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a car going at 30 miles per hour set out on an 80 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ? | let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 30 m per hour = 1.5 hours distance travelled by car a = 30 * 1.5 = 45 miles since car b catches up car a at 10 : 30 , time = 80 mins = 4 / 3 hour speed of car b = 45 / ( 4 / 3 ) = 60 miles per hour answer e | a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 60 | e | divide(80, divide(add(multiply(subtract(10, 9), const_60), subtract(30, 10)), const_60)) | subtract(n4,n2)|subtract(n0,n4)|multiply(#0,const_60)|add(#2,#1)|divide(#3,const_60)|divide(n1,#4) | physics | allenai/math_qa |
the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio o | "4 : 5 3 : 2 - - - - - - - 12 : 15 : 10 12 : 10 = = > 6.5 answer a" | a ) 6 : 5 , b ) 4 : 7 , c ) 3 : 5 , d ) 5 : 7 , e ) 8 : 9 | a | divide(multiply(4, 3), multiply(5, 2)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)| | other | allenai/math_qa |
what percentage of numbers from 1 to 60 have 1 or 9 in the unit ' s digit ? | "clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 60 are 1 , 9 , 11 , 19 , 21 , 29 , 31 , 39 , 41 , 49 , 51 , 59 number of such number = 11 answer : c" | a ) 12 , b ) 14.11 , c ) 18.33 , d ) 20 , e ) 21 | c | multiply(divide(multiply(const_2, divide(60, const_10)), 60), const_100) | divide(n1,const_10)|multiply(#0,const_2)|divide(#1,n1)|multiply(#2,const_100)| | gain | allenai/math_qa |
a car traveled 75 % of the way from town a to town b at an average speed of 90 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ? | "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 90 = 0.833 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 0.833 + t » 100 / 40 = 0.833 + t » 2.5 = 0.833 + t » t = 1.667 back to 2 nd part of the trip formula : 25 / s = 1.667 » s = 15 ans a" | a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5 | a | divide(subtract(add(40, 90), 75), subtract(divide(add(40, 90), 40), divide(75, 90))) | add(n1,n2)|divide(n0,n1)|divide(#0,n2)|subtract(#0,n0)|subtract(#2,#1)|divide(#3,#4)| | physics | allenai/math_qa |
david completes a piece of work in 5 days , john completes the same work in 9 days . if both of them work together , then the number of days required to complete the work is ? | ifa can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 5 × 9 / 14 = 3.2 days answer : a | a ) 3.2 days , b ) 8 days , c ) 10 days , d ) 12 days , e ) 14 days | a | inverse(add(inverse(9), inverse(5))) | inverse(n1)|inverse(n0)|add(#0,#1)|inverse(#2) | physics | allenai/math_qa |
the tax on a commodity is diminished by 24 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ? | "100 * 100 = 10000 76 * 112 = 8512 10000 - - - - - - - 1488 100 - - - - - - - ? = 15 % answer : c" | a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 % | c | subtract(const_100, divide(multiply(add(const_100, 12), subtract(const_100, 24)), 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 |
the smallest 5 digit number exactly divisible by 41 is ? | "the smallest 5 - digit number = 10000 . 41 ) 10000 ( 243 82 - - - 180 164 - - - - 160 123 - - - 37 - - - required number = 10000 + ( 41 - 37 ) = 10004 . option b" | a ) 10003 , b ) 10004 , c ) 10007 , d ) 10009 , e ) 10010 | b | add(multiply(const_1000, const_100), subtract(41, reminder(multiply(const_1000, const_100), 41))) | multiply(const_100,const_1000)|reminder(#0,n1)|subtract(n1,#1)|add(#0,#2)| | general | allenai/math_qa |
what is the largest 4 digit number exactly divisible by 50 ? | "largest 4 digit number = 9999 9999 ÷ 50 = 199 , remainder = 49 hence largest 4 digit number exactly divisible by 50 = 9999 - 49 = 9950 answer : c" | a ) 4676 , b ) 4678 , c ) 9950 , d ) 9504 , e ) 9936 | c | multiply(floor(divide(power(const_10, 4), 50)), 50) | power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)| | general | allenai/math_qa |
when sold at a 40 % discount , a sweater nets the merchant a 20 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ? | "et the marked up price = 100 . . selling price = 100 - 40 % of 100 = 60 . . profit = 20 % . . therefore the wholesale purchase cost = x . . . . 1.2 x = 60 or x = 50 . . . marked price was 100 so 50 over 50 . . . so answer is 100 % . . answer : e" | a ) 20 % , b ) 40 % , c ) 50 % , d ) 80 % , e ) 100 % | e | subtract(const_100, divide(subtract(const_100, 40), add(const_1, divide(20, const_100)))) | divide(n1,const_100)|subtract(const_100,n0)|add(#0,const_1)|divide(#1,#2)|subtract(const_100,#3)| | gain | allenai/math_qa |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 12 , the how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 12 5 x = 10 x = 2 . hence , b ' s age = 2 x = 4 years . b )" | a ) 10 years , b ) 4 years , c ) 6 years , d ) 15 years , e ) 16 years | b | divide(multiply(subtract(12, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general | allenai/math_qa |
a boy is travelling from his home to school at 5 km / hr and reached 5 min late . next day he travelled at 10 km / hr and reached 10 min early . distance between home and school ? | "let the distance be x t 1 = x / 5 hr t 2 = x / 10 hr difference in time = 5 + 10 = 15 = 1 / 4 hr x / 5 - x / 10 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer is a" | a ) 2.5 km , b ) 3 km , c ) 4 km , d ) 5.6 km , e ) 6.5 km | a | divide(add(divide(5, const_60), divide(10, const_60)), divide(const_1, 10)) | divide(n1,const_60)|divide(n3,const_60)|divide(const_1,n2)|add(#0,#1)|divide(#3,#2)| | physics | allenai/math_qa |
a certain store sells all maps at one price and all books at another price . on monday the store sold 12 maps and 10 books for a total of $ 38.00 , and on tuesday the store sold 12 maps and 9 books for a total of $ 30.00 . at this store , how much less does a map sell for than a book ? | "12 x + 10 y = 38 12 x + 9 y = 30 subtracting 1 from 2 y = 8 therefore x = 3.5 difference in price = 4.5 e" | a ) $ 0.25 , b ) $ 0.50 , c ) $ 0.75 , d ) $ 1.00 , e ) $ 4.5 | e | divide(subtract(30.00, negate(multiply(9, divide(subtract(multiply(38.00, const_4), multiply(30.00, const_2)), subtract(multiply(10, const_4), multiply(9, const_2)))))), 12) | multiply(n2,const_4)|multiply(n5,const_2)|multiply(n1,const_4)|multiply(n4,const_2)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)|multiply(n4,#6)|negate(#7)|subtract(n5,#8)|divide(#9,n3)| | general | allenai/math_qa |
a larger cube has 125 cubic inch as a volume and in the cube there are 125 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 125 smaller cubes and the surface area of the larger cube , in square inch ? | "volume of larger cube = 125 = 5 ^ 3 side of larger cube = 5 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 5 ^ 2 = 150 surface area of 27 smaller cubes = 125 * 6 * 1 = 750 difference = 750 - 150 = 600 answer : b" | a ) 54 , b ) 600 , c ) 81 , d ) 108 , e ) 120 | b | subtract(multiply(surface_cube(cube_edge_by_volume(1)), 125), surface_cube(cube_edge_by_volume(125))) | cube_edge_by_volume(n2)|cube_edge_by_volume(n0)|surface_cube(#0)|surface_cube(#1)|multiply(n0,#2)|subtract(#4,#3)| | geometry | allenai/math_qa |
a man walks at a rate of 10 mph . after every ten miles , he rests for 5 minutes . how much time does he take to walk 50 miles ? | to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 5 = 20 minutes . total time = 300 + 20 = 320 minutes . answer : c . | a ) 300 , b ) 318 , c ) 320 , d ) 324 , e ) 330 | c | add(multiply(5, const_4), multiply(divide(50, 10), const_60)) | divide(n2,n0)|multiply(n1,const_4)|multiply(#0,const_60)|add(#1,#2) | physics | allenai/math_qa |
find the greatest number which on dividing 1428 and 2206 , leaves a reminder of 9 and 13 respectively | "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1428 - 9 ) and ( 2206 - 13 ) = hcf ( 1419 , 2193 ) = 129 option c" | a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 141 | c | gcd(subtract(1428, 9), subtract(2206, 13)) | subtract(n0,n2)|subtract(n1,n3)|gcd(#0,#1)| | general | allenai/math_qa |
in an it company , there are a total of 100 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ? | "you could pick 50 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 55 . c" | a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 65 | c | add(subtract(80, 100), subtract(50, 35)) | subtract(n2,n0)|subtract(n1,n3)|add(#0,#1)| | general | allenai/math_qa |
find the average marks of all the students in 2 separate classes , if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 | sum of the marks for the class of 55 students = 55 * 60 = 3300 sum of the marks for the class of 48 students = 48 * 58 = 2784 sum of the marks for the class of 103 students = 3300 + 2784 = 6084 average marks of all the students = 6084 / 103 = 59.1 answer : e | a ) 55.1 , b ) 51.1 , c ) 53.1 , d ) 52.1 , e ) 59.1 | e | divide(add(multiply(55, 60), multiply(48, 58)), add(55, 48)) | add(n1,n3)|multiply(n1,n2)|multiply(n3,n4)|add(#1,#2)|divide(#3,#0) | general | allenai/math_qa |
a rectangular box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ? | total area of cross roads = 60 x + 40 x − x 2 but total area of the cross roads = 291 m 2 hence , 60 x + 40 x − x 2 = 291 ⇒ 100 x − x 2 = 291 ⇒ x 2 − 100 x + 291 = 0 ⇒ ( x − 97 ) ( x − 3 ) = 0 ⇒ x = 3 answer : a | ['a ) 3 m', 'b ) 4 m', 'c ) 5 m', 'd ) 6 m', 'e ) 2 m'] | a | divide(subtract(const_100, sqrt(subtract(power(const_100, const_2), multiply(subtract(multiply(60, 40), 2109), const_4)))), const_2) | multiply(n0,n1)|power(const_100,const_2)|subtract(#0,n2)|multiply(#2,const_4)|subtract(#1,#3)|sqrt(#4)|subtract(const_100,#5)|divide(#6,const_2) | geometry | allenai/math_qa |
a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds . what is the length of the train in meters ? | train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d is the answer . | a ) 400 meters , b ) 1111 meters , c ) 160 meters , d ) 850 meters , e ) none of these | d | multiply(multiply(subtract(100, 64), const_0_2778), 85) | subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1) | physics | allenai/math_qa |
if it takes a machine 1 ⁄ 3 minute to produce one item , how many items will it produce in 2 hours ? | "1 item takes 1 / 3 min so it takes 120 min to produce x x / 3 = 120 the x = 360 answer : e" | a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 80 , d ) 120 , e ) 360 | e | divide(multiply(2, const_60), divide(1, 3)) | divide(n0,n1)|multiply(n2,const_60)|divide(#1,#0)| | physics | allenai/math_qa |
youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 6 minutes more to walk to work than to ride his bike to work , then x equals ? | "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 360 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 360 - - - - > 40 x = 360 - - > x = 9 . option c" | a ) 4 , b ) 7 , c ) 9 , d ) 15 , e ) 20 | c | divide(multiply(6, const_3), const_2) | multiply(n2,const_3)|divide(#0,const_2)| | physics | allenai/math_qa |
find the surface area of a 10 cm * 4 cm * 3 cm brick . | explanation : surface area of a cuboid = 2 ( lb + bh + hl ) cm square so , surface area of a brick = 2 ( 10 * 4 + 4 * 3 + 3 * 10 ) cm square = 2 ( 82 ) cm square = 164 cm square option d | ['a ) 154 cm square', 'b ) 156 cm square', 'c ) 160 cm square', 'd ) 164 cm square', 'e ) none of these'] | d | surface_rectangular_prism(3, 4, 10) | surface_rectangular_prism(n0,n1,n2) | geometry | allenai/math_qa |
in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many f cents does a liter of kerosene cost ? [ one dollar has 100 cents . ] | "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer f = 44 . d" | a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55 | d | multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.33, 100)) | divide(const_1,const_2)|multiply(n1,n2)|divide(n0,#0)|divide(#2,const_12)|multiply(#3,#1)| | general | allenai/math_qa |
company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . the two companies merge , every employee stays with the resulting company , and no new employees are added . if the resulting company í s workforce consists of 25 percent managers , what percent of the workforce originated from company a ? | let say company a has x employes and b has y employees . now they merge and total no of employees = x + y employees . per the question company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . we translate it into equation as follows : . 1 x + . 3 y = . 25 ( x + y ) = > x + 3 y = 2.5 ( x + y ) = > . 5 y = 1.5 x = > y = 3 x . now we know total employee = x + y . we need to find % age of x in total ( x + y ) ie x / ( x + y ) x 100 % = > x / ( 3 x + x ) [ substitute y = 3 x ] = > x / 4 x x 100 % = > . 25 x 100 % = > 25 % . answer : c | a ) 10 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 75 % | c | subtract(subtract(add(divide(multiply(divide(60, 30), 25), 10), 90), 60), 10) | divide(n4,n2)|multiply(n5,#0)|divide(#1,n0)|add(n1,#2)|subtract(#3,n4)|subtract(#4,n0) | general | allenai/math_qa |
if 1 = 3 2 = 6 3 = 9 4 = 12 5 = 15 then 9 = ? hint : its a logic riddle not a mathematical riddle | c 3 as stated 3 = 9 = > 9 = 3 answer is c | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | subtract(subtract(divide(multiply(add(3, 3), 9), 15), const_0_33), const_0_33) | add(n1,n1)|multiply(n5,#0)|divide(#1,n9)|subtract(#2,const_0_33)|subtract(#3,const_0_33) | other | allenai/math_qa |
what is the least number which should be added to 2697 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ? | "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2697 by 60 , the remainder is 57 . the number to be added = 60 - 57 = 3 . the answer is a ." | a ) 3 , b ) 11 , c ) 19 , d ) 27 , e ) 35 | a | add(3, add(4, add(6, add(5, multiply(5, const_2))))) | multiply(n1,const_2)|add(n1,#0)|add(n2,#1)|add(n3,#2)|add(n4,#3)| | general | allenai/math_qa |
the average of first 20 even numbers is ? | "sum of 20 even numbers = 20 * 21 = 420 average = 420 / 20 = 21 answer : e" | a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 21 | e | add(20, const_1) | add(n0,const_1)| | general | allenai/math_qa |
rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 83 . how much was lent at 5 % ? | "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 83 5 x / 100 + 90 – 6 x / 100 = 83 x / 100 = 7 = > x = 700 answer : d" | a ) 299 , b ) 566 , c ) 678 , d ) 700 , e ) 8277 | d | multiply(add(5, 6), const_100) | add(n1,n2)|multiply(#0,const_100)| | gain | allenai/math_qa |
find the area of trapezium whose parallel sides are 20 cm and 10 cm long , and the distance between them is 10 cm . | "explanation : area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 10 ) * ( 10 ) = 150 cm 2 answer : option c" | a ) 187 cm 2 , b ) 185 cm 2 , c ) 150 cm 2 , d ) 185 cm 2 , e ) 195 cm 2 | c | quadrilateral_area(10, 10, 20) | quadrilateral_area(n2,n1,n0)| | physics | allenai/math_qa |
the contents of two vessels containing copper and tin in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4 . the resulting mixture will have copper and tin in the ratio ? | "the ratio of copper and tin the new vessel = ( 1 / 3 * 1 / 5 + 2 / 7 * 4 / 5 ) : ( 2 / 3 * 1 / 5 + 5 / 7 * 4 / 5 ) = 31 / 105 : 74 / 105 = 31 : 74 answer is c" | a ) 15 : 32 , b ) 21 : 28 , c ) 31 : 74 , d ) 33 : 37 , e ) 41 : 92 | c | divide(add(multiply(1, 2), multiply(2, 2)), add(multiply(2, 2), multiply(5, 2))) | multiply(n0,n1)|multiply(n2,n2)|multiply(n1,n1)|multiply(n2,n3)|add(#0,#1)|add(#2,#3)|divide(#4,#5)| | other | allenai/math_qa |
a bag making machine can make 20 bags per hour . if the company adjusts the machine to produce twice the amount per hour to satisfy expected rise in demand . how many bags can the machine make in the next 5 days if it works 10 hours a day ? | 20 * 2 = 40 bags per hour . 5 days * 10 hours * 40 bags per hour = 2,000 bags . answer is option a . | a ) 2,000 , b ) 1,000 , c ) 400 , d ) 50 , e ) 1,500 | a | divide(20, 10) | divide(n0,n2) | physics | allenai/math_qa |
if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to decreased by 10 percent , how much would she earn per week ? | "soln : - ( 406 / 116 ) 90 = 315 in this case long division does not take much time . ( 406 / 116 ) = 3.5 3.5 * 90 = rs . 315 answer : d" | a ) rs . 415 , b ) rs . 325 , c ) rs . 352 , d ) rs . 315 , e ) rs . 425 | d | add(divide(406, add(const_1, divide(16, const_100))), multiply(divide(10, const_100), divide(406, add(const_1, divide(16, const_100))))) | divide(n0,const_100)|divide(n2,const_100)|add(#0,const_1)|divide(n1,#2)|multiply(#1,#3)|add(#3,#4)| | general | allenai/math_qa |
when m divided by 288 , the remainder is 47 . find the remainder when the same m is divided by 24 ? | 23 option d | a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 26 | d | reminder(47, 24) | reminder(n1,n2) | physics | allenai/math_qa |
8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 5 such machines to perform the same job ? | "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 5 machines 5 units of work ( 5 machines ) - - - > 1 hour for 48 units of work 5 * 9.6 - - - > 1 * 9.6 hours e 9.6 hours" | a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 9.6 hours | e | divide(multiply(6, 8), 5) | multiply(n0,n1)|divide(#0,n2)| | physics | allenai/math_qa |
if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ? | "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 18 years investment will become $ 8,000 * 2 = $ 16,000 and in another 18 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c ." | a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000 | c | multiply(multiply(8000, const_2), const_2) | multiply(n1,const_2)|multiply(#0,const_2)| | general | allenai/math_qa |
kamal was 4 times as old as his son 8 years ago . after 8 years , kamal will be twice as old as his son . find out the present age of kamal . | let age of the son before 8 years = x then , age of kamal before 8 years ago = 4 x after 8 years , kamal will be twice as old as his son ⇒ 4 x + 16 = 2 ( x + 16 ) ⇒ x = 8 present age of kamal = 4 x + 8 = 4 × 8 + 8 = 40 answer is c . | a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50 | c | add(multiply(divide(multiply(4, 4), const_2), const_4), 8) | multiply(n0,n0)|divide(#0,const_2)|multiply(#1,const_4)|add(n1,#2) | general | allenai/math_qa |
4 - fifths of 3 - eighths of a number is 24 . what is 250 per cent of that number ? | let the number = x . 4 ⁄ 5 × 3 ⁄ 8 x = 24 or x = 24 × 2 × 5 / 3 = 80 ∴ 250 per cent of the number = 250 ⁄ 100 × 80 = 200 answer d | a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) none of these | d | multiply(divide(24, multiply(divide(4, add(const_1, const_4)), divide(3, add(const_4, const_4)))), divide(250, const_100)) | add(const_1,const_4)|add(const_4,const_4)|divide(n3,const_100)|divide(n0,#0)|divide(n1,#1)|multiply(#3,#4)|divide(n2,#5)|multiply(#6,#2) | general | allenai/math_qa |
when asked what the time is , a person answered that the amount of time left is 1 / 2 of the time already completed . what is the time . | "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 1 / 2 x ⇒ x = 16 time is 4 pm answer : d" | a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 4 pm , e ) 6 pm | d | subtract(multiply(1, const_12), divide(multiply(1, const_12), add(divide(1, 2), const_1))) | divide(n0,n1)|multiply(const_12,n0)|add(#0,const_1)|divide(#1,#2)|subtract(#1,#3)| | general | allenai/math_qa |
if the cost price of 15 articles is same as the selling price of 25 articles . find the gain or loss percentage ? | "explanation : 15 cp = 25 sp cost price cp = 25 selling price sp = 15 formula = ( sp - cp ) / cp * 100 = ( 15 - 25 ) / 25 * 100 = 40 % loss answer : option d" | a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 40 % loss , e ) 50 % loss | d | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 25), 15)), divide(multiply(const_100, 25), 15))) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)|divide(#2,#1)|multiply(#3,const_100)| | gain | allenai/math_qa |
the cost price of a radio is rs . 1390 and it was sold for rs . 890 , find the loss % ? | "1390 - - - - 500 100 - - - - ? = > 35 % answer : d" | a ) 18 % , b ) 12 % , c ) 22 % , d ) 35 % , e ) 21 % | d | multiply(divide(subtract(1390, 890), 1390), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain | allenai/math_qa |
a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ? | "the ratio of economy to luxury cars is 5 : 2 - - > e : l = 5 : 2 = 20 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 8 : 15 . answer : b ." | a ) 9 : 8 , b ) 8 : 15 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2 | b | divide(divide(multiply(const_4, 3), multiply(3, 3)), divide(multiply(3, const_4), multiply(2, const_4))) | multiply(n3,const_4)|multiply(n3,n3)|multiply(n1,const_4)|divide(#0,#1)|divide(#0,#2)|divide(#3,#4)| | other | allenai/math_qa |
if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ? | "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 9 years investment will become $ 8,000 * 2 = $ 16,000 and in another 9 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c ." | a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000 | c | multiply(multiply(8000, const_2), const_2) | multiply(n1,const_2)|multiply(#0,const_2)| | general | allenai/math_qa |
the average salary of all the workers in a workshop is $ 1000 . the average salary of 5 technicians is $ 5000 and the average salary of the rest is $ 500 . the total number of workers in the shop is ? | "let the total number of workers be x 1000 x = 5000 * 5 + 500 ( x - 5 ) x = 25 answer is a" | a ) 25 , b ) 20 , c ) 15 , d ) 30 , e ) 18 | a | divide(subtract(multiply(5, 5000), multiply(500, 5)), subtract(1000, 500)) | multiply(n1,n2)|multiply(n1,n3)|subtract(n0,n3)|subtract(#0,#1)|divide(#3,#2)| | general | allenai/math_qa |
how many of the positive factors of 14 are not factors of 21 ? | "factors of 14 - 1 , 2 , 7 , 14 , factors of 21 - 1 , 3 , 7 , 21 , comparing both , we have three factors of 14 which are not factors of 21 - 2,14 the answer is c" | a ) 4 , b ) 3 , c ) 1 , d ) 2 , e ) 0 | c | divide(21, 14) | divide(n1,n0)| | other | allenai/math_qa |
the present worth of $ 3600 due in 2 years at 20 % per annum compound interest is ? | present worth = 3600 / ( 1 + 20 / 100 ) ^ 2 = 3600 * 5 / 6 * 5 / 6 = $ 2500 answer is e | a ) $ 1200 , b ) $ 1850 , c ) $ 2010 , d ) $ 3200 , e ) $ 2500 | e | divide(3600, power(add(divide(20, const_100), const_1), 2)) | divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|divide(n0,#2) | gain | allenai/math_qa |
find 80 / ? = ? / 20 | "answer let 80 / y = y / 20 then , y 2 = 80 x 20 = 1600 ∴ y = √ 1600 = 40 . option : a" | a ) 40 , b ) 400 , c ) 800 , d ) 1600 , e ) none | a | divide(80, 20) | divide(n0,n1)| | general | allenai/math_qa |
the average monthly income of a and b is rs . 5050 . the average monthly income of b and c is rs . 6250 and the average monthly income of a and c is rs . 5200 . what is the monthly income of a ? | "explanation : let monthly income of a = a monthly income of b = b monthly income of c = c a + b = 2 × 5050 . . . . ( equation 1 ) b + c = 2 × 6250 . . . . ( equation 2 ) a + c = 2 × 5200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > a + b + a + c - ( b + c ) = ( 2 × 5050 ) + ( 2 × 5200 ) - ( 2 × 6250 ) = > 2 a = 2 ( 5050 + 5200 - 6250 ) = > a = 4000 i . e . , monthly income of a = 4000 answer is c" | a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6200 | c | subtract(multiply(const_2, 5050), divide(add(multiply(const_2, 5050), subtract(multiply(const_2, 6250), multiply(const_2, 5200))), const_2)) | multiply(n0,const_2)|multiply(n1,const_2)|multiply(n2,const_2)|subtract(#1,#2)|add(#0,#3)|divide(#4,const_2)|subtract(#0,#5)| | general | allenai/math_qa |
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is | "solution let the toatl number of workers be x . then 8000 x = ( 10000 x 7 ) + 6000 ( x - 7 ) x = 14 . answer e" | a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 14 | e | add(7, divide(multiply(7, subtract(10000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | general | allenai/math_qa |
a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 56 then find the correct average marks up to two decimal places . | "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 56 = 2530 correct average = 2530 / 35 = 72.28 answer : b" | a ) 73.41 , b ) 72.28 , c ) 72.43 , d ) 73.43 , e ) can not be determined | b | divide(subtract(multiply(35, 72), subtract(56, 46)), 35) | multiply(n0,n2)|subtract(n4,n3)|subtract(#0,#1)|divide(#2,n0)| | general | allenai/math_qa |
a person want to give his money of $ 5400 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ? | "b ' s share = 5400 * 3 / 9 = $ 1800 answer is b" | a ) $ 2000 , b ) $ 1800 , c ) $ 2500 , d ) $ 1500 , e ) $ 1600 | b | multiply(divide(3, add(add(2, 3), 4)), 5400) | add(n1,n2)|add(n4,#0)|divide(n1,#1)|multiply(n0,#2)| | other | allenai/math_qa |
if the sum of a number and its square is 306 , what is the number ? | "explanation : let the integer be x . then , x + x 2 = 306 x 2 + x - 306 = 0 ( x + 18 ) ( x – 17 ) = 0 x = 17 answer : d" | a ) 16 , b ) 77 , c ) 25 , d ) 17 , e ) 171 | d | floor(sqrt(306)) | sqrt(n0)|floor(#0)| | geometry | allenai/math_qa |
the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is ? | "let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m ^ 2 = 153600 m ^ 2 . answer : a" | a ) 153600 , b ) 153629 , c ) 151299 , d ) 153129 , e ) 152109 | a | rectangle_area(divide(divide(multiply(multiply(divide(12, multiply(const_10, multiply(const_3, const_2))), 8), const_1000), add(3, 2)), const_2), multiply(divide(divide(multiply(multiply(divide(12, multiply(const_10, multiply(const_3, const_2))), 8), const_1000), add(3, 2)), const_2), 2)) | add(n0,n1)|multiply(const_2,const_3)|multiply(#1,const_10)|divide(n2,#2)|multiply(n3,#3)|multiply(#4,const_1000)|divide(#5,#0)|divide(#6,const_2)|multiply(n1,#7)|rectangle_area(#7,#8)| | physics | allenai/math_qa |
a number x is 18 times another number y . the percentage that y is less than x is | "say y = 1 and x = 18 . then y = 1 is less than x = 18 by ( 18 - 1 ) / 18 * 100 = 17 / 18 * 100 = 94.4 % . answer : d ." | a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 94.4 % , e ) 1 % | d | multiply(divide(subtract(18, const_1), 18), const_100) | subtract(n0,const_1)|divide(#0,n0)|multiply(#1,const_100)| | general | allenai/math_qa |
the number 90 can be written as the sum of the squares of 4 different positive integers . what is the sum of these 4 integers ? | "4 ^ 2 + 3 ^ 2 + 8 ^ 2 + 1 ^ 2 = 90 - - > 1 + 3 + 8 + 4 = 16 . b" | a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13 | b | add(add(add(const_4, const_3), add(const_3, const_2)), 4) | add(const_3,const_4)|add(const_2,const_3)|add(#0,#1)|add(n1,#2)| | geometry | allenai/math_qa |
find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively . | "required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 _______ 1651 ) 2032 ( 1 1651 1651 _______ 381 ) 1651 ( 4 1524 _________ 127 ) 381 ( 3 381 0 required number = 127 . answer is c ." | a ) 121 , b ) 124 , c ) 127 , d ) 122 , e ) 129 | c | gcd(subtract(1657, 6), subtract(2037, 5)) | subtract(n0,n2)|subtract(n1,n3)|gcd(#0,#1)| | general | allenai/math_qa |
78654 * 9999 | "explanation : 78654 * ( 10000 - 1 ) = 786540000 - 78654 = 786461346 option d" | a ) 784598562 , b ) 765858254 , c ) 784569825 , d ) 786461346 , e ) none of these | d | multiply(divide(78654, 9999), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general | allenai/math_qa |
what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 10 ? | "9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 the answer is d . 20" | a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30 | d | multiply(subtract(9, 10), 10) | subtract(n1,n2)|multiply(n2,#0)| | general | allenai/math_qa |
four numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number . | answer : a | a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112 | a | add(multiply(multiply(2, 4), const_100), multiply(3, 4)) | multiply(n0,n2)|multiply(n1,n2)|multiply(#0,const_100)|add(#2,#1)| | general | allenai/math_qa |
if one root of the equation 2 x ^ 2 + 3 x – k = 0 is 7 , what is the value of k ? | we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 7 ^ 2 + 3 * 7 - k = 0 k = 98 + 21 = 119 the answer is c | a ) 100 , b ) 110 , c ) 119 , d ) 120 , e ) 112 | c | add(multiply(2, power(7, const_2)), multiply(3, 7)) | multiply(n2,n4)|power(n4,const_2)|multiply(n0,#1)|add(#2,#0) | general | allenai/math_qa |
the speed at which a man can row a boat in still water is 26 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 150 metres ? | speed of the boat downstream = 26 + 4 = 30 kmph = 30 * 5 / 18 = 8.33 m / s hence time taken to cover 150 m = 150 / 8.33 = 18 seconds . answer : a | a ) 18 , b ) 27 , c ) 28 , d ) 12 , e ) 25 | a | divide(150, multiply(add(26, 4), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)| | physics | allenai/math_qa |
the revenue from sales items in 1996 increases by x percent , compared in 1995 and the revenue in 1997 decreases by x percent , compared in 1996 . if the revenue from sales items in 1997 decreases by 4 percent , compared in 1995 , what is the value of x ? | 1995 - let the value be z 1996 - x % increase - z ( 1 + x / 100 ) 1997 - x % decrease - z ( 1 + x / 100 ) ( 1 - x / 100 ) from 95 to 97 decrease is 4 % hence , [ z - { z ( 1 + x / 100 ) ( 1 - x / 100 ) } ] / z = 4 / 100 solving x = 20 % c is the answer | a ) 10 , b ) 15 , c ) 20 , d ) 30 , e ) 35 | c | sqrt(multiply(4, const_100)) | multiply(n5,const_100)|sqrt(#0) | general | allenai/math_qa |
the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 4 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ? | "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 4 th year = 50 , 5 th year = 50 - 4 = 46 6 th year = 46 - 5 = 41 the correct answer is b ." | a ) 36 , b ) 41 , c ) 38 , d ) 40 , e ) 42 | b | add(divide(add(subtract(subtract(4, const_1), const_1), add(50, subtract(4, const_1))), const_3), const_3) | subtract(n0,const_1)|add(n1,#0)|subtract(#0,const_1)|add(#1,#2)|divide(#3,const_3)|add(#4,const_3)| | general | allenai/math_qa |
if a - b = 6 and a 2 + b 2 = 48 , find the value of ab . | "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 48 - 36 = 12 ab = 6 . answer : d" | a ) 8 , b ) 10 , c ) 12 , d ) 6 , e ) 19 | d | divide(subtract(48, power(6, 2)), 2) | power(n0,n1)|subtract(n3,#0)|divide(#1,n1)| | general | allenai/math_qa |
how many multiples of 5 are there between 1 and 89 ? | "5 multiples are 5 , 10,15 , - - - - - - - - - , 80,85 it should be mentioned whether 1 and 89 are inclusive . the answer is ( 85 - 5 ) / 5 + 1 = 17 answer is d" | a ) 15 , b ) 20 , c ) 13 , d ) 17 , e ) 22 | d | add(divide(subtract(89, 1), 5), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | general | allenai/math_qa |
a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction q of the selected films are in color ? | it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose q = 60 / 62 = 30 / 31 of the selected films . answer : e . | a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31 | e | divide(6, add(divide(20, const_100), 6)) | divide(n0,const_100)|add(n1,#0)|divide(n1,#1) | general | allenai/math_qa |
the ratio of the present age of sandy to that of molly is 9 : 2 . sixteen years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ? | "let the present age of sandy be 9 x years and that of molly be 2 x years . ( 9 x + 16 ) / ( 2 x + 16 ) = 5 / 2 8 x = 48 x = 6 six years ago , sandy ' s age was 9 ( 6 ) - 6 = 48 the answer is d ." | a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54 | d | subtract(divide(multiply(subtract(multiply(5, add(const_10, 6)), multiply(2, add(const_10, 6))), 9), add(2, 2)), 6) | add(n4,const_10)|add(n1,n1)|multiply(n2,#0)|multiply(n1,#0)|subtract(#2,#3)|multiply(n0,#4)|divide(#5,#1)|subtract(#6,n4)| | general | allenai/math_qa |
35 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ? | "binders books days 35 1400 21 x 1600 20 x / 35 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 42 answer : c" | a ) 87 , b ) 18 , c ) 42 , d ) 16 , e ) 10 | c | divide(divide(1600, 20), divide(1400, multiply(35, 21))) | divide(n3,n4)|multiply(n0,n2)|divide(n1,#1)|divide(#0,#2)| | physics | allenai/math_qa |
in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 8 , 1 ) , ( 1 , 1 ) , ( 1 , - 7 and ( - 8 , - 7 ) ? | "length of side 1 = 8 + 1 = 9 length of side 2 = 7 + 1 = 8 area of rectangle = 9 * 8 = 72 c is the answer" | a ) 144 , b ) 36 , c ) 72 , d ) 56 , e ) 112 | c | multiply(add(8, 1), add(1, 7)) | add(n0,n1)|add(n1,n5)|multiply(#0,#1)| | geometry | allenai/math_qa |
a leak in the bottom of a tank can empty the full tank in 9 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ? | "solution work done by the inlet in 1 hour = ( 1 / 9 - 1 / 12 ) = 1 / 36 work done by the inlet in 1 min . = ( 1 / 36 × 1 / 60 ) = 0.000463 volume of 0.000463 part = 6 litres . therefore , volume of whole = 1 / 0.000463 x 6 ‹ = › 12960 litres . answer b" | a ) 7580 , b ) 12960 , c ) 8290 , d ) 8640 , e ) none | b | divide(multiply(6, multiply(12, const_60)), subtract(divide(multiply(12, const_60), multiply(9, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)| | physics | allenai/math_qa |
if the least common addition of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is | "( x + y ) = 10 and both x an y are prime . the only values of x and y can be 7 and 3 ( x = 7 and y = 3 ) 2 x + y = 2 * 7 + 3 = 17 correct option : d" | a ) 7 , b ) 9 , c ) 14 , d ) 17 , e ) 21 | d | add(add(multiply(10, const_2), divide(10, 2)), add(const_3, const_3)) | add(const_3,const_3)|divide(n0,n1)|multiply(n0,const_2)|add(#1,#2)|add(#3,#0)| | general | allenai/math_qa |
a cube of edge 5 cm is cut into cubes of each edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to | solution required ratio = ( 6 x 1 x 1 / 6 x 5 x 5 ) ‹ = › 1 / 25 ‹ = › 1 : 125 . answer b | ['a ) 1 : 5', 'b ) 1 : 25', 'c ) 1 : 125', 'd ) 1 : 625', 'e ) none'] | b | divide(surface_cube(1), surface_cube(5)) | surface_cube(n1)|surface_cube(n0)|divide(#0,#1) | geometry | allenai/math_qa |
what is the ratio between perimeters of two squares one having 2 times the diagonal then the other ? | "d = 2 d d = d a √ 2 = 2 d a √ 2 = d a = 2 d / √ 2 a = d / √ 2 = > 2 : 1 answer : d" | a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 2 : 1 , e ) 3 : 3 | d | divide(2, divide(2, 2)) | divide(n0,n0)|divide(n0,#0)| | geometry | allenai/math_qa |
what is 25 % of 25 % equal to | "solution 25 % of 25 % = 25 / 100 x 25 / 100 = 1 / 16 = 0.0625 answer d" | a ) 0.625 , b ) 0.0625 , c ) 6.25 , d ) 0.00625 , e ) none | d | divide(multiply(25, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)| | gain | allenai/math_qa |
a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ? | "let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a" | a ) 30 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 . | a | inverse(add(inverse(45), divide(inverse(45), const_2))) | inverse(n0)|divide(#0,const_2)|add(#1,#0)|inverse(#2)| | physics | allenai/math_qa |
a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 2 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . | the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 2 bottles of apple juice is 6 c 2 * 4 c 4 = 15 * 1 = 15 p ( selling 2 bottles of apple juice ) = 15 / 210 = 5 / 70 = 1 / 14 the answer is c . | a ) 1 / 7 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 21 | c | divide(choose(6, 2), choose(10, 6)) | choose(n1,n3)|choose(n0,n1)|divide(#0,#1) | probability | allenai/math_qa |
the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 18 % ? | "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 82 gain % = 18 / 64 * 100 = 28.125 % . answer : option d" | a ) 37.5 % , b ) 48 % , c ) 50.5 % , d ) 28.125 % , e ) 56 % | d | multiply(subtract(divide(subtract(const_100, 18), 64), const_1), const_100) | subtract(const_100,n1)|divide(#0,n0)|subtract(#1,const_1)|multiply(#2,const_100)| | gain | allenai/math_qa |
the average of 25 results is 8 . the average of first 12 of them is 14 and that of last 12 is 17 . find the 13 result ? | "13 th result = sum of 25 results - sum of 24 results 18 * 25 - 14 * 12 + 17 * 12 = 78 answer is d" | a ) 52 , b ) 68 , c ) 78 , d ) 92 , e ) 65 | d | subtract(subtract(multiply(25, 8), multiply(12, 17)), multiply(12, 14)) | multiply(n0,n1)|multiply(n2,n5)|multiply(n2,n3)|subtract(#0,#1)|subtract(#3,#2)| | general | allenai/math_qa |
find value for x from below equation ? x + 1 = 2 | "1 . subtract 1 from both sides : x + 1 - 1 = 2 - 1 2 . simplify both sides : x = 1 b" | a ) - 5 , b ) 1 , c ) 4 , d ) 3 , e ) 2 | b | subtract(2, 1) | subtract(n1,n0)| | general | allenai/math_qa |
if 36 men do a work in 70 days , in how many days will 40 men do it ? | "36 * 70 = 40 * x x = 63 days answer : b" | a ) 64 , b ) 63 , c ) 65 , d ) 66 , e ) 67 | b | divide(multiply(36, 70), 40) | multiply(n0,n1)|divide(#0,n2)| | physics | allenai/math_qa |
rajat , vikas and abhishek are submitting questions in the ratio 7 : 3 : 2 . if total number of questions submitted by them is 24 . find the number of questions submitted by vikas . | explanation : number of questions submitted by vikas = ( 24 * 3 ) / ( 7 + 3 + 2 ) = 6 answer : d | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | divide(24, const_4) | divide(n3,const_4) | other | allenai/math_qa |
a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ? | explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 180 - 50 ) m = 130 m . answer : c | a ) 100 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these | c | subtract(180, multiply(divide(3, const_60), const_1000)) | divide(n3,const_60)|multiply(#0,const_1000)|subtract(n0,#1) | physics | allenai/math_qa |
if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 39 , find the value of ab . | "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 39 - 9 = 30 ab = 15 . answer is a ." | a ) 15 , b ) 8 , c ) 4 , d ) 10 , e ) 3 | a | divide(subtract(39, power(3, 2)), 2) | power(n0,n1)|subtract(n3,#0)|divide(#1,n1)| | general | allenai/math_qa |
in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , 7 ) . what is the least possible value of the slope of line l ? | "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , 7 ) should satisfy the equation . hence x = t and y = 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( 7 - 5 ) / ( 4 - 2 ) = 1 imo option d is correct answer ." | a ) 6 , b ) 2 , c ) - 2 , d ) 1 , e ) - 10 | d | divide(subtract(7, 5), subtract(sqrt(add(9, 7)), sqrt(add(5, 9)))) | add(n1,n3)|add(n1,n2)|subtract(n3,n2)|sqrt(#0)|sqrt(#1)|subtract(#3,#4)|divide(#2,#5)| | general | allenai/math_qa |
an error 4 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ? | "percentage error in calculated area = ( 4 + 4 + ( 4 ã — 4 ) / 100 ) % = 8.16 % answer : c" | a ) 4.05 % , b ) 4.02 % , c ) 8.16 % , d ) 3 % , e ) 2 % | c | divide(multiply(subtract(square_area(add(const_100, 4)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | gain | allenai/math_qa |
if ( 5 ^ 7 ) ( 9 ^ 4 ) = 3 ( 15 ^ x ) , what is the value of x ? | "( 5 ^ 7 ) ( 9 ^ 4 ) = 3 ( 15 ^ x ) = > 5 ^ 7 * 3 ^ 8 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 7 * 3 ^ 8 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 7 answer a" | a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15 | a | divide(log(divide(multiply(power(5, 7), power(9, 4)), 3)), log(15)) | log(n5)|power(n0,n1)|power(n2,n3)|multiply(#1,#2)|divide(#3,n4)|log(#4)|divide(#5,#0)| | general | allenai/math_qa |
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ? | "3 x * 2 x = 4704 = > x = 28 2 ( 84 + 56 ) = 280 m 280 * 1 / 2 = rs . 140 answer : c" | a ) 287 , b ) 1287 , c ) 140 , d ) 988 , e ) 271 | c | divide(multiply(50, rectangle_perimeter(sqrt(divide(multiply(4704, 2), 3)), divide(4704, sqrt(divide(multiply(4704, 2), 3))))), const_100) | multiply(n1,n2)|divide(#0,n0)|sqrt(#1)|divide(n2,#2)|rectangle_perimeter(#3,#2)|multiply(n3,#4)|divide(#5,const_100)| | physics | allenai/math_qa |
how many times will the digit 6 be written when listing the integers from 1 to 1000 ? | "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 6 ) 3000 / 10 = 300 times . answer : e ." | a ) 150 , b ) 280 , c ) 310 , d ) 420 , e ) 300 | e | multiply(multiply(multiply(1, const_10), const_10), const_3) | multiply(n1,const_10)|multiply(#0,const_10)|multiply(#1,const_3)| | general | allenai/math_qa |
in a graduate physics course , 60 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is single ? | "let assume there are 100 students of which 60 are male and 40 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 60 = 17 males are married if 30 is the total number of students who are married and out of that 17 are males then the remaining 13 will be females who are married . total females = 40 married females = 13 then single females = 40 - 13 = 27 we need to find the fraction of female students who are single i . e single female students / total female student = 27 / 40 [ d ]" | a ) 2 / 7 , b ) 17 / 30 , c ) 1 / 2 , d ) 27 / 40 , e ) 5 / 7 | d | divide(const_10, 30) | divide(const_10,n1)| | gain | allenai/math_qa |
a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be | "time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer : b ." | a ) 45 min , b ) 60 min , c ) 55 min , d ) 70 min , e ) 80 min | b | divide(multiply(48, divide(50, const_60)), divide(40, const_60)) | divide(n0,const_60)|divide(n2,const_60)|multiply(n1,#0)|divide(#2,#1)| | physics | allenai/math_qa |
the wages earned by robin is 49 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ? | "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 149 and $ 160 respectively . charles earns $ 49 more than robin who earns $ 149 . therefore , charles ' wage is 49 / 149 * 100 = 32.88 % . the correct choice is ( e )" | a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 32.88 % | e | multiply(divide(subtract(add(const_100, 60), add(const_100, 49)), add(const_100, 49)), const_100) | add(n1,const_100)|add(n0,const_100)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)| | general | allenai/math_qa |
the triplicate ratio of 1 : 8 is ? | "13 : 83 = 1 : 512 answer : d" | a ) 1 : 0 , b ) 1 : 8 , c ) 1 : 7 , d ) 1 : 512 , e ) 1 : 1 | d | divide(power(const_2.0, 8), power(const_3.0, 8)) | power(const_2.0,n1)|power(const_3.0,n1)|divide(#0,#1)| | other | allenai/math_qa |
amar takes as much time in running 24 meters as a car takes in covering 60 meters . what will be the distance covered by amar during the time the car covers 2.2 km ? | "distance covered by amar = 24 / 60 ( 2.2 km ) = 2 / 5 ( 2200 ) = 880 m answer : d" | a ) 700 m , b ) 500 m , c ) 870 m , d ) 880 m , e ) 840 m | d | divide(multiply(24, multiply(2.2, const_1000)), 60) | multiply(n2,const_1000)|multiply(n0,#0)|divide(#1,n1)| | physics | allenai/math_qa |
find the sum lend at c . i . at 5 p . c per annum will amount to rs . 740 in 2 years ? | "explanation : 740 = p ( 21 / 20 ) 2 p = 671 answer : e" | a ) 221 , b ) 287 , c ) 400 , d ) 288 , e ) 671 | e | divide(740, power(add(const_1, divide(5, const_100)), 2)) | divide(n0,const_100)|add(#0,const_1)|power(#1,n2)|divide(n1,#2)| | general | allenai/math_qa |
tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many l minutes it takes john to reach the station ? | since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , l 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c . | a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min | c | multiply(subtract(divide(divide(multiply(multiply(subtract(15, 10), divide(15, const_60)), const_60), 10), const_2), const_0_25), 10) | divide(n0,const_60)|subtract(n0,n1)|multiply(#0,#1)|multiply(#2,const_60)|divide(#3,n1)|divide(#4,const_2)|subtract(#5,const_0_25)|multiply(n1,#6) | physics | allenai/math_qa |
two brothers took the gmat exam , the higher score is u and the lower one is v . if the difference between the two scores is equal to their average , what is the value of v / u ? | answer is d : 1 / 3 u - v = ( u + v ) / 2 solving for v / u = 1 / 3 d | a ) 3 , b ) 2 , c ) 1 / 2 , d ) 1 / 3 , e ) there is n ' t enough data to answer the question . | d | divide(const_1, const_3) | divide(const_1,const_3) | general | allenai/math_qa |
250 men work for 16 days and finish a work . how many men would do a job 3 times the previous one in 20 days ? | number of men needed to finish the required work ( variation , proportion method ) = 3 * 16 * 250 / 20 = 600 answer : c | a ) 700 , b ) 666 , c ) 600 , d ) 400 , e ) 800 | c | divide(multiply(3, multiply(250, 16)), 20) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n3) | physics | allenai/math_qa |
a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 200 square feet , what is the total length of the fence , in feet ? | two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 200 ie x ^ 2 = 100 ie x = 10 l = 20 w = 10 total lenght of fence = 2 * 10 + 20 = 40 my answer is d | ['a ) 10', 'b ) 20', 'c ) 30', 'd ) 40', 'e ) 80'] | d | add(add(multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1)), add(multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1)), multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1)))), divide(200, add(add(add(multiply(add(const_1, const_1), const_2), const_1), multiply(const_2, add(multiply(add(const_1, const_1), const_2), const_1))), add(multiply(add(const_1, const_1), const_2), const_1)))) | add(const_1,const_1)|multiply(#0,const_2)|add(#1,const_1)|multiply(#2,const_2)|add(#3,#3)|add(#2,#3)|add(#4,#3)|add(#5,#2)|divide(n0,#7)|add(#6,#8) | geometry | allenai/math_qa |
light glows for every 13 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am | the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 13 = 382 . so total 383 times light ll glow answer : c | a ) 381 , b ) 382 , c ) 383 , d ) 384 , e ) 385 | c | divide(add(add(const_2, 47), multiply(add(20, add(const_2, const_60)), const_60)), 13) | add(n6,const_2)|add(const_2,const_60)|add(n5,#1)|multiply(#2,const_60)|add(#0,#3)|divide(#4,n0) | physics | allenai/math_qa |
the probability of two events a and b are 0.25 and 0.35 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________ | "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 35 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : a" | a ) 0.55 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6 | a | subtract(const_1, subtract(add(0.25, 0.35), 0.15)) | add(n0,n1)|subtract(#0,n2)|subtract(const_1,#1)| | other | allenai/math_qa |
if a and b get profits of rs . 18,000 and rs . 15,000 respectively at the end of year then ratio of their investments are | "ratio = 18000 / 15000 = 6 : 5 answer : a" | a ) 6 : 5 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5 | a | divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), multiply(add(const_2, const_3), const_2))) | add(const_2,const_3)|multiply(const_2,const_3)|multiply(#1,const_100)|multiply(#0,const_2)|multiply(#2,const_100)|divide(#4,#3)|divide(#4,#5)| | gain | allenai/math_qa |
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