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what is the perimeter of a square with area 9 p ^ 2 / 64 ? | area of square , ( side ) ^ 2 = ( 3 p / 8 ) ^ 2 therefore side of the square = 3 p / 8 perimeter of square = 4 * side = 4 * ( 3 p / 8 ) = 3 p / 2 answer is a . | ['a ) 3 p / 2', 'b ) 3 p ^ 2 / 4', 'c ) 3 p', 'd ) 3 p ^ 2', 'e ) 4 p / 3'] | a | multiply(divide(sqrt(9), sqrt(64)), const_4) | sqrt(n0)|sqrt(n2)|divide(#0,#1)|multiply(#2,const_4) | geometry | allenai/math_qa |
what does the hexa number e 78 in radix 7 . | conversion of hexa decimal to decimal ( e 78 ) = ( 8 * 16 ^ 0 ) + ( 7 * 16 ^ 1 ) + ( 14 * 16 ^ 2 ) = 8 + 112 + 3584 = 3704 conversion of decimal to radix 7 3704 / 7 : reminder : 1 and dividend : 529 529 / 7 : reminder : 4 and dividend : 75 75 / 7 : reminder : 5 and dividend : 10 10 / 7 : reminder : 3 and dividend : 1 1 / 7 : reminder 1 then finally result is : 13541 answer : d | a ) 12455 , b ) 14153 , c ) 14256 , d ) 13541 , e ) 14541 | d | subtract(add(multiply(78, 7), multiply(add(const_10, const_3), multiply(const_100, const_10))), add(const_4, const_1)) | add(const_10,const_3)|add(const_1,const_4)|multiply(n0,n1)|multiply(const_10,const_100)|multiply(#0,#3)|add(#2,#4)|subtract(#5,#1) | general | allenai/math_qa |
find the mean proportional between 81 & 100 ? | "formula = β a Γ b a = 81 and b = 100 β 81 Γ 100 = 9 Γ 10 = 90 e" | a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 65 , e ) e ) 90 | e | divide(add(81, 100), const_2) | add(n0,n1)|divide(#0,const_2)| | general | allenai/math_qa |
75 boys can complete a work in 26 days . how many men need to complete twice the work in 20 days | "one man can complete the work in 26 * 75 = 1950 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1950 m = 195 workers answer : b" | a ) 160 , b ) 195 , c ) 180 , d ) 190 , e ) 200 | b | divide(multiply(75, multiply(26, const_2)), 20) | multiply(n1,const_2)|multiply(n0,#0)|divide(#1,n2)| | physics | allenai/math_qa |
the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.40 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ? | "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 Γ’ β¬ β 6 = 666 * 1.4 = 932.4 answer : c" | a ) 399 , b ) 272 , c ) 932.4 , d ) 277 , e ) 311 | c | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 1.40), 3) | multiply(n3,const_2)|sqrt(n0)|multiply(#1,const_4)|subtract(#2,#0)|multiply(n2,#3)|multiply(#4,n1)| | physics | allenai/math_qa |
you collect pens . suppose you start out with 5 . mike gives you another 20 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 10 pens . how many pens do you have at the end ? | "solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 Γ£ β 2 = 50 pens . sharon takes 10 pens from you : 50 - 10 = 40 pens . so you have 40 at the end . correct answer : b" | a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43 | b | subtract(multiply(add(20, 5), const_2), 10) | add(n0,n1)|multiply(#0,const_2)|subtract(#1,n2)| | general | allenai/math_qa |
a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ? | at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 44 seconds . thus x = 4 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 92 seconds . answer c | a ) a . 72 , b ) b . 50 , c ) c . 92 , d ) d . 46 , e ) e . 44 | c | multiply(divide(44, add(6, add(const_1, const_4))), add(12, add(6, add(const_1, const_4)))) | add(const_1,const_4)|add(n0,#0)|add(n3,#1)|divide(n2,#1)|multiply(#2,#3) | general | allenai/math_qa |
convert 300 inches into centimeter ? | "1 inch = 2.54 cm 300 inches = 300 * 2.54 = 762 cm answer is e" | a ) 762 cm , b ) 750 cm , c ) 650 cm , d ) 710 cm , e ) 754 cm | e | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 300), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)| | physics | allenai/math_qa |
the ratio of the present ages of ramesh and mahesh is 2 : 5 . 10 years hence , the ratio of their ages will be 10 : 15 . find the difference in their present ages ? | let the present ages of ramesh and mahesh be 2 x and 5 x years respectively . ( 2 x + 10 ) / ( 5 x + 10 ) = 10 / 15 6 x + 30 = 10 x + 20 = > x = 2.5 difference in their ages will be the same at all times . this difference = difference of their present ages = > 5 x - 2 x = 3 x = > 7.5 years answer : a | a ) 7.5 , b ) 6 , c ) 5.5 , d ) 6.5 , e ) 5 | a | divide(15, 2) | divide(n4,n0) | general | allenai/math_qa |
what is the sum of the digits of integer k , if k = ( 10 ^ 50 - 50 ) | "there are 51 digits in 10 ^ 50 when we subtract 50 from it , there will be 50 digits left . 10 ^ 50 can be written as 9999999 . . . . ( 50 times ) + 1 so , 10 ^ 50 - 50 = 9999999 . . . . ( 50 times ) + 1 - 50 = 9999999 . . . . ( 50 times ) - 49 consider the last 2 digits , 99 - 49 = 50 the last 2 digits will be 50 . and our number would be 99999 . . . . . . 99950 with 2 less 9 s after subtraction . number of 9 s left are 48 and the last two digits are 50 the sum of the digits will be ( 48 * 9 ) + 5 + 0 = 437 answer : - b" | a ) 337 , b ) 437 , c ) 457 , d ) 537 , e ) 412 | b | add(multiply(subtract(10, const_1), subtract(50, const_2)), 10) | subtract(n0,const_1)|subtract(n1,const_2)|multiply(#0,#1)|add(#2,n0)| | general | allenai/math_qa |
the sale price sarees listed for rs . 600 after successive discount is 20 % and 5 % is ? | "600 * ( 80 / 100 ) * ( 95 / 100 ) = 456 answer : c" | a ) 227 , b ) 358 , c ) 456 , d ) 787 , e ) 191 | c | subtract(subtract(600, divide(multiply(600, 20), const_100)), divide(multiply(subtract(600, divide(multiply(600, 20), const_100)), 5), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain | allenai/math_qa |
the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 16000 , then find the annual income of a ? | b ' s monthly income = 16000 * 112 / 100 = rs . 17920 b ' s monthly income = 2 parts - - - - > rs . 17920 a ' s monthly income = 5 parts = 5 / 2 * 17920 = rs . 44800 a ' s annual income = rs . 44800 * 12 = rs . 537600 answer : a | a ) rs . 537600 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these | a | multiply(multiply(multiply(16000, add(const_1, divide(12, const_100))), divide(5, 2)), 12) | divide(n0,n1)|divide(n2,const_100)|add(#1,const_1)|multiply(n3,#2)|multiply(#0,#3)|multiply(n2,#4) | other | allenai/math_qa |
a train travels from new york to chicago , a distance of approximately 480 miles , at an average rate of 40 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time ) | "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 480 / 40 = 12 hours . therefore , the train depart from new york at 7 : 00 - 12 hours = 7 : 00 in the morning , new york time . answer : e ." | a ) 3 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00 | e | subtract(multiply(add(6, const_1), const_3), divide(480, 40)) | add(n2,const_1)|divide(n0,n1)|multiply(#0,const_3)|subtract(#2,#1)| | physics | allenai/math_qa |
each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 50 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ? | "annie earned 40 x + 10 ( 2 x ) = 60 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 60 x ( 1.5 x ) ( h ) = 75 x h = 50 hours the answer is c ." | a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60 | c | add(divide(subtract(add(40, 2), 30), 1.5), 30) | add(n2,n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)| | general | allenai/math_qa |
the average of first five multiples of 7 is ? | "average = 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 105 / 5 = 21 . answer : e" | a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 21 | e | add(7, const_1) | add(n0,const_1)| | general | allenai/math_qa |
76 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ? | "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 76 = 33.25 answer : c" | a ) 13.25 , b ) 38.25 , c ) 33.25 , d ) 34.25 , e ) 31.25 | c | divide(multiply(divide(add(const_4, const_3), add(add(const_4, const_3), const_2)), 76), const_2) | add(const_3,const_4)|add(#0,const_2)|divide(#0,#1)|multiply(n0,#2)|divide(#3,const_2)| | general | allenai/math_qa |
in the first 10 overs of a cricket game , the run rate was only 2.1 . what should be the rate in the remaining 30 overs to reach the target of 282 runs ? | "required run rate = [ 282 - ( 2.1 * 10 ) ] / 30 = 261 / 30 = 8.70 answer : d" | a ) 6.25 , b ) 8.28 , c ) 6.11 , d ) 8.7 , e ) 8.11 | d | divide(subtract(282, multiply(10, 2.1)), 30) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain | allenai/math_qa |
two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 21 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ? | "e 63 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 21 mph = 63 miles" | a ) 54 , b ) 66 , c ) 68 , d ) 60 , e ) 63 | e | multiply(21, divide(divide(36, 2), 6)) | divide(n1,n3)|divide(#0,n0)|multiply(n2,#1)| | physics | allenai/math_qa |
a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 35 % impurities to the product . find the net profit percentage of the dealer ? | "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 35 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.75 . so his profit is $ 6.75 - $ 4 = $ 2 and his profit percent is ( 2.75 / 4 ) * 100 = 68.75 % answer : - c" | a ) 44 % , b ) 40 % , c ) 68.75 % , d ) 56.25 % , e ) 36 % | c | multiply(subtract(divide(add(const_100, 35), subtract(const_100, 20)), const_1), const_100) | add(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)|subtract(#2,const_1)|multiply(#3,const_100)| | general | allenai/math_qa |
16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 6 girls will take to construct ? | "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 6 girls = 8 Γ£ β 6 / 4 + 12 = 12 + 6 = 18 girls 8 days to complete the work answer : option d" | a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days | d | divide(const_1, add(multiply(6, divide(divide(const_1, 6), 24)), multiply(8, divide(divide(const_1, 6), 16)))) | divide(const_1,n2)|divide(#0,n1)|divide(#0,n0)|multiply(n4,#1)|multiply(n3,#2)|add(#3,#4)|divide(const_1,#5)| | physics | allenai/math_qa |
if 22 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ? | "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 22 lines is 22 c 2 = 231 the answer is c ." | a ) 125 , b ) 187 , c ) 231 , d ) 375 , e ) 460 | c | divide(factorial(22), multiply(factorial(subtract(22, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | physics | allenai/math_qa |
if 5 a + 7 b = g , where a and b are positive integers , what is the largest possible value of g for which exactly one pair of integers ( a , b ) makes the equation true ? | 5 * a 1 + 7 * b 1 = g 5 * a 2 + 7 * b 2 = g 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 to a we will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 from a , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer | a ) 35 , b ) 48 , c ) 69 , d ) 70 , e ) 74 | d | add(multiply(5, 7), multiply(7, 5)) | multiply(n0,n1)|add(#0,#0) | general | allenai/math_qa |
when positive integer x is divided by 9 , the quotient is y and the remainder is 4 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 1 . what is the value of 5 y β x ? | "( 1 ) x = 9 y + 4 ( 2 ) 2 x = 14 y + 1 ( 2 ) - ( 1 ) : x = 5 y - 3 5 y - x = 3 the answer is b ." | a ) - 3 , b ) 3 , c ) - 4 , d ) 4 , e ) - 5 | b | subtract(multiply(5, divide(subtract(multiply(2, 4), 1), subtract(multiply(7, 2), multiply(2, 9)))), add(multiply(9, divide(subtract(multiply(2, 4), 1), subtract(multiply(7, 2), multiply(2, 9)))), 4)) | multiply(n1,n2)|multiply(n3,n4)|multiply(n0,n2)|subtract(#0,n5)|subtract(#1,#2)|divide(#3,#4)|multiply(n6,#5)|multiply(n0,#5)|add(n1,#7)|subtract(#6,#8)| | general | allenai/math_qa |
a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number t of tickets sold by the male members of the association | "given that , total average t sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ." | a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66 | c | subtract(multiply(66, add(1, 2)), multiply(70, 2)) | add(n2,n3)|multiply(n1,n3)|multiply(n0,#0)|subtract(#2,#1)| | general | allenai/math_qa |
the batting average of a particular batsman is 63 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score . | explanation : total runs scored by the batsman = 63 * 46 = 2898 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2898 β 2552 = 346 runs . let the highest score be x , hence the lowest score = x β 150 x + ( x - 150 ) = 346 2 x = 496 x = 248 runs answer e | a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 248 | e | divide(add(150, subtract(multiply(63, 46), multiply(58, subtract(46, const_2)))), const_2) | multiply(n0,n1)|subtract(n1,const_2)|multiply(n3,#1)|subtract(#0,#2)|add(n2,#3)|divide(#4,const_2) | general | allenai/math_qa |
if 3 ^ x * 4 ^ y = 19683 and x β y = 9 , then x = ? | since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b . | a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | b | subtract(9, divide(log(divide(power(3, 9), 19683)), log(multiply(3, 4)))) | multiply(n0,n1)|power(n0,n3)|divide(#1,n2)|log(#0)|log(#2)|divide(#4,#3)|subtract(n3,#5) | general | allenai/math_qa |
elena β s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ? | "number of cups flour needed for 3 ounces of butter = 4 number of cups flour needed for 1 ounce of butter = 4 / 3 number of cups flour needed for 12 ounces of butter = 4 / 3 * 12 = 16 answer e" | a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 16 | e | multiply(4, 4) | multiply(n1,n2)| | general | allenai/math_qa |
a car is running at a speed of 120 kmph . what distance will it cover in 12 sec ? | "speed = 120 kmph = 120 * 5 / 18 = 33 m / s distance covered in 12 sec = 33 * 12 = 396 m answer is a" | a ) 396 m , b ) 267 m , c ) 180 m , d ) 200 m , e ) 250 m | a | multiply(divide(120, const_3_6), 12) | divide(n0,const_3_6)|multiply(n1,#0)| | physics | allenai/math_qa |
a 600 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ? | "speed = 600 / 18 = 100 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 100 / 3 = > x = 1300 m . l = 1300 - 600 = 700 m answer : option b" | a ) 800 , b ) 700 , c ) 360 , d ) 370 , e ) 380 | b | subtract(multiply(speed(600, 18), 39), 600) | speed(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | physics | allenai/math_qa |
6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days c do they need to finish the same job ? | let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time c = 3 days to finish the task imo a | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | a | divide(subtract(multiply(6, 8), multiply(3, 6)), add(6, 4)) | add(n0,n3)|multiply(n0,n1)|multiply(n0,n2)|subtract(#1,#2)|divide(#3,#0) | physics | allenai/math_qa |
if p # q denotes the least common multiple of p and q , then q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ? | "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ." | a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72 | c | add(divide(subtract(multiply(18, 24), multiply(12, 16)), const_2), 24) | multiply(n2,n3)|multiply(n0,n1)|subtract(#0,#1)|divide(#2,const_2)|add(n3,#3)| | general | allenai/math_qa |
there are , in a certain league , 20 teams , and each team face another team for a total of 4 times . how many games are played in the season ? | "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 760 option b ." | a ) 450 , b ) 760 , c ) 110 , d ) 180 , e ) 400 | b | multiply(multiply(subtract(20, const_1), 4), divide(20, const_2)) | divide(n0,const_2)|subtract(n0,const_1)|multiply(#1,n1)|multiply(#0,#2)| | general | allenai/math_qa |
a train 110 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ? | "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 110 * 3 / 55 ] sec = 6 sec answer : b" | a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4 sec , e ) 2 sec | b | multiply(const_3600, divide(divide(110, const_1000), add(60, 6))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | physics | allenai/math_qa |
40 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ? | "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 40 = 53.33 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 53.33 = 80 litres . answer a" | a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these | a | multiply(1200, multiply(800, divide(40, multiply(800, 600)))) | multiply(n1,n2)|divide(n0,#0)|multiply(n2,#1)|multiply(n4,#2)| | physics | allenai/math_qa |
dexter and prexter are competing with each other in a friendly community competition in a pool of 50 m length and the race is for 1000 m . dexter crosses 50 m in 2 min and prexter in 3 min 15 sec . each time they meet / cross each other , they do handshake ' s . how many such handshake ' s will happen if they start from the same end at the same time ? | explanation : when dexter completes second round , they do handshake once . now for every round which dexter completes , there will be one hand shake as the ratio of speed is 13 : 8 . d and p will meet at the pool end only after d completes 26 rounds . in the 20 th round , d finish the race and the total handshake ' s will be : 20 β 1 = 19 . answer : c | a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22 | c | subtract(divide(1000, 50), const_1) | divide(n1,n0)|subtract(#0,const_1) | physics | allenai/math_qa |
john makes $ 40 a week from his job . he earns a raise andnow makes $ 55 a week . what is the % increase ? | "increase = ( 15 / 40 ) * 100 = 37.5 % . e" | a ) 15 % , b ) 16.66 % , c ) 17.8 % , d ) 19 % , e ) 37.5 % | e | multiply(divide(subtract(55, 40), 40), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain | allenai/math_qa |
simple interest on a certain sum at a certain annual rate of interest is 1 / 25 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is : | "explanation : let sum = x . then , s . i . = x / 25 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 25 ? r ^ 2 = 100 / 25 = 4 r = 2 hence , rate of interest = 2 % . answer : b" | a ) 5 % , b ) 2 % , c ) 6 % , d ) 8 % , e ) 3 % | b | divide(add(multiply(floor(sqrt(multiply(divide(1, 25), const_100))), const_10), 1), const_3) | divide(n0,n1)|multiply(#0,const_100)|sqrt(#1)|floor(#2)|multiply(#3,const_10)|add(#4,n0)|divide(#5,const_3)| | gain | allenai/math_qa |
the average monthly salary of 20 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ? | "explanation : manager ' s monthly salary rs . ( 1700 * 21 - 1600 * 20 ) = rs . 3700 . answer : a ) 3700" | a ) 3700 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 2891 | a | subtract(multiply(add(1600, 100), add(20, const_1)), multiply(1600, 20)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general | allenai/math_qa |
compound interest of rs . 4000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) . | 10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 4000 [ 1 + ( 5 / 100 ) ] ^ 3 - 4000 = 4000 [ ( 21 / 20 ) ^ 3 - 1 ] = 4000 ( 9261 - 8000 ) / 8000 = 4 * 1261 / 8 = 630 answer : d | a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 630 , e ) none of the above | d | subtract(multiply(4000, power(add(const_1, divide(divide(10, const_2), const_100)), multiply(add(1, divide(1, 2)), const_2))), 4000) | divide(n1,const_2)|divide(n2,n4)|add(n2,#1)|divide(#0,const_100)|add(#3,const_1)|multiply(#2,const_2)|power(#4,#5)|multiply(n0,#6)|subtract(#7,n0) | gain | allenai/math_qa |
matt gets a $ 1,300 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 400 , how many sales has matt made ? | "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1300 new average = ( xy + 1300 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1300 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1300 ) = ( xy + x + 150 y + 150 ) i . e . ( 1150 ) = ( x + 150 y ) new commission = 400 = 150 + x i . e . x = 250 i . e . y = 6 new sales = y + 1 = 7 answer : option d" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | divide(subtract(const_1000, const_100), subtract(400, subtract(400, 150))) | subtract(const_1000,const_100)|subtract(n2,n1)|subtract(n2,#1)|divide(#0,#2)| | general | allenai/math_qa |
find the probability that a non leap year selected at random will have 53 sundays | "there are 365 days in a leap year : 52 weeks and 1 more days . so , 52 sundays and 1 days . this 1 days can be { mon , tue , wed , thu , fri , sat , sun } ( 7 cases ) . in order to have 53 sundays we should have sun case . the probability of that is 1 / 7 . answer : e ." | a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7 | e | divide(const_2, add(const_3, const_4)) | add(const_3,const_4)|divide(const_2,#0)| | probability | allenai/math_qa |
a train 120 m long is running with a speed of 66 km / hr . in what time will it pass a man who is roller skating at 12 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 66 + 12 = 78 km / hr . = 78 * 5 / 18 = 65 / 3 m / sec . time taken to pass the man = 150 * 3 / 65 = 6.92 sec . answer : b" | a ) 4.92 , b ) 6.92 , c ) 7.92 , d ) 4.92 , e ) 2.92 | b | divide(120, multiply(add(const_60.0, 12), const_0_2778)) | add(const_60.0,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics | allenai/math_qa |
what is the probability that the sum of two dice will yield a 7 , and then when both are thrown again , their sum will again yield a 7 ? assume that each die has 6 sides with faces numbered 1 to 6 . | "in order to get the sum of the two dices to be 7 , there are six combinations that satisfy this requirement . 1 + 6 = 7 2 + 5 = 7 3 + 4 = 7 4 + 3 = 7 5 + 2 = 7 6 + 1 = 7 each combination has 1 / 36 of probability of occurrence , or in total 6 / 36 for the six combinations , which is 1 / 6 . in order to get the probability of this occurring twice in a row we multiply 1 / 6 * 1 / 6 and we get 1 / 36 . the answer is b ." | a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3 | b | multiply(divide(6, power(6, const_2)), divide(6, power(6, const_2))) | power(n2,const_2)|divide(n2,#0)|multiply(#1,#1)| | probability | allenai/math_qa |
x , a , z , and b are single digit positive integers . x = 1 / 8 a . z = 1 / 8 b . ( 10 a + b ) β ( 10 x + z ) could not equal | "a = 8 x , b = 8 z therefore ( 8 x . 10 + 8 z ) - ( 10 x + z ) = ( 8 - 1 ) ( 10 x + z ) = 7 . ( 10 x + z ) number should be divisible by 7 e" | a ) 28 , b ) 35 , c ) 49 , d ) 63 , e ) 55 | e | add(add(subtract(add(multiply(8, 8), multiply(8, 10)), add(multiply(8, 10), 8)), 10), const_3) | multiply(n1,n1)|multiply(n1,n4)|add(#0,#1)|add(n1,#1)|subtract(#2,#3)|add(n4,#4)|add(#5,const_3)| | general | allenai/math_qa |
a and b β s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a β s salary ? | "explanation : ( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 a = 1500 answer is d" | a ) rs . 500 , b ) rs . 750 , c ) rs . 1250 , d ) rs . 1500 , e ) rs . 1520 | d | divide(multiply(multiply(multiply(const_2, multiply(const_4, add(const_2, const_3))), const_100), subtract(const_1, divide(85, const_100))), add(subtract(const_1, divide(95, const_100)), subtract(const_1, divide(85, const_100)))) | add(const_2,const_3)|divide(n2,const_100)|divide(n1,const_100)|multiply(#0,const_4)|subtract(const_1,#1)|subtract(const_1,#2)|add(#5,#4)|multiply(#3,const_2)|multiply(#7,const_100)|multiply(#8,#4)|divide(#9,#6)| | gain | allenai/math_qa |
a thief goes away with a santro car at a speed of 30 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ? | "- - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - | 60 30 d = 30 rs = 60 Γ’ β¬ β 30 = 30 t = 30 / 30 = 1 hours answer : a" | a ) 1 hours , b ) 2 hours , c ) 2 / 3 hours , d ) 1 / 3 hours , e ) 2 / 5 hours | a | subtract(divide(multiply(divide(const_1, const_2), 30), subtract(60, 30)), 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 |
how many prime numbers are between 15 / 7 and 131 / 6 ? | "15 / 7 = 3 - 131 / 6 = 22 - prime numbers between 3 and 22 are 5 , 7 , 11 , 13 , 17 , and 19 - sign signifies that the number is marginally less . answer d" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | floor(const_2) | floor(const_2)| | general | allenai/math_qa |
a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get : | "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a β s amount = 120 Γ 15 = rs . 1800 . answer : option c" | a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1800 , d ) rs . 2000 , e ) none of these | c | multiply(divide(divide(multiply(15, const_2), 10), add(divide(multiply(15, const_2), 10), divide(multiply(15, const_2), 15))), 3000) | multiply(n1,const_2)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)|divide(#1,#3)|multiply(n2,#4)| | physics | allenai/math_qa |
a train moves at average speed of 60 kmph reaches its destination on time . what its average speed becomes 50 kmph , then it reaches its destination 15 late . find the length of the journey ? | "difference between timings = 15 min = 1 / 4 hr let the length of the journey be x km . then x / 50 - x / 60 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer ( b )" | a ) 4.86 km , b ) 2.5 km , c ) 6.86 km , d ) 5.867 km , e ) 3.25 km | b | multiply(divide(divide(multiply(50, 15), subtract(60, 50)), const_60), 60) | multiply(n1,n2)|subtract(n0,n1)|divide(#0,#1)|divide(#2,const_60)|multiply(n0,#3)| | physics | allenai/math_qa |
the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.5 kg . the weight of the new student is | "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.5 weight of the new student = ( 30 * 27.5 β 29 * 28 ) = 825 - 812 = 13 answer : d" | a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 13 kg , e ) none of these | d | subtract(multiply(add(29, const_1), 27.5), multiply(29, 28)) | add(n0,const_1)|multiply(n0,n1)|multiply(n2,#0)|subtract(#2,#1)| | general | allenai/math_qa |
working alone at their respective constant rates , a can complete a task in β a β days and b in β b β days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 14 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ? | "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 8 no . of days when b works = 6 β 8 x + 6 y = 1 when b starts : no . of days when a works = 7 no . of days when a works = 7 β 7 x + 7 y = 1 solving the above two equations for xy x = 1 / 14 y = 1 / 14 β total work done by ab in a day = 1 / 14 + 1 / 14 = 2 / 28 = 1 / 14 β no . of days to complete the work when both work together = 14 answer : b" | a ) 12 , b ) 14 , c ) 10 , d ) 11 , e ) 13 | b | inverse(add(inverse(subtract(14, const_1)), inverse(add(14, 2)))) | add(n0,n1)|subtract(n1,const_1)|inverse(#1)|inverse(#0)|add(#2,#3)|inverse(#4)| | physics | allenai/math_qa |
there are 12 pieces of radioactive metal a that look identical . 11 of the pieces give the same radiation count when measured , the 12 th piece is a counterfeit and gives a different radiation level , which may be more or less than the other 11 . we are given a radiation scale , which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different , which set has the higher level of radiation . what is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ? | first of all if you are down to just 3 pieces and you know that if the offending piece is less or more active , then it takes exactly 1 measurement to find out the offending piece . so you know you have to reduce the problem to three . now when you are down to either a or b after measurement 1 , you need the next measurement to ( a ) reduce the problem set to 3 and ( b ) to know whether anser is more or less . now you can not compare a group of 4 to 4 , as in the best case it will only reduce the problem to 4 elements which is not good enough . if you have to choose a set of 3 to compare , you can not pick any 3 on the same side from the same set ( a or b ) because if you do this , a quick check will show you that in every choice there is a case where you can only get down to 4 elements . eg . if you weighed { 1 , 23 } v / s { 5 , 910 } and they were equal you ' re problem would only reduce to { 46 , 78 } the easiest way to solve this then is to compare 3 to 3 , and make sure each side has elements from both ab such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only . which is why the sets { 1 , 59 } and { 2 , 67 } or { a , b , c } { a , b , b } . the extra element from c is just taken to make the problem symmetric so to say , we have 8 elements and we make it 9 , to compose 3 sets of 3 each . = b | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | b | add(subtract(12, 11), 2) | subtract(n0,n1)|add(n4,#0) | general | allenai/math_qa |
jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 9 / 49 , what is the probability that the next one she draws will be pink ? | the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 9 / 49 = ( 3 / 7 ) * ( 3 / 7 ) therefore probability that the next one she draws is pink = 4 / 7 option ( b ) | a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49 | b | subtract(const_1, sqrt(divide(9, 49))) | divide(n0,n1)|sqrt(#0)|subtract(const_1,#1) | general | allenai/math_qa |
carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 2 inches tall . how tall are the sculpture andbase together ? | "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 2 = 36 36 / 12 = 3.0 feet answer : d" | a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.0 feet , e ) 3.5 feet | d | divide(add(add(multiply(add(2, 10), 2), 10), 2), add(2, 10)) | add(n0,n1)|multiply(n0,#0)|add(#1,n1)|add(n2,#2)|divide(#3,#0)| | geometry | allenai/math_qa |
a jeep takes 7 hours to cover a distance of 420 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 7 distance = 420 3 / 2 of 7 hours = 7 * 3 / 2 = 10.5 hours required speed = 420 / 10.5 = 40 kmph c )" | a ) 48 kmph , b ) 52 kmph , c ) 40 kmph , d ) 63 kmph , e ) 65 kmph | c | divide(420, multiply(divide(3, 2), 7)) | divide(n2,n3)|multiply(n0,#0)|divide(n1,#1)| | physics | allenai/math_qa |
a and b start a business , with a investing the total capital of rs . 5000 , 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 . 500 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 . 5000 = 10 % * 2500 = 250 . amount received by a per annum for being a working partner = 500 * 12 = rs . 1000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 250 + 1000 + 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 ( 250 + 1000 + p ) = 2 ( p ) p = 1250 total profit = 2 p + 1000 = 2 * 1250 + 1000 = 3500 answer : b | a ) a ) 2500 , b ) b ) 3500 , c ) c ) 5000 , d ) d ) 6000 , e ) e ) 8000 | b | add(multiply(multiply(divide(divide(5000, const_2), 10), const_3), const_4), 500) | divide(n0,const_2)|divide(#0,n1)|multiply(#1,const_3)|multiply(#2,const_4)|add(n2,#3) | gain | allenai/math_qa |
the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 3000 resolutions ? | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 3000 resolutions . = 3000 * 2 * 22 / 7 * 22.4 = 422400 cm = 4224 m answer : d" | a ) 2187 m , b ) 3704 m , c ) 4179 m , d ) 4224 m , e ) 4297 m | d | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 3000), const_100) | add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)| | physics | allenai/math_qa |
a factory produces 6000 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ? | "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 4 days ) by 4 . 6000 / 4 = 1500 toys correct answer b" | a ) 4436 toys , b ) 1500 toys , c ) 6113 toys , d ) 2354 toys , e ) 1375 toys | b | divide(6000, 4) | divide(n0,n1)| | physics | allenai/math_qa |
a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a β s share , 4 times b β s share and 7 times c β s share are all equal . the share of c is ? | given total sum = rs . 427 and given that 3 times a β s share , 4 times b β s share and 7 times c β s share are all equal . = > 3 a = 4 b = 7 c but given = > a + b + c = 427 now express a and b in terms of c i . e = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c | a ) 23 , b ) 87 , c ) 84 , d ) 26 , e ) 19 | c | divide(427, add(divide(7, 7), add(divide(7, 3), divide(7, 4)))) | divide(n3,n1)|divide(n3,n2)|divide(n3,n3)|add(#0,#1)|add(#3,#2)|divide(n0,#4) | general | allenai/math_qa |
in how many ways can the integer 800 be expressed as a product of two different positive integers ? | "800 = ( 2 ^ 5 ) * ( 5 ^ 2 ) since 800 is not a perfect square , no of ways = 7 answer b" | a ) 10 , b ) 7 , c ) 5 , d ) 4 , e ) 2 | b | subtract(divide(divide(800, const_1), const_3), const_3) | divide(n0,const_1)|divide(#0,const_3)|subtract(#1,const_3)| | general | allenai/math_qa |
the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 6 revolutions ? ( use Γ― β¬ = 22 Γ’ Β β 7 ) | "required area covered in 5 revolutions = 6 Γ£ β 2 Γ― β¬ rh = 6 Γ£ β 2 Γ£ β 22 Γ’ Β β 7 Γ£ β 0.7 Γ£ β 2 = 52.8 m 2 answer c" | a ) 40 m 2 , b ) 44 m 2 , c ) 52.8 m 2 , d ) 36 m 2 , e ) none of these | c | multiply(6, multiply(multiply(multiply(2, divide(22, 7)), divide(1.4, 2)), 2)) | divide(n0,n1)|divide(n3,n4)|multiply(#1,n1)|multiply(#0,#2)|multiply(n1,#3)|multiply(n2,#4)| | physics | allenai/math_qa |
ajay can walk 6 km in 1 hour . in how many hours he can walk 45 km ? | "1 hour he walk 6 km he walk 45 km in = 45 / 6 * 1 = 7.5 hours answer is c" | a ) 5 hrs , b ) 10 hrs , c ) 7.5 hrs , d ) 20 hrs , e ) 30 hrs | c | divide(45, 6) | divide(n2,n0)| | physics | allenai/math_qa |
a sum of rs . 2200 has been divided among a , b and c such that a gets 1 / 4 of what b gets and b gets 1 / 5 of what c gets . what is b ' s share ? | "let c ' s share = rs . x then b ' s share = x / 5 a ' s share = x / 5 Γ 1 / 4 = x / 20 hence , x + x / 5 + x / 20 = 2200 β x ( 1 + 1 / 5 + 1 / 20 ) = 2200 β x ( 25 / 20 ) = 2200 β x ( 5 / 4 ) = 2200 β x = 2200 Γ 4 / 5 = 440 Γ 4 = rs . 1760 b ' s share = x / 5 = 1760 / 5 = rs . 352 answer is b ." | a ) 342 , b ) 352 , c ) 322 , d ) 332 , e ) 362 | b | subtract(subtract(multiply(divide(2200, const_10), const_2), const_12), const_12) | divide(n0,const_10)|multiply(#0,const_2)|subtract(#1,const_12)|subtract(#2,const_12)| | general | allenai/math_qa |
if i earn a profit 50 $ in a day and i have 9 employees . after keeping 10 percent profit for me , and distribute remianing money equally among my employees then how much each employee would get ? | since i earned $ 50 sp 10 percent would be 5 $ and 45 $ would remain . dividing 45 by 9 , each employee would get 5 $ each and hince option d is correct . | a ) $ 3 , b ) $ 7 , c ) $ 1 , d ) $ 5 , e ) $ 9 | d | divide(multiply(50, subtract(const_100, 10)), multiply(const_100, 9)) | multiply(n1,const_100)|subtract(const_100,n2)|multiply(n0,#1)|divide(#2,#0) | gain | allenai/math_qa |
if 6 spiders make 6 webs in 6 days , then 1 spider will make 1 web in how many days ? | "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 6 webs 6 : 1 1 x 6 x x = 6 x 1 x 6 = > x = 6 answer is b" | a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | b | multiply(1, 6) | multiply(n0,n3)| | physics | allenai/math_qa |
a coin is tossed 8 times . what is the probability of getting exactly 7 heads ? | "the number of possible outcomes is 2 ^ 8 = 256 there are 8 ways to get exactly 7 heads . p ( exactly 7 heads ) = 8 / 256 = 1 / 32 the answer is c ." | a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128 | c | multiply(power(divide(const_1, const_2), 7), multiply(choose(8, 7), divide(const_1, const_2))) | choose(n0,n1)|divide(const_1,const_2)|multiply(#0,#1)|power(#1,n1)|multiply(#2,#3)| | probability | allenai/math_qa |
aarti can do a piece of work in 5 days . in how many days will she complete three time of work of same type ? | we have the important relation , more work , more time ( days ) a piece of work can be done in 5 days . three times of work of same type can be done in 5 x 3 = 15 days answer e | a ) 6 days , b ) 18 days , c ) 21 days , d ) 3 days , e ) 15 days | e | multiply(const_3, 5) | multiply(n0,const_3) | physics | allenai/math_qa |
n and m are each 3 - digit integers . each of the numbers 3,4 , 5 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ? | "you have 6 digits : 3 , 4 , 5 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 3 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . 487 and 536 ( difference is 49 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 685 and 734 ( difference is 49 ) b" | a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131 | b | subtract(subtract(const_100, multiply(subtract(8, 3,4), const_10)), const_1) | subtract(n5,n1)|multiply(#0,const_10)|subtract(const_100,#1)|subtract(#2,const_1)| | general | allenai/math_qa |
a certain pair of used shoes can be repaired for $ 13.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ? | "1 ) cost of repairing = 13.5 ( for one year ) , therefore for 2 years it would be $ 27 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 32 - 27 ) / ( 27 ) * 100 = 18.51 % . ans is e" | a ) 17.69 , b ) 14.85 , c ) 21.3 , d ) 16.5 , e ) 18.51 | e | multiply(const_100, divide(subtract(32.00, multiply(13.50, 2)), multiply(13.50, 2))) | multiply(n0,n3)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | general | allenai/math_qa |
if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is : | "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a" | a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km | a | multiply(10, divide(20, subtract(14, 10))) | subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)| | general | allenai/math_qa |
in a sports club with 30 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ? | "17 + 19 = 36 but where as total number is 30 - 2 = 28 therefore answer is 36 - 28 = 8 hence answer is e" | a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | e | subtract(add(add(17, 19), 2), 30) | add(n1,n2)|add(n3,#0)|subtract(#1,n0)| | other | allenai/math_qa |
if the price of petrol increases by 30 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ? | "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 30 ) i . e 130 . now , his consumption should be reduced to : - = ( 130 β 100 ) / 130 β 100 . hence , the consumption should be reduced to 23 % . answer : b" | a ) 25 % , b ) 23 % , c ) 16.67 % , d ) 33.33 % , e ) none of these | b | multiply(subtract(const_1, divide(const_100, add(const_100, 30))), const_100) | add(n0,const_100)|divide(const_100,#0)|subtract(const_1,#1)|multiply(#2,const_100)| | general | allenai/math_qa |
the sale price sarees listed for rs . 390 after successive discount is 14 % and 15 % is ? | "390 * ( 86 / 100 ) * ( 85 / 100 ) = 285 answer : a" | a ) 285 , b ) 277 , c ) 290 , d ) 662 , e ) 262 | a | subtract(subtract(390, divide(multiply(390, 14), const_100)), divide(multiply(subtract(390, divide(multiply(390, 14), const_100)), 15), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain | allenai/math_qa |
two vessels contains equal number of mixtures milk and water in the ratio 8 : 2 and 9 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ? | "the ratio of milk and water in the new vessel is = ( 8 / 10 + 9 / 10 ) : ( 2 / 10 + 1 / 10 ) = 17 / 10 : 3 / 10 = 17 : 3 answer is e" | a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 17 : 3 | e | divide(add(multiply(8, divide(add(9, 1), add(8, 2))), 9), add(multiply(2, divide(add(9, 1), add(8, 2))), 1)) | add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(n0,#2)|multiply(n1,#2)|add(n2,#3)|add(n3,#4)|divide(#5,#6)| | other | allenai/math_qa |
last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.6 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ? | "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.6 ( x ) + 0.5 ( 1 - x ) = 0.75 0.1 x = 0.75 - 0.5 x = 0.25 / 0.1 x = 1 / 4 therefore the answer is a : 1 / 4 ." | a ) 1 / 4 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16 | a | divide(subtract(0.75, 0.5), subtract(0.6, 0.5)) | subtract(n2,n0)|subtract(n1,n0)|divide(#0,#1)| | gain | allenai/math_qa |
on dividing 17698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ? | "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 17698 - 14 ) / 89 = 199 answer ( a )" | a ) 199 , b ) 154 , c ) 852 , d ) 741 , e ) 785 | a | divide(subtract(17698, 14), 89) | subtract(n0,n2)|divide(#0,n1)| | general | allenai/math_qa |
a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount q of paint , in gallons , that must be purchased in order to measure out the portions needed for the mixture ? | "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture q , so not acceptable . so correct ans is 2.5 gallons . b" | a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4 | b | add(multiply(const_0_25, 2), multiply(2, 5)) | multiply(const_0_25,n2)|multiply(n1,n2)|add(#0,#1)| | general | allenai/math_qa |
jerry travels 8 miles at an average speed of 40 miles per hour , stops for 15 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry β s average speed , in miles per hour , for this trip ? | total time taken by jerry = ( 8 / 40 ) * 60 minutes + 15 minutes + ( 20 / 60 ) * 60 minutes = 47 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 47 / 60 ) hours = 28 * 60 / 47 = 35 miles per hour answer : option a | a ) 35 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5 | a | divide(add(8, 20), add(add(divide(8, 40), divide(15, const_60)), divide(20, 60))) | add(n0,n3)|divide(n0,n1)|divide(n2,const_60)|divide(n3,n4)|add(#1,#2)|add(#4,#3)|divide(#0,#5) | physics | allenai/math_qa |
which no . need to add to 859622 to get a no . exactly divisible by 456 ? | dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 β 62 = 394 should be added to 859622 . e | a ) 546577 , b ) 674645 , c ) 566578 , d ) 465766 , e ) 859622 | e | subtract(859622, reminder(859622, 456)) | reminder(n0,n1)|subtract(n0,#0) | general | allenai/math_qa |
when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.90 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ? | "total no . of boxes = 3060000 / ( 20 Γ 20 Γ 15 ) = 510 total cost = 510 Γ $ 0.9 = $ 459 answer c" | a ) $ 255 , b ) $ 275 , c ) $ 459 , d ) $ 1,250 , e ) $ 2,550 | c | multiply(divide(multiply(3.06, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 15)), 0.90) | multiply(const_1000,const_1000)|multiply(n0,n0)|multiply(n4,#0)|multiply(n2,#1)|divide(#2,#3)|multiply(n3,#4)| | general | allenai/math_qa |
if 3 people a , b , c can do a work simultaneously in 6 days . a and b can do work in 10 days . b and c can do work in 15 days . c and a can do the same work in 20 days . in how many days that a can complete the same work alone ? | a + b + c = 1 / 6 ( one day work ) a + b = 1 / 10 ; b + c = 1 / 15 ; c + a + 1 / 20 b = 1 / 15 - c ; c = 1 / 20 - a ; - - - - - - - - - ( 2 ) substitute equation 2 in a + b = 1 / 10 a = 1 / 10 - b ; a = 1 / 10 - 1 / 15 + c ; a = 1 / 10 - 1 / 15 + 1 / 20 - a ; 2 a = 1 / 10 - 1 / 15 + 1 / 20 ; a = 1 / 24 ( one day work ) that is the no of days that a can work alone is 24 days the option d is answer | a ) 20 , b ) 25 , c ) 30 , d ) 24 , e ) 19 | d | divide(const_1, subtract(divide(add(add(divide(const_1, 10), divide(const_1, 15)), divide(const_1, 20)), const_2), divide(const_1, 15))) | divide(const_1,n2)|divide(const_1,n3)|divide(const_1,n4)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|subtract(#5,#1)|divide(const_1,#6) | physics | allenai/math_qa |
kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 2 / 7 and 5 / 9 , respectively , what is the probability that kyle and catherine , but not david will solve the problem ? | p ( kyle will solve ) = 1 / 3 p ( david will not solve ) = 1 - 2 / 7 = 5 / 7 p ( catherine will solve ) = 5 / 9 p = ( 1 / 3 ) * ( 5 / 7 ) * ( 5 / 9 ) = 25 / 189 answer : c | a ) 35 / 189 , b ) 33 / 129 , c ) 25 / 189 , d ) 24 / 113 , e ) 20 / 189 | c | divide(multiply(5, 5), add(multiply(const_60, const_3), multiply(const_3, const_3))) | multiply(n4,n4)|multiply(const_3,const_60)|multiply(const_3,const_3)|add(#1,#2)|divide(#0,#3) | general | allenai/math_qa |
a number whose fifth part increased by 3 is equal to its fourth part diminished by 3 is ? | "answer let the number be n . then , ( n / 5 ) + 3 = ( n / 4 ) - 3 Γ’ β‘ β ( n / 4 ) - ( n / 5 ) = 6 Γ’ β‘ β ( 5 n - 4 n ) / 20 = 6 Γ’ Λ Β΄ n = 120 option : a" | a ) 120 , b ) 180 , c ) 200 , d ) 220 , e ) none | a | divide(add(3, 3), subtract(divide(const_1, 3), divide(const_1, add(const_1, 3)))) | add(n0,n1)|add(const_1,n0)|divide(const_1,n0)|divide(const_1,#1)|subtract(#2,#3)|divide(#0,#4)| | general | allenai/math_qa |
there are 7 red shoes & 3 green shoes . if two of red shoes are drawn what is the probability of getting red shoes | "taking 2 red shoe the probablity is 7 c 2 from 10 shoes probablity of taking 2 red shoe is 7 c 2 / 10 c 2 = 7 / 15 answer : d" | a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 15 , d ) 7 / 15 , e ) 7 / 16 | d | divide(choose(7, const_2), choose(add(7, 3), const_2)) | add(n0,n1)|choose(n0,const_2)|choose(#0,const_2)|divide(#1,#2)| | probability | allenai/math_qa |
what is the number of integers from 1 to 900 ( inclusive ) that are divisible by neither 11 nor by 35 ? | "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 892 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? c" | a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945 | c | subtract(900, subtract(add(divide(900, 11), divide(900, 35)), divide(900, multiply(11, 35)))) | divide(n1,n2)|divide(n1,n3)|multiply(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,#4)|subtract(n1,#5)| | other | allenai/math_qa |
ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of ( a - b ) / 2 ? | "answer is 10 yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 ( a - b ) / 2 = 110 - 100 = 10 / 2 = 5 ans : d" | a ) 1 , b ) 10 , c ) 19 , d ) 5 , e ) 2 | d | subtract(multiply(divide(20, 2), add(divide(20, 2), 1)), multiply(divide(add(19, 1), 2), add(divide(subtract(19, 1), 2), 1))) | add(n2,n3)|divide(n1,n0)|subtract(n3,n2)|add(n2,#1)|divide(#2,n0)|divide(#0,n0)|add(n2,#4)|multiply(#3,#1)|multiply(#6,#5)|subtract(#7,#8)| | general | allenai/math_qa |
the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 149 , what is the difference between the ages of patrick and monica ? | "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 149 x = 4 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 4 = 64 answer b" | a ) 27 , b ) 64 , c ) 45 , d ) 72 , e ) 18 | b | subtract(multiply(multiply(5, 5), divide(149, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(149, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5))))) | multiply(n0,n0)|multiply(n1,n0)|multiply(n1,n3)|add(#0,#1)|add(#3,#2)|divide(n4,#4)|multiply(#5,#2)|multiply(#5,#0)|subtract(#6,#7)| | general | allenai/math_qa |
nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ? | "b its is . let price = x ( x - 1 ) 8 = 6 x x = 4 hence total money = 6 * 4 = 24" | a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40 | b | multiply(divide(multiply(1, 8), subtract(8, 6)), 6) | multiply(n1,n2)|subtract(n2,n0)|divide(#0,#1)|multiply(n0,#2)| | general | allenai/math_qa |
there are 6 people in the elevator . their average weight is 160 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person . | "solution average of 7 people after the last one enters = 151 . Γ’ Λ Β΄ required weight = ( 7 x 151 ) - ( 6 x 160 ) = 1057 - 960 = 97 . answer a" | a ) 97 , b ) 168 , c ) 189 , d ) 190 , e ) 200 | a | subtract(multiply(151, 7), multiply(6, 160)) | multiply(n2,n3)|multiply(n0,n1)|subtract(#0,#1)| | general | allenai/math_qa |
a rectangular grass field is 75 m * 40 m , it has a path of 2.5 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 + 40 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : c | ['a ) s . 1350', 'b ) s . 1327', 'c ) s . 1200', 'd ) s . 1397', 'e ) s . 1927'] | c | multiply(subtract(rectangle_area(add(75, multiply(2.5, const_2)), add(40, multiply(2.5, const_2))), rectangle_area(75, 40)), 2) | multiply(n2,const_2)|rectangle_area(n0,n1)|add(n0,#0)|add(n1,#0)|rectangle_area(#2,#3)|subtract(#4,#1)|multiply(n3,#5) | geometry | allenai/math_qa |
if radius of a circle is diminished by 10 % then its area is diminished by | explanation : let old radius = 10 units . new radius is diminshed by 10 % . so new radius = 90 % ( 10 ) = 9 units . old area = Ο Γ r 2 = 100 Ο new area = Ο Γ 92 = 81 Ο change = 19 Ο / 100 Ο Γ 100 = 19 % answer : b | ['a ) 22', 'b ) 19', 'c ) 877', 'd ) 26', 'e ) 271'] | b | multiply(divide(subtract(circle_area(const_1), circle_area(subtract(const_1, divide(10, const_100)))), circle_area(const_1)), const_100) | circle_area(const_1)|divide(n0,const_100)|subtract(const_1,#1)|circle_area(#2)|subtract(#0,#3)|divide(#4,#0)|multiply(#5,const_100) | geometry | allenai/math_qa |
the average weight of 5 person ' s increases by 4 kg when a new person comes in place of one of them weighing 50 kg . what is the weight of the new person ? | "total increase in weight = 5 Γ 4 = 20 if x is the weight of the new person , total increase in weight = x β 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : a" | a ) 70 , b ) 86.5 , c ) 80 , d ) 88.5 , e ) 75 | a | add(multiply(5, 4), 50) | multiply(n0,n1)|add(n2,#0)| | general | allenai/math_qa |
i chose a number and divide it by 6 . then i subtracted 15 from the result and got 5 . what was the number i chose ? | "solution : let xx be the number i chose , then x / 6 Γ’ Λ β 15 = 5 x / 6 = 20 x = 120 answer c" | a ) 600 , b ) 700 , c ) 120 , d ) 900 , e ) none | c | multiply(add(15, 5), 6) | add(n1,n2)|multiply(n0,#0)| | general | allenai/math_qa |
a family pays $ 850 per year for an insurance plan that pays 80 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 = 850 $ family needs to pay 20 % of first 1000 $ in expense = 200 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 850 + 200 = 1050 $ total amount paid by insurance plan for first 1000 $ = 850 $ total amount paid by family will equal amount paid by plan when medical expense = 1250 $ ( since insurance plan will pay 100 % of amount that exceeds 1050 $ ) answer b" | a ) $ 1,000 , b ) $ 1,250 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200 | b | subtract(1,000, 850) | subtract(n2,n0)| | general | allenai/math_qa |
what is x if x + 3 y = 10 and y = 3 ? | "substitute y by 3 in x + 3 y = 10 x + 3 ( 3 ) = 10 x + 9 = 10 if we substitute x by 1 in x + 9 = 10 , we have 1 + 9 = 10 . hence x = 1 correct answer a" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | a | subtract(10, multiply(3, 3)) | multiply(n0,n2)|subtract(n1,#0)| | general | allenai/math_qa |
a man is 40 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is | "explanation : let ' s son age is x , then father age is x + 40 . = > 2 ( x + 6 ) = ( x + 40 + 6 ) = > 2 x + 12 = x + 46 = > x = 34 years answer : option d" | a ) 31 years , b ) 32 years , c ) 33 years , d ) 34 years , e ) 35 years | d | divide(subtract(40, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general | allenai/math_qa |
julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 112 and $ 120 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ? | $ 112 for 2 years = $ 56 per year . extra $ 8 yearned with the compound interest is the percent yearned on percent . so , $ 8 is yearned on $ 56 , which means that the interest = 7 % . this on the other hand means that half of the savings = 56 * 7 = $ 392 . twice of that = $ 784 . answer : b . | a ) 600 , b ) 784 , c ) 1080 , d ) 1200 , e ) 1440 | b | divide(112, divide(multiply(const_2, subtract(120, 112)), 112)) | subtract(n1,n0)|multiply(#0,const_2)|divide(#1,n0)|divide(n0,#2) | gain | allenai/math_qa |
sachin is younger than rahul by 7 years . if the ratio of their ages is 6 : 9 , find the age of sachin | "explanation : if rahul age is x , then sachin age is x - 7 , so , 9 x - 63 = 6 x 3 x = 63 x = 21 so sachin age is 21 - 7 = 14 answer : b ) 14" | a ) 24.5 , b ) 14 , c ) 24.21 , d ) 27 , e ) 25 | b | multiply(divide(7, subtract(9, 6)), 6) | subtract(n2,n1)|divide(n0,#0)|multiply(n1,#1)| | other | allenai/math_qa |
find the number of divisors of 1728 . ? | "1728 = 2 ^ 6 * 3 ^ 3 hence the number of factors = ( 6 + 1 ) x ( 3 + 1 ) = 7 x 4 = 28 . we know that if a number represented in standard form ( a ^ m * b ^ n ) , then the number of factors is given by ( m + 1 ) ( n + 1 ) . answer is 28 answer : c" | a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30 | c | add(const_2, const_2) | add(const_2,const_2)| | general | allenai/math_qa |
if the sides of a triangle are 26 cm , 25 cm and 10 cm , what is its area ? | "the triangle with sides 26 cm , 25 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 25 * 10 = 125 cm 2 answer : option e" | a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 125 | e | divide(multiply(25, 10), const_2) | multiply(n1,n2)|divide(#0,const_2)| | geometry | allenai/math_qa |
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