(n2,#0)|
general
allenai/math_qa
how many 4 x 4 x 4 cubes could fit in a 9 x 13 x 16 box ?
the answer is c ) 29 . 9 x 13 x 16 gives the box an area of 1,872 . if you divide 1,872 by 64 ( the total of 4 x 4 x 4 ) , you get 29.25 . this means 29 full boxes will fit in the larger box .
a ) 22 , b ) 28 , c ) 29 , d ) 31 , e ) 32
c
volume_rectangular_prism(9, 13, 16)
volume_rectangular_prism(n3,n4,n5)|
geometry
allenai/math_qa
what is the sum of the local values of the digits 2 , 3 , 4 , 5 in the number 2345 ?
2000 + 300 + 40 + 5 = 2345 answer a
a ) 2345 , b ) 4500 , c ) 5000 , d ) 6000 , e ) 7000
a
add(5, add(add(multiply(2, const_1000), multiply(3, const_100)), multiply(const_10, 4)))
multiply(n0,const_1000)|multiply(n1,const_100)|multiply(n2,const_10)|add(#0,#1)|add(#3,#2)|add(n3,#4)
general
allenai/math_qa
how many integers from 101 to 700 , inclusive , remains the value unchanged when the digits were reversed ?
"question is asking for palindrome first digit possibilities - 1 through 6 = 6 7 is not possible here because it would result in a number greater than 7 ( i . e 707 , 717 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 6 * 10 = 60 answer is b ."
a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
b
divide(700, const_10)
divide(n1,const_10)|
general
allenai/math_qa
2 minute is taken to travel the diagonal of square field at 3 km / hour . calculate the area of field ?
speed of man = [ 3 * 5 / 18 ] m / sec . = 5 / 6 m / sec . , distance travel in 2 minute = { 5 / 6 * 2 * 60 } m . = 100 m . diagonal of square field = 100 m area of field = 1 / 2 * diagonal ^ 2 = [ 1 / 2 * 100 * 100 ] sq . m = 5000 sq . m = 5000 / 100 = 50 are ( 1 are = 100 sq . m ) answer c
['a ) 25 are', 'b ) 30 are', 'c ) 50 are', 'd ) 60 are', 'e ) 45 are']
c
divide(divide(power(multiply(multiply(2, multiply(multiply(2, 3), const_10)), divide(multiply(3, const_1000), multiply(multiply(const_180, const_10), const_2))), const_2), 2), const_100)
multiply(n1,const_1000)|multiply(const_10,const_180)|multiply(n0,n1)|multiply(#1,const_2)|multiply(#2,const_10)|divide(#0,#3)|multiply(n0,#4)|multiply(#5,#6)|power(#7,const_2)|divide(#8,n0)|divide(#9,const_100)
geometry
allenai/math_qa
if x = 6 and y = βˆ’ 2 , what is the value of ( x βˆ’ 2 y ) ^ y ?
"( x βˆ’ 2 y ) ^ y = ( 6 βˆ’ 2 ( βˆ’ 2 ) ) ^ βˆ’ 2 = 1 / ( 6 + 4 ) ^ 2 = 1 / 100 = 0.01 answer : b"
a ) βˆ’ 100 , b ) 0.01 , c ) 0.25 , d ) 4 , e ) 8
b
divide(divide(2, 2), const_1000)
divide(n1,n1)|divide(#0,const_1000)|
general
allenai/math_qa
what is the % change in the area of a rectangle when its length increases by 30 % and its width decreases by 30 % ?
"( 13 / 10 ) * ( 7 / 10 ) = 91 / 100 of original area 91 / 100 is a 9 % decrease from 100 / 100 - > d"
a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 9 % decrease , e ) insufficient data
d
subtract(const_100, divide(multiply(add(const_100, 30), subtract(const_100, 30)), const_100))
add(n0,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)|
geometry
allenai/math_qa