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when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 83.2 , what is the value of n ? | here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e | a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81 | e | divide(add(multiply(divide(subtract(multiply(83.2, const_10), const_2), const_10), divide(11, divide(const_2, const_10))), 11), divide(11, divide(const_2, const_10))) | divide(const_2,const_10)|multiply(n1,const_10)|divide(n0,#0)|subtract(#1,const_2)|divide(#3,const_10)|multiply(#4,#2)|add(n0,#5)|divide(#6,#2) | general | allenai/math_qa |
if p ' s height is 40 % less than that of q , how much percent q ' s height is more than that of p ? | excess of q ' s height over p = ( 40 / ( 100 - 40 ) ) * 100 = = > 66.66 % answer b | a ) 75.56 % , b ) 66.66 % , c ) 70.05 % , d ) 80 % , e ) 85 % | b | multiply(const_100, divide(40, subtract(const_100, 40))) | subtract(const_100,n0)|divide(n0,#0)|multiply(#1,const_100) | general | allenai/math_qa |
the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 800 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ? | "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 800 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 800 * 2 * ( 4 / 5 ) = 1280 2160 + 1280 = 3440 solving for units gives us 3.44 so the answer is c" | a ) 3.84 , b ) 1.75 , c ) 3.44 , d ) 2.72 , e ) none of these | c | divide(divide(multiply(4, add(multiply(3, 900), multiply(2, 800))), add(3, 2)), const_1000) | add(n2,n3)|multiply(n0,n2)|multiply(n1,n3)|add(#1,#2)|multiply(n4,#3)|divide(#4,#0)|divide(#5,const_1000)| | other | allenai/math_qa |
a and b go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 60 kmph . after how much time will they meet for the first time at the starting point ? | "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 36 * 5 / 18 ) , 600 / ( 60 * 5 / 18 ) } = 180 sec . answer : e" | a ) 120 sec , b ) 176 sec , c ) 178 sec , d ) 187 sec , e ) 180 sec | e | divide(600, subtract(multiply(60, const_0_2778), multiply(36, const_0_2778))) | multiply(n2,const_0_2778)|multiply(n1,const_0_2778)|subtract(#0,#1)|divide(n0,#2)| | physics | allenai/math_qa |
a cubical block of metal weighs 5 pounds . how much will another cube of the same metal weigh if its sides are twice as long ? | for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 5 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 5 pounds = 40 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 5 * 8 = 40 so answer is b | ['a ) 48', 'b ) 40', 'c ) 24', 'd ) 18', 'e ) 12'] | b | multiply(5, multiply(const_2, const_4)) | multiply(const_2,const_4)|multiply(n0,#0) | geometry | 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 . 13600 after a year ? | "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 13600 = 4080 answer : e" | a ) 3630 , b ) 9232 , c ) 8828 , d ) 2387 , e ) 4080 | e | multiply(divide(6300, add(add(6300, 4200), 10500)), 13600) | add(n0,n1)|add(n2,#0)|divide(n0,#1)|multiply(n3,#2)| | gain | allenai/math_qa |
a can finish a work in 8 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ? | "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 8 b ' s 1 day work = 1 / 4 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 8 + 1 / 4 ) = 3 / 8 so in one day 3 / 8 work will be done answer : d" | a ) 3 / 5 , b ) 3 / 6 , c ) 3 / 7 , d ) 3 / 8 , e ) none of these | d | add(divide(const_1, 8), multiply(divide(const_1, 8), const_2)) | divide(const_1,n0)|multiply(#0,const_2)|add(#0,#1)| | physics | allenai/math_qa |
find the value of e from ( 14 ) ^ 2 x 5 ^ 3 ã · 568 = e . | given exp . = ( 14 ) ^ 2 x 5 ^ 3 ã · 568 = e = 196 x 125 ã · 568 43.1 b | a ) 13.1 , b ) 43.1 , c ) 40.1 , d ) 23.1 , e ) 45.1 | b | divide(multiply(power(14, 2), power(5, 3)), 568) | power(n0,n1)|power(n2,n3)|multiply(#0,#1)|divide(#2,n4) | general | allenai/math_qa |
the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle | "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : option c" | a ) a ) 72 , b ) b ) 828 , c ) c ) 25 , d ) d ) 34 , e ) e ) 35 | c | triangle_area(2.5, 20) | triangle_area(n0,n1)| | geometry | allenai/math_qa |
the ratio of spinsters to cats is 2 to 9 . if there are 42 more cats than spinsters , how many spinsters are there ? | "let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 42 x = 6 and the number of spinsters is 2 ( 6 ) = 12 . the answer is d ." | a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | d | multiply(divide(42, subtract(9, 2)), 2) | subtract(n1,n0)|divide(n2,#0)|multiply(n0,#1)| | other | allenai/math_qa |
one pipe can fill a tank 3 times as fast as another pipe . if together the two pipes can fill tank in 40 min , then the slower pipe alone will be able to fill the tank in ? | let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 40 4 / x = 1 / 40 = > x = 160 min . answer : a | a ) 160 , b ) 787 , c ) 144 , d ) 128 , e ) 121 | a | divide(40, divide(const_1, add(3, const_1))) | add(n0,const_1)|divide(const_1,#0)|divide(n1,#1) | physics | allenai/math_qa |
pure milk costs 3.60 per litre . a milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre . how many litres of water does he add ? | in mixture , quantity of pure milk / quantity of water = 3 − 0 / 3.6 − 3 = 3 / 0.6 = 5 / 1 since in every 5 litres of milk , he adds 1 litre of water . ∴ in every 25 litres of milk , he adds 5 litres of water . answer b | a ) 2 litres , b ) 5 litres , c ) 7 litres , d ) 11 litres , e ) none of these | b | divide(subtract(multiply(25, 3.6), multiply(25, 3)), 3) | multiply(n0,n1)|multiply(n1,n2)|subtract(#0,#1)|divide(#2,n2) | general | allenai/math_qa |
the difference between the local value and the face value of 7 in the numeral 32675149 is ? | "( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 d )" | a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of these | d | subtract(multiply(7, const_1000), 7) | multiply(n0,const_1000)|subtract(#0,n0)| | general | allenai/math_qa |
a train 200 m long is running with a speed of 54 kmph . in what will it pass a car whose speed at 36 kmph in the direction opposite to that in which the train is going | "explanation : speed of the train relative to man = ( 54 + 36 ) kmph = 90 × 5 / 18 m / sec = 25 m / sec . time taken by the train to cross the car = time taken by it to cover 200 m at 25 m / sec = ( 200 × 1 / 25 ) sec = 8 sec answer : option a" | a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 15 sec | a | multiply(divide(divide(200, const_1000), subtract(54, 36)), const_3600) | divide(n0,const_1000)|subtract(n1,n2)|divide(#0,#1)|multiply(#2,const_3600)| | physics | allenai/math_qa |
a certain psychologist charges $ 40 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 375 , what is the total charge to a patient who receives only 2 hours of therapy ? | let the charge for first hour = x + 40 then charge for each additional hour = x x + 40 + 4 x = 375 = > 5 x = 335 = > x = 67 total charge for patient for 3 hours of therapy = x + 40 + x = 2 x + 40 = 174 $ answer d | a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 174 , e ) $ 192 | d | add(multiply(divide(subtract(375, 40), 5), 2), 40) | subtract(n2,n0)|divide(#0,n1)|multiply(n3,#1)|add(n0,#2) | general | allenai/math_qa |
a farmer spent $ 34 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ? | "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 34 = $ 13.6 on chicken feed , thus he spent the remaining 34 - 13.6 = $ 20.4 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 13.6 - - > x = $ 17 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17 + 20.4 = $ 37.4 . answer : a ." | a ) $ 37.40 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60 | a | add(multiply(34, divide(40, const_100)), 34) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | gain | allenai/math_qa |
find the cube root of 185193 . | "observe unit digit here is 3 so unit digit of the answer is 7 . now omit 193 . now find after which perfect cube 193 lies . it is 125 . so our tenth place is 5 . so answer is 57 . answer : b" | a ) 33 , b ) 57 , c ) 99 , d ) 17 , e ) 01 | b | circle_area(185193) | circle_area(n0)| | geometry | allenai/math_qa |
a circular rim a having a diameter of 45 inches is rotating at the rate of x inches / min . another circular rim b with a diameter of 30 inches is rotating at the rate of y inches / min . what is the value of y in terms of x , if both the rims reach their starting positions at the same time after every rotation . | t = s 1 / v 1 = s 2 / v 2 or , 45 / x = 30 / y or , y = 45 x / 30 = 3 x / 2 ( answer a ) | ['a ) 3 x / 2', 'b ) 4 x / 5', 'c ) 7 x / 5', 'd ) 5 x / 7', 'e ) 3 x / 4'] | a | divide(multiply(const_3, 45), const_2) | multiply(n0,const_3)|divide(#0,const_2) | geometry | allenai/math_qa |
an iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm . if the sides of the sheet are in the ratio 1 : 5 , the sides are : | sol . let the sides of the sheet be x and 5 x . then , ⇒ x * 5 x * 1 / 2 = 10 * 10 * 10 ⇒ 5 x ² = 2000 ⇒ x ² = 400 ⇒ x = 20 . ∴ the sides are 20 cm and 100 cm . answer a | ['a ) 10 cm 20 cm', 'b ) 2 cm 10 cm', 'c ) 100 cm 20 cm', 'd ) 30 cm 100 cm', 'e ) none'] | a | sqrt(divide(divide(volume_cube(10), 0.5), 5)) | volume_cube(n0)|divide(#0,n1)|divide(#1,n3)|sqrt(#2) | geometry | allenai/math_qa |
a precious stone weighing 35 grams worth rs . 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5 . if the price varies as the square of the weight then find the loss incurred . | the price varies as the square of the weight , p = k x w 2 12250 = k x 352 k = 10 thus , p = 10 w 2 when the two pieces are in the ratio 2 : 5 ( weight wise ) then we know that their weights must be 10 g and 25 g respectively . their values should be : 10 g piece : 10 x 102 = rs . 1000 ; 25 g piece : 10 x 252 = rs . 6250 . total value of stone now , = 1000 + 6250 = rs . 7250 loss incurred = 12250 - 7250 = rs . 5000 answer : d | a ) rs . 5750 , b ) rs . 6000 , c ) rs . 5500 , d ) rs . 5000 , e ) rs . 7000 | d | subtract(subtract(subtract(subtract(add(multiply(const_100, const_100), divide(divide(multiply(const_100, const_100), const_2), 2)), const_100), const_100), divide(const_100, const_2)), add(multiply(divide(subtract(subtract(subtract(add(multiply(const_100, const_100), divide(divide(multiply(const_100, const_100), const_2), 2)), const_100), const_100), divide(const_100, const_2)), power(35, const_2)), power(multiply(5, 2), const_2)), multiply(divide(subtract(subtract(subtract(add(multiply(const_100, const_100), divide(divide(multiply(const_100, const_100), const_2), 2)), const_100), const_100), divide(const_100, const_2)), power(35, const_2)), power(multiply(5, 5), const_2)))) | divide(const_100,const_2)|multiply(const_100,const_100)|multiply(n2,n3)|multiply(n3,n3)|power(n0,const_2)|divide(#1,const_2)|power(#2,const_2)|power(#3,const_2)|divide(#5,n2)|add(#8,#1)|subtract(#9,const_100)|subtract(#10,const_100)|subtract(#11,#0)|divide(#12,#4)|multiply(#13,#6)|multiply(#13,#7)|add(#14,#15)|subtract(#12,#16) | other | allenai/math_qa |
the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits m of the larger integer ? | really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) . | a ) m = 2 , b ) m = 5 , c ) m = 8 , d ) 10 , e ) 11 | a | divide(sqrt(subtract(power(add(divide(1000, const_10), const_1), const_2), power(subtract(add(divide(1000, const_10), const_1), const_2), const_2))), const_10) | divide(n0,const_10)|add(#0,const_1)|power(#1,const_2)|subtract(#1,const_2)|power(#3,const_2)|subtract(#2,#4)|sqrt(#5)|divide(#6,const_10) | general | allenai/math_qa |
the tax on a commodity is diminished by 20 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ? | "explanation : 100 * 100 = 10000 80 * 115 = 9200 10000 - - - - - - - 800 100 - - - - - - - ? = 8 % e )" | a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 8 % | e | subtract(const_100, divide(multiply(add(const_100, 15), subtract(const_100, 20)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | general | allenai/math_qa |
a field is 90 metre long and 50 metre broad . a 25 metre long , 20 metre broad and 4 metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field . how much the level of field will rise ? | area of field = 90 x 50 = 4500 m 2 area of field dug out = 25 x 20 = 500 m 2 therefore , area of remaining field = 4500 m 2 - 500 m 2 = 4000 m 2 volume of the earth dug out = 25 x 20 x 4 = 2000 m 3 therefore , field will rise by 2000 / 4000 = 0.5 metre answer a | a ) 0.5 metre , b ) 0.3 metre , c ) 0.8 metre , d ) 0.6 metre , e ) 0.7 metre | a | divide(multiply(multiply(25, 20), 4), subtract(multiply(90, 50), multiply(25, 20))) | multiply(n2,n3)|multiply(n0,n1)|multiply(n4,#0)|subtract(#1,#0)|divide(#2,#3) | physics | allenai/math_qa |
if x and y are both odd prime numbers and x < y , how many distinct positive integer factors does 2 xy have ? | the solution should be the same for all numbers that fulfill the condition above . as x and y are odd prime numbers , they must be > 2 . also , they must be distinct as x < y . i choose x = 3 and y = 5 : how many factors does 2 x 3 x 5 = 30 have : 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 = 8 distinct positive integer factors . hence , the correct answer is d . | a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12 | d | multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1)) | add(const_1,const_1)|multiply(n0,#0)|multiply(#0,#1) | other | allenai/math_qa |
a bag consists of 50 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? | "bag consists of 50 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 50 - 5 - 9 = 36 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 50 + 36 / 50 = 45 / 50 = 9 / 10 hence , answer will be e ." | a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 9 / 10 | e | divide(add(subtract(50, add(5, 9)), 9), 50) | add(n1,n2)|subtract(n0,#0)|add(n2,#1)|divide(#2,n0)| | probability | allenai/math_qa |
a thief is spotted by a policeman from a distance of 175 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ? | relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 175 m / 1000 ) x 1 / 2 hr = 7 / 80 hr . in 7 / 80 hrs , the thief covers a distance of 8 x 7 / 80 km = 7 / 10 km = 700 m answer is d . | a ) 350 m , b ) 200 m , c ) 400 m , d ) 700 m , e ) none of them | d | divide(multiply(175, 8), subtract(10, 8)) | multiply(n0,n1)|subtract(n2,n1)|divide(#0,#1) | physics | allenai/math_qa |
if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 7 children have two children of the same sex and one of the opposite sex ? | "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 7 = 7 c 2 total possible outcomes - 2 ^ 7 ( each child can be either a girl or a boy ) probability = 2 c 1 * 7 c 2 / 2 ^ 7 = 2 * 7 / 2 * 2 * 2 * 2 * 2 * 2 * 2 = 7 / 64 ans = d" | a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 7 / 64 , e ) 3 / 5 | d | divide(const_2, 7) | divide(const_2,n0)| | general | allenai/math_qa |
one - fourth of a number is greater than one - fifth of the number succeeding it by 1 . find the number . | number is 24 as 1 / 4 th of 24 = 6 1 / 5 th of 25 ( 24 + 1 ) = 5 6 = 5 + 1 answer : a | a ) 24 , b ) 42 , c ) 36 , d ) 48 , e ) 50 | a | divide(add(divide(const_2, const_10), 1), subtract(divide(1, const_4), divide(const_2, const_10))) | divide(const_2,const_10)|divide(n0,const_4)|add(n0,#0)|subtract(#1,#0)|divide(#2,#3) | general | allenai/math_qa |
in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each 100 m in length both trains running with a speed of 80 kmph ? | d = 100 m + 100 m = 200 m * 1 / 1000 = 0.2 kms rs = 80 + 80 = 160 kmph t = ( 0.2 / 160 ) * 3600 = 4.5 sec answer : a | a ) 4.5 sec , b ) 4.8 sec , c ) 4.2 sec , d ) 5.0 sec , e ) 5.2 sec | a | divide(add(100, 100), multiply(add(80, 80), const_0_2778)) | add(n0,n0)|add(n1,n1)|multiply(#1,const_0_2778)|divide(#0,#2) | physics | allenai/math_qa |
two goods trains each 625 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ? | "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 625 + 625 = 1250 m . required time = 1250 * 6 / 125 = 60 sec . answer : option d" | a ) 40 , b ) 45 , c ) 48 , d ) 60 , e ) 44 | d | add(45, 30) | add(n1,n2)| | physics | allenai/math_qa |
total number of people attending a party is 600 . 70 % of the men are wearing black shirt and rest are wearing red . if 60 % of the total people are women then how many men are wearing red shirts ? | number of woman in the party = 0.60 * 600 = 360 number of men in the party = 600 - 360 = 240 % of men wearing red shirts = 100 - 70 = 30 % number of men wearing red shirt = 0.30 * 240 = 72 . b is the correct answer | a ) 168 , b ) 72 , c ) 56 , d ) 170 , e ) 60 | b | multiply(divide(subtract(const_100, 70), const_100), multiply(divide(subtract(const_100, 60), const_100), 600)) | subtract(const_100,n1)|subtract(const_100,n2)|divide(#0,const_100)|divide(#1,const_100)|multiply(n0,#3)|multiply(#2,#4) | gain | allenai/math_qa |
in a company of 12 employees , 5 employees earn $ 36000 , 4 employees earn $ 45000 , and the 3 highest - paid employees earn the same amount . if the average annual salary for the 12 employees is $ 47500 , what is the annual salary for each of the highest - paid employees ? | 5 * 36,000 + 4 * 45,000 + 3 x = 12 * 47,500 3 x = 570,000 - 180,000 - 180,000 3 x = 210,000 x = 70,000 the answer is c . | a ) $ 60,000 , b ) $ 65,000 , c ) $ 70,000 , d ) $ 75,000 , e ) $ 80,000 | c | subtract(divide(divide(subtract(multiply(12, 47500), add(multiply(5, 36000), multiply(4, 45000))), 3), const_1000), 5) | multiply(n0,n7)|multiply(n1,n2)|multiply(n3,n4)|add(#1,#2)|subtract(#0,#3)|divide(#4,n5)|divide(#5,const_1000)|subtract(#6,n1) | general | allenai/math_qa |
a couple spent $ 158.40 in total while dining out and paid this amount using a credit card . the $ 158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ? | "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 158.40 x = 120 the correct answer is b ." | a ) $ 115 , b ) $ 120 , c ) $ 125 , d ) $ 130 , e ) $ 135 | b | divide(multiply(divide(multiply(158.40, const_100), add(const_100, 20)), const_100), add(const_100, 10)) | add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|divide(#2,#0)|multiply(#3,const_100)|divide(#4,#1)| | general | allenai/math_qa |
5 cylinders are built successively , the first is 4 meters tall and the following cylinders are each 4 meters taller than the previous . if the perimeter is 10 pi m , what is the total surface area of the 5 cylinders , excluding the bases of each cylinder ? | s . a . = h x p + 2 x a we need to excude the bottom area , so the formula becomes : s . a . = h x p + a p = 2 pi x r , so 10 pi = 2 pi x r r = 5 since we have 5 cylinders with different heights the equation becomes s . a . = ( 4 + 8 + 12 + 16 + 20 ) x 10 pi + 5 x pi x r ^ 2 60 x 10 pi + 5 pi x 5 ^ 2 600 pi + 125 pi = 725 pi sq . m . answer is a | ['a ) 725 pi sq m', 'b ) 1025 pi sq m', 'c ) 600 pi sq m', 'd ) 125 pi sq m', 'e ) 850 pi sq m'] | a | surface_cylinder(divide(10, const_2), add(add(multiply(4, const_4), add(multiply(4, const_3), add(4, multiply(4, const_2)))), add(multiply(4, const_3), add(4, multiply(4, const_2))))) | divide(n3,const_2)|multiply(n1,const_2)|multiply(n1,const_3)|multiply(n1,const_4)|add(n1,#1)|add(#4,#2)|add(#5,#3)|add(#6,#5)|surface_cylinder(#0,#7) | geometry | allenai/math_qa |
what is the smallest positive integer that can be multiplied by 605 to make it a perfect square ? | "605 is multiplied by 5 gives 3025 its a square root of 55 answer is 5 - option c" | a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11 | c | add(const_3, const_4) | add(const_3,const_4)| | geometry | allenai/math_qa |
1 , 6 , 24 , 60 , 120 , 210 , ___ ? | "it follow the pattern like this . . 2 ^ 3 - 2 = 6 3 ^ 3 - 3 = 24 4 ^ 3 - 4 = 60 5 ^ 3 - 5 = 120 6 ^ 3 - 6 = 210 so . . . 7 ^ 3 - 7 = 336 answer : a" | a ) 336 , b ) 366 , c ) 330 , d ) 660 , e ) 770 | a | subtract(negate(60), multiply(subtract(6, 24), divide(subtract(6, 24), subtract(1, 6)))) | negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)| | general | allenai/math_qa |
the ratio of three numbers is 1 : 2 : 3 and their sum is 60 . the second number of the three numbers is ? | "1 : 2 : 3 total parts = 6 6 parts - - > 60 1 part - - - - > 10 the second number of the three numbers is = 2 * 10 = 20 answer : c" | a ) 24 , b ) 26 , c ) 20 , d ) 29 , e ) 30 | c | sqrt(divide(60, add(power(3, 2), add(power(1, 2), power(2, 2))))) | power(n0,n1)|power(n1,n1)|power(n2,n1)|add(#0,#1)|add(#3,#2)|divide(n3,#4)|sqrt(#5)| | other | allenai/math_qa |
how many integers from 101 to 600 , inclusive , remains the value unchanged when the digits were reversed ? | "question is asking for palindrome first digit possibilities - 1 through 5 = 5 6 is not possible here because it would result in a number greater than 6 ( i . e 606 , 616 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 5 * 10 = 50 answer is a ." | a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | a | divide(const_100.0, const_10) | divide(const_100.0,const_10)| | general | allenai/math_qa |
a manufacturer is using glass as the surface for the multi - touch screen of its smartphone . the glass on the manufactured phone has a 4 % probability of not passing quality control tests . the quality control manager bundles the smartphone in groups of 10 . if that bundle has any smartphone that does not pass the quality control test , the entire bundle of 10 is rejected . what is the probability that a smartphone bundle that will be rejected by quality control ? | find the probability of the opposite event and subtract from 1 . the opposite event is that bundle will not be rejected by quality control , which will happen if all 10 phones pass the test , so p ( all 10 phones pass test ) = 0.96 ^ 10 . p ( at least one phone do not pass the test ) = 1 - p ( all 10 phones pass test ) = 1 - 0.96 ^ 10 . answer : e . | a ) 0.25 , b ) . 05 ^ 10 , c ) 1 - 0.95 ^ 10 , d ) 1 - 0.05 ^ 10 , e ) 1 - 0.96 ^ 10 | e | subtract(const_1, power(subtract(const_1, divide(4, const_100)), 10)) | divide(n0,const_100)|subtract(const_1,#0)|power(#1,n1)|subtract(const_1,#2) | general | allenai/math_qa |
a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ? | "a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 600 and 400 . difference in profit share = 600 - 400 = 200 answer : a" | a ) s . 200 , b ) s . 100 , c ) s . 300 , d ) s . 50 , e ) s . 90 | a | subtract(divide(divide(1000, add(divide(1, 2), divide(1, 3))), 2), divide(divide(1000, add(divide(1, 2), divide(1, 3))), 3)) | divide(n1,n2)|divide(n1,n4)|add(#0,#1)|divide(n0,#2)|divide(#3,n2)|divide(#3,n4)|subtract(#4,#5)| | general | allenai/math_qa |
a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 900 . find the sum ? | "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 900 = > 30 x / 100 - 24 x / 100 = 900 = > 6 x / 100 = 900 = > x = 15000 . answer : c" | a ) s . 7000 , b ) s . 9000 , c ) s . 15000 , d ) s . 17000 , e ) s . 27000 | c | divide(900, divide(multiply(subtract(15, 12), const_2), const_100)) | subtract(n0,n1)|multiply(#0,const_2)|divide(#1,const_100)|divide(n2,#2)| | gain | allenai/math_qa |
in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 22 to the thrice of the remainder . the dividend is | "divisor = ( 6 * 3 ) + 22 = 40 5 * quotient = 40 quotient = 8 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 8 ) + 6 = 166 . b )" | a ) 74 , b ) 166 , c ) 86 , d ) 92 , e ) 98 | b | add(multiply(add(multiply(6, const_3), 22), divide(add(multiply(6, const_3), 22), 5)), 6) | multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)| | general | allenai/math_qa |
if 80 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ? | "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 80 + 75 - { both correctly } + 5 { both correctly } = 60 . answer : a ." | a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 % | a | subtract(add(add(80, 75), 5), const_100) | add(n0,n1)|add(n2,#0)|subtract(#1,const_100)| | other | allenai/math_qa |
if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 8 children have two children of the same sex and one of the opposite sex ? | "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 8 = 8 c 2 total possible outcomes - 2 ^ 8 ( each child can be either a girl or a boy ) probability = 2 c 1 * 8 c 2 / 2 ^ 8 = 2 * 8 / 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 16 / 256 = 1 / 16 ans = d" | a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 16 , e ) 3 / 5 | d | divide(const_2, 8) | divide(const_2,n0)| | general | allenai/math_qa |
j is 25 % less than p and 20 % less than t . t is t % less than p . what is the value of t ? | usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( t / 100 ) ] * p i . e . 100 - t = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . t = 6.25 answer : option d | a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2 | d | divide(multiply(25, 25), const_100) | multiply(n0,n0)|divide(#0,const_100) | gain | allenai/math_qa |
a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 7000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ? | "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 7000 ) = rs . 875 answer = e" | a ) s . 375 , b ) s . 400 , c ) s . 600 , d ) s . 800 , e ) s . 875 | e | multiply(multiply(subtract(inverse(3), add(inverse(8), inverse(6))), 7000), 3) | inverse(n3)|inverse(n1)|inverse(n0)|add(#1,#2)|subtract(#0,#3)|multiply(n2,#4)|multiply(n3,#5)| | physics | allenai/math_qa |
the total marks obtained by a student in mathematics and physics is 40 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . | "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 40 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 40 + 20 ) / 2 = 30 . answer : e" | a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 30 | e | divide(add(40, 20), const_2) | add(n0,n1)|divide(#0,const_2)| | general | allenai/math_qa |
how long does a train 110 meters long running at the rate of 36 km / hr take to cross a bridge 132 meters in length ? | "distance = length of train + length of bridge = 110 + 132 = 242 speed = 36 km / hr = 36 * 5 / 18 = 10 m / s required time = 242 / 10 = 24.2 seconds answer is a" | a ) 24.2 sec , b ) 30.6 sec , c ) 32.6 sec , d ) 28.1 sec , e ) 20.4 sec | a | divide(add(110, 132), multiply(36, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | gain | allenai/math_qa |
five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 seconds respectively . in 20 minutes , how many times do they toll together ? | "l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 20 min they will toll 10 times . as they have initially tolled once , the answer will be 10 + 1 = 11 . answer : a" | a ) 11 , b ) 10 , c ) 15 , d ) 16 , e ) 17 | a | divide(10, divide(multiply(multiply(2, multiply(multiply(add(2, const_3), 2), const_3)), 2), 10)) | add(n0,const_3)|multiply(n0,#0)|multiply(#1,const_3)|multiply(n0,#2)|multiply(n0,#3)|divide(#4,n4)|divide(n4,#5)| | physics | allenai/math_qa |
if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 555 will be : | "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 555 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 55 3.7 z = 555 , z = 150 answer : . d" | a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 150 , e ) none of these | d | divide(555, add(add(multiply(add(const_1, divide(25, const_100)), add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))), const_1)) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#3,#2)|add(#2,#4)|add(#5,const_1)|divide(n2,#6)| | general | allenai/math_qa |
how many multiples of 5 are there between 5 to 75 ? | "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 . answer : d" | a ) 9 , b ) 18 , c ) 17 , d ) 13 , e ) can not be determined | d | add(divide(subtract(75, 5), 5), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | general | allenai/math_qa |
a car traveling at a certain constant speed takes 20 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 36 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ? | "36 * t = 1 km = > t = 1 / 36 km / h v * ( t + 20 / 3600 ) = 1 v ( 1 / 36 + 20 / 3600 ) = 1 v ( 120 / 3600 ) = 1 v = 30 km / h the answer is d ." | a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32 | d | divide(1, divide(add(multiply(const_3600, divide(1, 36)), 20), const_3600)) | divide(n1,n3)|multiply(#0,const_3600)|add(n0,#1)|divide(#2,const_3600)|divide(n1,#3)| | physics | allenai/math_qa |
the average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years . find the average age of the women ? | explanation : 24 + 26 + 6 * 3 = 68 / 2 = 34 answer : c | a ) 37 , b ) 26 , c ) 34 , d ) 18 , e ) 11 | c | divide(add(add(24, 26), multiply(6, 3)), const_2) | add(n2,n3)|multiply(n0,n1)|add(#0,#1)|divide(#2,const_2) | general | allenai/math_qa |
what is the smallest 6 digit number exactly divisible by 111 ? | "smallest 6 digit number = 100000 100000 / 111 = 900 , remainder = 100 . hence 11 more should be added to 100000 to get the smallest 6 digit number exactly divisible by 111 = > smallest 6 digit number exactly divisible by 111 = 100000 + 11 = 100011 answer is c" | a ) 100010 , b ) 100012 , c ) 100011 , d ) 100013 , e ) 120012 | c | divide(6, power(const_2, const_3)) | power(const_2,const_3)|divide(n0,#0)| | general | allenai/math_qa |
a and b start a business , with a investing the total capital of rs . 25000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 250 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ? | "interest received by a from b = 10 % of half of rs . 25000 = 10 % * 12500 = 1250 . amount received by a per annum for being a working partner = 250 * 12 = rs . 3000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 1250 + 3000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 1250 + 3000 + p ) = 2 ( p ) p = 4250 total profit = 2 p + 3000 = 2 * 4250 + 3000 = 11500 answer : e" | a ) a ) 22500 , b ) b ) 33500 , c ) c ) 22510 , d ) d ) 33510 , e ) e ) 11500 | e | add(multiply(multiply(divide(divide(25000, const_2), 10), const_3), const_4), 250) | divide(n0,const_2)|divide(#0,n1)|multiply(#1,const_3)|multiply(#2,const_4)|add(n2,#3)| | gain | allenai/math_qa |
what is the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % ? | let original length = l original breadth = b then original area = lb length is increased by 20 % ⇒ new length = l × 120100 = 1.2 l breadth is increased by 20 % ⇒ new breadth = b × 120100 = 1.2 b new area = 1.2 l × 1.2 b = 1.44 lb increase in area = new area - original area = 1.44 lb − lb = 0.44 lb percentage increase in area = increase in areaoriginal area × 100 = 0.44 lblb × 100 = 44 % answer is d . | a ) 42 % , b ) 43 % , c ) 45 % , d ) 44 % , e ) 46 % | d | divide(subtract(multiply(add(const_100, 20), add(const_100, 20)), multiply(const_100, const_100)), const_100) | add(n0,const_100)|multiply(const_100,const_100)|multiply(#0,#0)|subtract(#2,#1)|divide(#3,const_100) | geometry | allenai/math_qa |
sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 9 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ? | "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 9 x = 8 / 9 x so if gold card balance is transferred then the rest unspent will be 8 / 9 x - x / 6 = 13 / 18 x so the ans is d" | a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 13 / 18 , e ) 11 / 15 | d | subtract(1, add(multiply(inverse(3), inverse(const_2)), inverse(9))) | inverse(n3)|inverse(n1)|inverse(const_2)|multiply(#1,#2)|add(#0,#3)|subtract(n0,#4)| | general | allenai/math_qa |
the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam . | "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 10 x = > x = 20 . answer : a" | a ) 20 , b ) 27 , c ) 25 , d ) 99 , e ) 21 | a | divide(subtract(multiply(90, 5), multiply(5, 50)), subtract(90, 80)) | multiply(n1,n3)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | general | allenai/math_qa |
at a certain organisation , the number of male members went up by 13 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ? | men increase by 13 % = = > 1.13 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.13 m + 0.94 f = 1.012 * ( m + f ) 1.13 m + 0.94 f = 1.012 m + 1.012 f 1.13 m - 1.012 m = 1.012 f - 0.94 f 0.108 m = 0.072 f m / f = ( 0.072 ) / ( 0.118 ) = 72 / 118 = 3 / 5 answer = ( d ) | a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 5 , e ) 2 : 1 | d | divide(subtract(multiply(add(const_1, divide(1.2, const_100)), const_1000), multiply(subtract(const_1, divide(6, const_100)), const_1000)), subtract(multiply(add(const_1, divide(13, const_100)), const_1000), multiply(add(const_1, divide(1.2, const_100)), const_1000))) | divide(n4,const_100)|divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#2,const_1)|subtract(const_1,#1)|multiply(#3,const_1000)|multiply(#5,const_1000)|multiply(#4,const_1000)|subtract(#6,#7)|subtract(#8,#6)|divide(#9,#10) | other | allenai/math_qa |
a water tank is one - fifth full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ? | the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 15 = 3 minutes the answer is a . | a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15 | a | multiply(divide(const_1, add(const_1, const_4)), divide(const_1, subtract(divide(const_1, 6), divide(const_1, 10)))) | add(const_1,const_4)|divide(const_1,n1)|divide(const_1,n0)|divide(const_1,#0)|subtract(#1,#2)|divide(const_1,#4)|multiply(#3,#5) | physics | allenai/math_qa |
a train passes a station platform in 20 sec and a man standing on the platform in 12 sec . if the speed of the train is 72 km / hr . what is the length of the platform ? | "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 12 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 20 = 20 = > x = 160 m . answer : c" | a ) 227 , b ) 140 , c ) 160 , d ) 120 , e ) 171 | c | multiply(12, multiply(72, const_0_2778)) | multiply(n2,const_0_2778)|multiply(n1,#0)| | physics | allenai/math_qa |
the area of a base of a cone is 30 cm 2 . if the height of the cone is 6 cm , find its volume ? | π r 2 = 30 h = 6 1 / 3 * 30 * 6 = 60 answer : d | ['a ) 87', 'b ) 16', 'c ) 17', 'd ) 60', 'e ) 18'] | d | divide(multiply(30, 6), const_3) | multiply(n0,n2)|divide(#0,const_3) | geometry | allenai/math_qa |
what is the area of a square field whose diagonal of length 26 m ? | "d 2 / 2 = ( 26 * 26 ) / 2 = 338 answer : c" | a ) 287 , b ) 269 , c ) 338 , d ) 200 , e ) 230 | c | divide(square_area(26), const_2) | square_area(n0)|divide(#0,const_2)| | geometry | allenai/math_qa |
12 times a number gives 156 . the number is | "explanation : let the number be ' n ' 12 × n = 156 ⇒ n = 13 correct option : c" | a ) 11 , b ) 12 , c ) 13 , d ) none , e ) can not be determined | c | divide(156, divide(156, 12)) | divide(n1,n0)|divide(n1,#0)| | general | allenai/math_qa |
two unbiased coins are tossed . what is the probability of getting two heads ? | "s = { hh , ht , th , tt } e = event of getting 2 heads e = { tt } p ( e ) = 1 / 4 answer is b" | a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 2 / 7 | b | negate_prob(divide(const_1, power(const_2, const_3))) | power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)| | probability | allenai/math_qa |
total 60 cows 20 cow gives each 2 liter milk 20 cow gives each 3 / 4 liter milk 20 cow gives each 1 / 4 liter milk this is split into 3 son per each 20 cows & 20 liter milk how ? | 20 cow 2 liter each = 40 liter 20 cow 3 / 4 liter each = 3 / 4 = 0.75 * 20 = 15 20 cow 1 / 4 liter each = 1 / 4 = 0.25 * 20 = 5 add 40 + 15 + 5 = 60 milk split into 3 son each 20 liter then 60 / 3 = 20 answer : a | a ) 20 , b ) 10 , c ) 15 , d ) 16 , e ) 18 | a | add(add(divide(3, 4), multiply(divide(3, 4), 20)), multiply(const_0_25, 20)) | divide(n4,n5)|multiply(n1,const_0_25)|multiply(n1,#0)|add(#0,#2)|add(#3,#1) | general | allenai/math_qa |
martin has to secure 80 % marks to clear his exam of class 9 th . he got 200 marks and failed by 200 marks . what is the maximum marks ? | a 500 to pass the exam ravish needs 200 + 200 = 400 marks . = > ( 400 / 80 ) * 100 = 500 | a ) 500 , b ) 505 , c ) 510 , d ) 515 , e ) 525 | a | divide(add(200, 200), divide(80, const_100)) | add(n2,n2)|divide(n0,const_100)|divide(#0,#1) | gain | allenai/math_qa |
a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area q covered by the two roads ? | "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads q = 1000 + 600 - 25 = 1575 answer : option c" | a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625 | c | add(rectangle_area(200, 5), rectangle_area(120, 5)) | rectangle_area(n0,n2)|rectangle_area(n1,n2)|add(#0,#1)| | geometry | allenai/math_qa |
in the land of oz only one or two - letter words are used . the local language has 68 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ? | "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . similarly : the number of 1 letter words ( x ) that can be made from 67 letters is 67 ; the number of 2 letter words ( xx ) that can be made from 67 letters is 67 * 67 , since each x can take 67 values . total : 67 + 67 * 67 . the difference is ( 68 + 68 * 68 ) - ( 67 + 67 * 67 ) = 136 . answer : e ." | a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 136 | e | add(add(const_1, 68), 68) | add(n0,const_1)|add(n0,#0)| | general | allenai/math_qa |
if the speed of a man is 45 km per hour , then what is the distance traveled by him in 30 seconds ? | "the distance traveled in 30 sec = 45 * ( 5 / 18 ) * 30 = 375 m answer : c" | a ) 275 m , b ) 360 m , c ) 375 m , d ) 420 m , e ) 480 m | c | multiply(multiply(45, const_0_2778), 30) | multiply(n0,const_0_2778)|multiply(n1,#0)| | physics | allenai/math_qa |
x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to ? | "given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d" | a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 0 , d ) 1 / 9 , e ) 1 / 5 | d | divide(multiply(1, power(2, const_2)), power(6, const_2)) | power(n0,const_2)|power(n2,const_2)|multiply(n1,#0)|divide(#2,#1)| | general | allenai/math_qa |
benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ? | cost of each apple = 4 dollars apples that benny can buy with the amount she has = 360 / 4 = 90 . apples that each kid gets evenly = 90 / 18 = 5 apples . so the answer is c = 5 | a ) 8 , b ) 9 , c ) 5 , d ) 7 , e ) 10 | c | divide(divide(360, 4), multiply(9, const_2)) | divide(n1,n2)|multiply(n0,const_2)|divide(#0,#1) | general | allenai/math_qa |
x starts a business with rs . 45000 . y joins in the business after 8 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ? | "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 4 = 45 ã — 12 : 30 ã — 4 = 3 ã — 12 : 2 ã — 4 = 9 : 2 answer : option b" | a ) 1 : 2 , b ) 9 : 2 , c ) 1 : 3 , d ) 3 : 1 , e ) 1 : 1 | b | divide(multiply(45000, const_12), multiply(30000, add(const_4, const_3))) | add(const_3,const_4)|multiply(n0,const_12)|multiply(n2,#0)|divide(#1,#2)| | other | allenai/math_qa |
the sum of the 1 st and 3 rd of 3 consecutive odd integers is 131 less than 3 times the second integer . find the 3 integers ? | let x , x + 2 and x + 4 be three integers . the sum of the first x and third x + 4 is given by x + ( x + 4 ) 131 less than three times the second 3 ( x + 2 ) is given by 3 ( x + 2 ) - 131 ` ` the sum of the first and third is 131 less than three times the second ' ' gives x + ( x + 4 ) = 3 ( x + 2 ) - 131 solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 as an exercise , check that the sum of the first and third is 131 less than three times b | a ) 121 , b ) 133 , c ) 145 , d ) 150 , e ) 165 | b | add(subtract(131, 3), subtract(add(3, 3), 1)) | add(n1,n1)|subtract(n3,n1)|subtract(#0,n0)|add(#1,#2) | general | allenai/math_qa |
ritesh and co . generated revenue of rs . 2,500 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ? | "explanation : given , ritesh and co . generated revenue of rs . 2,500 in 2006 and that this was 12.5 % of the gross revenue . hence , if 2500 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 2500 . = > 20,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 20000 ) × 100 . = > 12.5 % . answer : a" | a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these | a | multiply(divide(add(multiply(const_2, multiply(multiply(const_2, add(const_1, const_4)), const_100)), multiply(add(const_1, const_4), const_100)), divide(add(multiply(multiply(const_2, add(const_1, const_4)), const_100), multiply(add(const_2, const_4), const_100)), divide(12.5, const_100))), const_100) | add(const_1,const_4)|add(const_2,const_4)|divide(n2,const_100)|multiply(#0,const_2)|multiply(#0,const_100)|multiply(#1,const_100)|multiply(#3,const_100)|add(#6,#5)|multiply(#6,const_2)|add(#8,#4)|divide(#7,#2)|divide(#9,#10)|multiply(#11,const_100)| | gain | allenai/math_qa |
the cost of 10 kg of apples is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is rs . 20.50 . find the total cost of 4 kg of apples , 3 kg of rice and 5 kg of flour ? | let the costs of each kg of apples and each kg of rice be rs . a and rs . r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = rs . 877.40 answer : b | a ) rs . 849.40 , b ) rs . 877.40 , c ) rs . 901.60 , d ) rs . 815.20 , e ) none of these | b | add(multiply(divide(multiply(24, divide(multiply(6, 20.5), 2)), const_10), 4), add(multiply(divide(multiply(6, 20.5), 2), const_3), multiply(5, 20.5))) | multiply(n2,n4)|multiply(n4,n7)|divide(#0,n3)|multiply(#2,const_3)|multiply(n1,#2)|add(#3,#1)|divide(#4,const_10)|multiply(n5,#6)|add(#5,#7) | general | allenai/math_qa |
the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 52.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ? | "$ 69 - $ 52 = 17 $ ( 17 / 69 ) * 100 = 24.6 % answer : b" | a ) 20.8 , b ) 24.6 , c ) 31.8 , d ) 32.5 , e ) 33.8 | b | multiply(divide(subtract(69.0, 52.0), 69.0), const_100) | subtract(n1,n0)|divide(#0,n1)|multiply(#1,const_100)| | gain | allenai/math_qa |
the rear – most end of a 66 foot truck exits a 330 foot tunnel exactly 6 seconds after the front – most end of the truck entered the tunnel . if the truck traveled the entire tunnel at a uniform speed , what is the speed of the truck in miles per hour ( 1 mile = 5,280 feet ) ? | total length will be 330 + 66 = 396 time = 6 secs speed = 396 / 6 = 66 feet / sec conversion to miles per hour = 66 * 3600 / 5280 = 45 . answer c | a ) 225 , b ) 90 , c ) 45 , d ) 37.5 , e ) 27 | c | divide(multiply(divide(add(330, 66), 6), const_3600), add(multiply(add(const_4, const_1), const_1000), subtract(multiply(const_3, const_100), multiply(const_2, const_10)))) | add(n0,n1)|add(const_1,const_4)|multiply(const_100,const_3)|multiply(const_10,const_2)|divide(#0,n2)|multiply(#1,const_1000)|subtract(#2,#3)|add(#5,#6)|multiply(#4,const_3600)|divide(#8,#7) | physics | allenai/math_qa |
the number of boxes in a warehouse can be divided evenly into 12 equal shipments by boat or 32 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ? | "answer is the lcm of 12 and 32 = 96 answer c" | a ) 27 , b ) 33 , c ) 96 , d ) 81 , e ) 162 | c | multiply(multiply(multiply(multiply(const_2, const_2), const_2), const_3), 12) | multiply(const_2,const_2)|multiply(#0,const_2)|multiply(#1,const_3)|multiply(n0,#2)| | general | allenai/math_qa |
each of 3 charities in novel grove estates has 8 persons serving on its board of directors . if exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors , then how many distinct persons serve on one or more boards of directors ? a . b . c . d . e . | each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b | a ) 8 , b ) 13 , c ) 16 , d ) 24 , e ) 27 | b | subtract(subtract(multiply(3, 8), 8), 3) | multiply(n0,n1)|subtract(#0,n1)|subtract(#1,n0) | general | allenai/math_qa |
if two girls starting from same point , walking in the opposite directions with 5 km / hr and 10 km / hr as average speeds respectively . then the distance between them after 5 hours is ? | "explanation : total distance = distance traveled by person a + distance traveled by person b = ( 5 ã — 5 ) + ( 10 ã — 5 ) = 25 + 50 = 75 km answer : d" | a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85 | d | multiply(add(5, 10), 5) | add(n0,n1)|multiply(n2,#0)| | physics | allenai/math_qa |
the simple interest on a sum of money will be rs . 800 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ? | "p - - - 10 - - - - 800 p - - - 5 - - - - - 400 3 p - - - 5 - - - - - 1200 - - - - - - = > 1600 answer : d" | a ) 8981 , b ) 3799 , c ) 1200 , d ) 1600 , e ) 1732 | d | add(multiply(multiply(divide(800, 10), 5), const_3), multiply(divide(800, 10), 5)) | divide(n0,n1)|multiply(n2,#0)|multiply(#1,const_3)|add(#2,#1)| | general | allenai/math_qa |
a 300 m long train crosses a platform in 54 sec while it crosses a signal pole in 18 sec . what is the length of the platform ? | "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 54 = 50 / 3 3 x + 900 = 2700 = > x = 600 m . answer : c" | a ) 287 , b ) 350 , c ) 600 , d ) 277 , e ) 122 | c | subtract(multiply(speed(300, 18), 54), 300) | speed(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | physics | allenai/math_qa |
a train is moving at 4 / 5 of its usual speed . the train is 45 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ? | new time = d / ( 4 v / 5 ) = 5 / 4 * usual time 45 minutes represents 1 / 4 of the usual time . the usual time is 4 * 45 minutes = 3 hours . the answer is e . | a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3 | e | divide(multiply(multiply(45, divide(4, 5)), inverse(subtract(const_1, divide(4, 5)))), const_60) | divide(n0,n1)|multiply(n2,#0)|subtract(const_1,#0)|inverse(#2)|multiply(#3,#1)|divide(#4,const_60) | physics | allenai/math_qa |
nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 1 screws and 5 nails ? | "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 1 s and 5 n = 1 s + 5 * 1 s = 6 s . . ratio = 15 s / 6 s = 15 / 6 = 5 / 2 b" | a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4 | b | divide(add(multiply(3, const_4), 3), const_10) | multiply(n1,const_4)|add(n1,#0)|divide(#1,const_10)| | general | allenai/math_qa |
veena ranks 65 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ? | "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 65 + 1 = 96 answer : a" | a ) 96 , b ) 108 , c ) 110 , d ) 90 , e ) 93 | a | subtract(subtract(subtract(182, 22), subtract(65, const_1)), const_4) | subtract(n1,n2)|subtract(n0,const_1)|subtract(#0,#1)|subtract(#2,const_4)| | other | allenai/math_qa |
of the people who responded to a market survey , 60 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 3 to 1 , how many people responded to the survey ? | "ratio = 3 : 1 = > 3 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 60 = > 3 x = 60 = > x = 20 hence total no . of respondents = 60 + 20 = 80 hence a is the answer ." | a ) 80 , b ) 150 , c ) 240 , d ) 360 , e ) 480 | a | add(divide(60, 3), 60) | divide(n0,n1)|add(n0,#0)| | other | allenai/math_qa |
25.25 / 1500 is equal to : | "25.25 / 2000 = 2525 / 200000 = 0.016833333 answer : e" | a ) 1.012526333 , b ) 0.012625333 , c ) 0.125263333 , d ) 0.126253333 , e ) 0.016833333 | e | divide(25.25, 1500) | divide(n0,n1)| | general | allenai/math_qa |
in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ? | "ratio of 2 bedroom apartment : 1 bedroom apartment = 2000 : 8000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : a" | a ) 20 % , b ) 25 % , c ) 50 % , d ) 60 % , e ) 27 % | a | divide(multiply(2,000, const_100), add(add(multiply(const_2, const_1000), const_100), 2,000)) | multiply(n0,const_100)|multiply(const_1000,const_2)|add(#1,const_100)|add(n0,#2)|divide(#0,#3)| | general | allenai/math_qa |
a family pays $ 800 per year for an insurance plan that pays 65 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total . | "upfront payment for insurance plan = 800 $ family needs to pay 35 % of first 1000 $ in expense = 350 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 350 = 1150 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1500 $ ( since insurance plan will pay 100 % of amount that exceeds 1150 $ ) answer d" | a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,500 , e ) $ 2,200 | d | subtract(1,000, 800) | subtract(n2,n0)| | general | allenai/math_qa |
the numbers { 1 , 3 , 6 , 7 , 7 , 7 } are used to form 3 2 - digit numbers . if the sum of these 3 numbers is a prime number p , what is the largest possible value of p ? | what is the largest possible sum of these three numbers that we can form ? maximize the first digit : 76 + 73 + 71 = 220 = even , so not a prime . let ' s try next largest sum , switch digits in 76 and we ' ll get : 67 + 73 + 71 = 211 = prime . answer : d . | a ) 97 , b ) 151 , c ) 209 , d ) 211 , e ) 219 | d | add(add(add(7, multiply(7, const_10)), add(multiply(7, const_10), 3)), add(multiply(6, const_10), 1)) | multiply(n3,const_10)|multiply(n2,const_10)|add(n3,#0)|add(n1,#0)|add(n0,#1)|add(#2,#3)|add(#5,#4) | general | allenai/math_qa |
speed of a boat in standing water is 8 kmph and the speed of the stream is 2 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is : | "sol . speed upstream = 6 kmph ; speed downstream = 10 kmph . ∴ total time taken = [ 210 / 6 + 210 / 10 ] hours = 56 hours . answer d" | a ) 48 hours , b ) 51 hours , c ) 36 hours , d ) 56 hours , e ) none | d | add(divide(210, add(8, 2)), divide(210, subtract(8, 2))) | add(n0,n1)|subtract(n0,n1)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)| | physics | allenai/math_qa |
bert and rebecca were looking at the price of a condominium . the price of the condominium was 80 % more than bert had in savings , and separately , the same price was also 20 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings . | "suppose bert had 100 so price becomes 180 , this 180 = 1.2 times r ' s saving . . so r ' s saving becomes 150 so required ratio is 100 : 150 = 2 : 3 answer : c" | a ) 1 : 4 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4 | c | divide(divide(const_100, add(const_100, 80)), divide(const_100, add(const_100, 20))) | add(n0,const_100)|add(n1,const_100)|divide(const_100,#0)|divide(const_100,#1)|divide(#2,#3)| | gain | allenai/math_qa |
jaclyn buys $ 20 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter | "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 475 answer : a" | a ) 475 , b ) 234 , c ) 289 , d ) 345 , e ) none of these | a | divide(divide(multiply(multiply(const_100, const_100), 9.5), const_100), const_4) | multiply(const_100,const_100)|multiply(n2,#0)|divide(#1,const_100)|divide(#2,const_4)| | gain | allenai/math_qa |
it takes 40 identical printing presses 9 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ? | "40 printing presses can do 1 / 9 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 9 = 1 / 12 of the job each hour . the answer is d ." | a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | d | divide(multiply(divide(const_1000, const_2), const_1000), multiply(divide(divide(multiply(divide(const_1000, const_2), const_1000), 40), 9), 30)) | divide(const_1000,const_2)|multiply(#0,const_1000)|divide(#1,n0)|divide(#2,n1)|multiply(n3,#3)|divide(#1,#4)| | physics | allenai/math_qa |
when 1 / 20 % of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is | "1 / 20 % of 6000 = 3 1 / 10 of 6000 = 600 600 - 3 = 598 ans : d" | a ) 50 , b ) 200 , c ) 380 , d ) 598 , e ) 400 | d | multiply(inverse(10), multiply(multiply(const_100, 10), add(const_4, const_4))) | add(const_4,const_4)|inverse(n4)|multiply(n4,const_100)|multiply(#0,#2)|multiply(#1,#3)| | general | allenai/math_qa |
there are 17 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ? | "the total number of stations = 19 from 19 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 19 p ₂ ways . ² ⁰ p ₂ = 19 * 18 = 342 . answer : d" | a ) 156 , b ) 167 , c ) 157 , d ) 342 , e ) 380 | d | multiply(add(17, const_1), add(add(17, const_1), const_1)) | add(n0,const_1)|add(#0,const_1)|multiply(#0,#1)| | physics | allenai/math_qa |
when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 213.28 , what is value of j ? | "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 213.28 here 213 is the quotient . given that remainder = 14 so , 213.28 = 213 + 14 / j so , j = 50" | a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60 | d | divide(14, subtract(213.28, add(const_100, add(multiply(const_4, const_10), const_2)))) | multiply(const_10,const_4)|add(#0,const_2)|add(#1,const_100)|subtract(n1,#2)|divide(n0,#3)| | general | allenai/math_qa |
there are 11 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ? | 11 c 2 = 55 the answer is c . | a ) 35 , b ) 45 , c ) 55 , d ) 65 , e ) 75 | c | divide(multiply(11, subtract(11, const_1)), const_2) | subtract(n0,const_1)|multiply(n0,#0)|divide(#1,const_2) | general | allenai/math_qa |
if ( - 7 ) ^ ( 8 x ) = 7 ^ ( 12 - 5 x ) and x is an integer , what is the value of x ? | "since x is an integer , ( - 7 ) ^ ( 8 x ) is always positive . so , 7 ^ 8 x = 7 ^ ( 13 - 5 x ) 8 x = 12 - 5 x 12 x = 12 x = 1 answer : c" | a ) 5 , b ) - 4 , c ) 1 , d ) 2 , e ) 3 | c | divide(12, 7) | divide(n3,n0)| | general | allenai/math_qa |
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