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q ' = 3 q - 3 , what is the value of ( 6 ' ) ' ? | ( 6 ' ) ' = ( 3 * 6 - 3 ) ' = 15 ' = 15 * 15 - 15 = 210 answer d | a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240 | d | multiply(subtract(multiply(subtract(multiply(3, 6), 3), 3), 3), subtract(6, const_1)) | multiply(n0,n2)|subtract(n2,const_1)|subtract(#0,n0)|multiply(n0,#2)|subtract(#3,n0)|multiply(#4,#1) | general | allenai/math_qa |
joe β s average ( arithmetic mean ) test score across 4 equally weighted tests was 40 . he was allowed to drop his lowest score . after doing so , his average test score improved to 45 . what is the lowest test score that was dropped ? | "the arithmetic mean of 4 equally weighted tests was 40 . so what we can assume is that we have 4 test scores , each 40 . he dropped his lowest score and the avg went to 45 . this means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 40 . so the lowest score = 40 - 15 = 25 answer ( b )" | a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80 | b | subtract(multiply(40, 4), multiply(45, const_3)) | multiply(n0,n1)|multiply(n2,const_3)|subtract(#0,#1)| | general | allenai/math_qa |
find the average of all the numbers between 40 and 80 which are divisible by 3 . | "sol . average = ( 42 + 45 + 48 + 51 + 54 + 57 + 60 + 63 + 66 + 69 + 72 + 75 + 78 / 13 ) = 780 / 5 = 60 . answer d" | a ) 15 , b ) 70 , c ) 20 , d ) 60 , e ) none | d | divide(add(add(40, const_4), subtract(80, const_4)), const_2) | add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)| | general | allenai/math_qa |
find the simple interest on $ 2000 for 3 years at 10 % per annum ? | "si = ptr / 100 = 2000 * 3 * 10 / 100 = $ 600 answer is d" | a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000 | d | multiply(2000, divide(3, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain | allenai/math_qa |
the speed of a car is 20 km in the first hour and 30 km in the second hour . what is the average speed of the car ? | "s = ( 20 + 30 ) / 2 = 25 kmph answer : a" | a ) 25 kmph , b ) 85 kmph , c ) 34 kmph , d ) 23 kmph , e ) 45 kmph | a | divide(add(20, 30), const_2) | add(n0,n1)|divide(#0,const_2)| | physics | allenai/math_qa |
a man rows his boat 90 km downstream and 5 ` km upstream , taking 3 hours each time . find the speed of the stream ? | "speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 51 / ( 3 ) = 17 kmph the speed of the stream = ( 30 - 17 ) / 2 = 7 kmph answer : a" | a ) 7 kmph , b ) 5 kmph , c ) 2 kmph , d ) 8 kmph , e ) 1 kmph | a | divide(subtract(divide(90, 3), divide(5, 3)), const_2) | divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)| | physics | allenai/math_qa |
an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 3 / 5 % , then the amount invested at 11 % was ? | "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 48 / 5 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 960000 x = 70000 sum invested at 9 % = rs . 70000 sum invested at 11 % = rs . ( 100000 - 70000 ) = rs . 30000 . answer : b" | a ) 23777 , b ) 30000 , c ) 29977 , d ) 26777 , e ) 19871 | b | divide(subtract(multiply(100000, divide(add(9, divide(3, 5)), const_100)), multiply(100000, divide(9, const_100))), subtract(divide(11, const_100), divide(9, const_100))) | divide(n4,n5)|divide(n1,const_100)|divide(n2,const_100)|add(n1,#0)|multiply(n0,#1)|subtract(#2,#1)|divide(#3,const_100)|multiply(n0,#6)|subtract(#7,#4)|divide(#8,#5)| | gain | allenai/math_qa |
what is the sum of all even numbers from 1 to 601 ? | "explanation : 600 / 2 = 300 300 * 301 = 90300 answer : c" | a ) 122821 , b ) 281228 , c ) 90300 , d ) 122850 , e ) 128111 | c | divide(multiply(1, 601), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general | allenai/math_qa |
calculate 469160 x 9999 = ? | "answer 469160 x 9999 = 469160 x ( 10000 - 1 ) = 4691600000 - 469160 = 4691130840 . option : a" | a ) 4691130840 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none | a | multiply(469160, 9999) | multiply(n0,n1)| | general | allenai/math_qa |
p is 50 % more efficient than q . p can complete a work in 25 days . if p and q work together , how many days will it take to complete the same work ? | "the work done by p in 1 day = 1 / 25 let work done by q in 1 day = q q Γ ( 150 / 100 ) = 1 / 25 q = 100 / ( 25 Γ 150 ) = 10 / ( 25 Γ 15 ) the work done by p and q in 1 day = 1 / 25 + 10 / ( 25 Γ 15 ) = 25 / ( 25 Γ 15 ) = 1 / 15 p and q together can do the work in 15 days . the answer is c ." | a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19 | c | divide(multiply(add(divide(50, const_100), const_1), 25), add(add(divide(50, const_100), const_1), const_1)) | divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(n1,#1)|divide(#3,#2)| | physics | allenai/math_qa |
the hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ? | for the 12 minutes the motor - cyclist continues to overtake the hiker , she is going at 24 miles per hour faster than the hiker . once the motor - cyclist stops , the hiker is going at 6 miles per hour while the motor - cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds . 24 / 6 * 12 or 48 minutes answer is ( d ) | a ) 30 , b ) 36 , c ) 40 , d ) 48 , e ) 60 | d | multiply(30, const_1_6) | multiply(n1,const_1_6) | physics | allenai/math_qa |
if a # b = ab β b + b ^ 2 , then 3 # 6 = | "solution - simply substitute 3 and 6 in equation in the place of a and b respectively . 3 # 6 = 3 * 6 - 6 + 6 ^ 2 = 18 - 6 + 36 = 48 . ans e" | a ) 2 , b ) 8 , c ) 15 , d ) 21 , e ) 48 | e | add(subtract(multiply(3, 6), 6), power(6, 2)) | multiply(n1,n2)|power(n2,n0)|subtract(#0,n2)|add(#1,#2)| | general | allenai/math_qa |
( x ) + 1789 + 9011 - 7819 = 90510 . calculate the value of x | "x + 1789 + 9011 - 7819 = 90510 = x + 1789 + 9011 = 90510 + 7819 = x + 10800 = 98329 = x = 98329 - 10800 = 87529 answer is c" | a ) 87501 , b ) 87599 , c ) 87529 , d ) 87520 , e ) 87521 | c | multiply(subtract(subtract(add(90510, 7819), 9011), 1789), divide(const_60, const_2)) | add(n2,n3)|divide(const_60,const_2)|subtract(#0,n1)|subtract(#2,n0)|multiply(#1,#3)| | general | allenai/math_qa |
a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 69 km downstream . | "speed of boat in still water = 13 km / hr speed of the stream = 6 km / hr speed downstream = ( 13 + 6 ) = 19 km / hr time taken to travel 69 km downstream = 69 Γ’ Β β 19 = 17 Γ’ Β β 4 = 3.6 hours answer is a" | a ) 3.6 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr | a | divide(69, add(13, 6)) | add(n0,n1)|divide(n2,#0)| | physics | allenai/math_qa |
a rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 10 apiece , what is the total cost for the number of carpet squares needed to cover the floor ? | "the width of the rectangular floor ( 8 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 10 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 8 / 2 ) * ( 10 / 2 ) = 20 . the total cost is 20 * 10 = $ 200 . the answer is , therefore , a ." | a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 960 , e ) $ 1,920 | a | multiply(8, 8) | multiply(n0,n0)| | geometry | allenai/math_qa |
if a - b = 10 and a ^ 2 + b ^ 2 = 150 , find the value of ab | "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 150 - 100 = 50 = > ab = 25 answer : c" | a ) 10 , b ) 12 , c ) 25 , d ) 18 , e ) 19 | c | multiply(multiply(add(10, divide(subtract(sqrt(150), 10), 2)), divide(subtract(sqrt(150), 10), 2)), 2) | sqrt(n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)|multiply(#3,#2)|multiply(n1,#4)| | general | allenai/math_qa |
there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 16 days more ? | "760 - - - - 22 760 - - - - 20 x - - - - - 16 x * 16 = 760 * 20 x = 950 760 - - - - - - - 190 answer : e" | a ) 122 , b ) 140 , c ) 199 , d ) 188 , e ) 190 | e | subtract(divide(multiply(760, subtract(22, const_2)), 16), 760) | subtract(n1,const_2)|multiply(n0,#0)|divide(#1,n2)|subtract(#2,n0)| | physics | allenai/math_qa |
a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days m will the work get over ? | "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )" | a ) 60 , b ) 70 , c ) m = 75 , d ) 80 , e ) 100 | c | divide(multiply(divide(multiply(10, 20), const_0_25), subtract(const_1, const_0_25)), subtract(10, 2)) | multiply(n1,n2)|subtract(const_1,const_0_25)|subtract(n1,n3)|divide(#0,const_0_25)|multiply(#3,#1)|divide(#4,#2)| | physics | allenai/math_qa |
a train 320 m in length crosses a telegraph post in 16 seconds . the speed of the train is ? | "s = 320 / 16 * 18 / 5 = 72 kmph answer : d" | a ) 22 kmph , b ) 77 kmph , c ) 54 kmph , d ) 72 kmph , e ) 88 kmph | d | multiply(const_3_6, divide(320, 16)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics | allenai/math_qa |
the tax on a commodity is diminished by 10 % and its consumption increased by 20 % . the effect on revenue is ? | "100 * 100 = 10000 90 * 120 = 10800 - - - - - - - - - - - 10000 - - - - - - - - - - - 800 100 - - - - - - - - - - - ? = > 8 % increase answer : b" | a ) 2 % decrease , b ) 8 % increase , c ) 9 % decrease , d ) 3 % decrease , e ) 2 % decrease | b | subtract(const_100, multiply(multiply(add(const_1, divide(20, const_100)), subtract(const_1, divide(10, const_100))), const_100)) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)| | general | allenai/math_qa |
two numbers are respectively 20 % and 50 % more than a third number . the ratio of the two numbers is | "explanation : let the third number be x . first number ( 120 / 100 ) * x = 6 x / 5 second number ( 150 / 100 ) * x = 3 x / 2 ratio = 6 x / 5 : 3 x / 2 = > 4 : 5 option c" | a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 6 : 5 , e ) 7 : 5 | c | subtract(const_100, multiply(divide(add(20, const_100), add(50, const_100)), const_100)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)| | other | allenai/math_qa |
the average salary of 16 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ? | total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a | a ) $ 18,714 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300 | a | divide(subtract(subtract(multiply(multiply(5, 4), multiply(const_4, const_4)), multiply(multiply(5, 5), 5)), multiply(4, 16)), add(const_2, 5)) | add(n2,const_2)|multiply(n2,n4)|multiply(const_4,const_4)|multiply(n2,n2)|multiply(n0,n4)|multiply(#1,#2)|multiply(n2,#3)|subtract(#5,#6)|subtract(#7,#4)|divide(#8,#0) | general | allenai/math_qa |
there is a 20 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ? | "p ( china and not malaysia ) = 0.2 * 0.4 = 0.08 p ( malaysia and not china ) = 0.6 * 0.8 = 0.48 total probability = 0.08 + 0.48 = 0.56 = 56 % the answer is c ." | a ) 40 % , b ) 48 % , c ) 56 % , d ) 64 % , e ) 72 % | c | divide(add(20, 60), multiply(multiply(const_5, const_5), const_4)) | add(n0,n1)|multiply(const_5,const_5)|multiply(#1,const_4)|divide(#0,#2)| | probability | allenai/math_qa |
if ( 10 ^ 4 * 3.456789 ) ^ 14 is written as a single term , how many digits would be to the right of the decimal place ? | 3.456789 ^ 14 has 6 * 14 = 84 decimal places . 10 ^ 56 moves the decimal place to the right 56 places . ( 10 ^ 4 * 3.456789 ) ^ 14 has 84 - 56 = 28 digits after the decimal point . the answer is d . | a ) 9 , b ) 14 , c ) 21 , d ) 28 , e ) 42 | d | multiply(14, const_2) | multiply(n3,const_2) | general | allenai/math_qa |
a 40 - liter solution of alcohol and water is 5 percent alcohol . if 4.5 liters of alcohol and 5.5 liters of water are added to this solution , what percent of the solution produced is alcohol ? | the percent of alcohol in the solution is ( 0.05 ( 40 ) + 4.5 ) / 50 = 6.5 / 50 = 13 % the answer is c . | a ) 7 % , b ) 10 % , c ) 13 % , d ) 16 % , e ) 19 % | c | multiply(divide(add(multiply(40, divide(5, const_100)), 4.5), add(40, add(4.5, 5.5))), const_100) | add(n2,n3)|divide(n1,const_100)|add(n0,#0)|multiply(n0,#1)|add(n2,#3)|divide(#4,#2)|multiply(#5,const_100) | general | allenai/math_qa |
if 2994 Γ£ Β· 14.5 = 175 , then 29.94 Γ£ Β· 1.45 = ? | "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 175 in the place of 2994 / 14.5 ] = 175 / 10 = 17.5 answer is c ." | a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2 | c | divide(175, divide(14.5, 1.45)) | divide(n1,n4)|divide(n2,#0)| | general | allenai/math_qa |
` ` how old are you , alchemerion ? ' ' asked one of the wizards appearances the wizards answer with a riddle , ` ` i am still very young as wizards go . i am only 3 times my son ' s age . my father is 40 year more than twice of my age . together the 3 of us are a 1240 year old ' ' . how old is alchemerion | let alchemerion be a let son be s let father be f a = 3 * s f = 40 + ( 2 * a ) therefore 1240 = ( s + f + a ) 1240 = ( a / 3 ) + ( 40 + ( 2 * a ) ) + a a = 360 answer : d | a ) 300 , b ) 320 , c ) 340 , d ) 360 , e ) 380 | d | multiply(divide(subtract(1240, 40), const_10), 3) | subtract(n3,n1)|divide(#0,const_10)|multiply(n0,#1) | general | allenai/math_qa |
the sum of ages of 10 children born at the intervals of 1 years each is 105 years . what is the age of the youngest child ? | "let the ages of children be x , ( x + 1 ) , ( x + 2 , ( x + 3 ) , ( x + 4 ) , ( x + 5 ) , ( x + 6 ) , ( x + 7 ) , ( x + 8 ) , and ( x + 9 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) + ( x + 7 ) + ( x + 8 ) + ( x + 9 ) = 105 10 x = 60 x = 6 age of the youngest child = x = 6 years . answer : e" | a ) 4 , b ) 5 , c ) 2 , d ) 7 , e ) 6 | e | subtract(subtract(divide(105, 10), 1), 1) | divide(n2,n0)|subtract(#0,n1)|subtract(#1,n1)| | general | allenai/math_qa |
express 22 mps in kmph ? | "22 * 18 / 5 = 79.2 kmph answer : a" | a ) 79.2 kmph , b ) 89.2 kmph , c ) 79.6 kmph , d ) 99.2 kmph , e ) 69.2 kmph | a | multiply(divide(22, const_1000), const_3600) | divide(n0,const_1000)|multiply(#0,const_3600)| | physics | allenai/math_qa |
there are 870 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 870 . hence , we have m + f = 870 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 870 / 3 = 290 solving the three equations yields the solution f = 290 , m = 580 , and d = 290 . the number of female democratic participants equals half the female participants equals 290 / 2 = 145 . answer : e" | a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 145 | e | divide(subtract(multiply(divide(870, const_3), const_4), 870), const_2) | divide(n0,const_3)|multiply(#0,const_4)|subtract(#1,n0)|divide(#2,const_2)| | general | allenai/math_qa |
data sufficiency question : if solution ( x ) with alcohol ( 14 % ) and solution ( y ) with alcohol ( 20 % ) mixed together to form 24 liters of mixture . | explanation : let a liters of first solution , and ' b ' liters of second solution has been taken . so using weighted average formula = n 1 Γ a 1 + n 2 Γ a 2 n 1 + n 2 n 1 Γ a 1 + n 2 Γ a 2 n 1 + n 2 = n 1 Γ 14 + n 2 Γ 20 n 1 + n 2 = 15 n 1 Γ 14 + n 2 Γ 20 n 1 + n 2 = 15 β n 1 = 5 n 2 β n 1 n 2 = 51 β n 1 = 5 n 2 β n 1 n 2 = 51 as total volume was given as 24 liters , first solution = 16 Γ 24 = 416 Γ 24 = 4 so statement 1 is sufficient . answer : a | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 3 | a | divide(add(multiply(multiply(const_0_25, 20), 14), 20), add(multiply(const_0_25, 20), const_1)) | multiply(n1,const_0_25)|add(#0,const_1)|multiply(n0,#0)|add(n1,#2)|divide(#3,#1) | gain | allenai/math_qa |
subtracting 4 % of a from a is equivalent to multiplying a by how much ? | "answer let a - 4 % of a = ab . β ( 96 x a ) / 100 = ab β΄ b = 0.96 correct option : a" | a ) 0.96 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none | a | divide(subtract(const_100, 4), const_100) | subtract(const_100,n0)|divide(#0,const_100)| | general | allenai/math_qa |
the perimeter of an isosceles right triangle is 8 + 8 sq rt 2 . what is the length of the hypotenuse of the triangle ? | "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 8 + 8 sqrt 2 or , a . ( 2 + sqrt 2 ) = 8 ( 1 + sqrt 2 ) , a = 8 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 8 * 2.414 / 3.414 = 0.707 * 8 then hypotenuse = 5.656 b" | a ) 4 , b ) 5.656 , c ) 5 , d ) 6 , e ) 7 | b | divide(multiply(8, sqrt(2)), 2) | sqrt(n2)|multiply(n0,#0)|divide(#1,n2)| | geometry | allenai/math_qa |
andrew purchased 14 kg of grapes at the rate of 54 per kg and 10 kg of mangoes at the rate of 62 per kg . how much amount did he pay to the shopkeeper ? | "cost of 14 kg grapes = 54 Γ 14 = 756 . cost of 10 kg of mangoes = 62 x 10 = 620 . total cost he has to pay = 756 + 620 = 1376 b" | a ) 1000 , b ) 1376 , c ) 1456 , d ) 1900 , e ) 1566 | b | add(multiply(14, 54), multiply(10, 62)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | gain | allenai/math_qa |
a circular racetrack is 3 miles in length and has signs posted to indicate each 1 / 10 mile increment . if a race car starts at a random location on the track and travels exactly one half mile , what is the probability that the car ends within a half mile of the sign indicating 2 1 / 2 miles ? | the car ends within a half mile of the sign indicating 2 1 / 2 miles means that the car will end in one mile interval , between the signs indicating 2 and 3 miles . now , it does n ' t matter where the car starts or what distance it travels , the probability will be p = ( favorable outcome ) / ( total # of outcomes ) = 1 / 3 ( as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared , so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1 / 3 ) . answer : c . | a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 3 , d ) 1 / 2 , e ) 2 / 3 | c | divide(10, multiply(3, const_10)) | multiply(n0,const_10)|divide(n2,#0) | general | allenai/math_qa |
in may , the groundskeeper at spring lake golf club built a circular green with an area of 95 Ο square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ? | area = Ο r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 95 Ο ) = 380 Ο the answer is e . | ['a ) 190 Ο', 'b ) 210 Ο', 'c ) 240 Ο', 'd ) 320 Ο', 'e ) 380 Ο'] | e | multiply(power(multiply(sqrt(95), const_2), const_2), const_pi) | sqrt(n0)|multiply(#0,const_2)|power(#1,const_2)|multiply(#2,const_pi) | geometry | allenai/math_qa |
there are 18 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ? | there are 18 balls in a jar . you take out 3 blue balls without putting 3 blue balls + 15 / 5 = 6 answer : e | a ) 12 , b ) 9 , c ) 8 , d ) 7 , e ) 6 | e | add(divide(subtract(18, 3), 5), 3) | subtract(n0,n1)|divide(#0,n3)|add(n1,#1) | probability | allenai/math_qa |
let the number which when multiplied by 12 is increased by 198 . | "solution let the number be x . then , 12 x - x = 198 βΉ = βΊ 11 x = 198 x βΉ = βΊ 18 . answer a" | a ) 18 , b ) 20 , c ) 26 , d ) 28 , e ) 30 | a | divide(198, subtract(12, const_1)) | subtract(n0,const_1)|divide(n1,#0)| | general | 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 . 14000 , then find the annual income of a ? | "b ' s monthly income = 14000 * 112 / 100 = rs . 15680 b ' s monthly income = 2 parts - - - - > rs . 15680 a ' s monthly income = 5 parts = 5 / 2 * 15680 = rs . 39200 a ' s annual income = rs . 39200 * 12 = rs . 470400 answer : d" | a ) rs . 420000 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 470400 , e ) none of these | d | multiply(multiply(multiply(14000, 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 |
what is the least value of k . so that 123 k 578 is divisible by 11 . | explanation : the difference of the sum of the digits at odd place and the sum of the digits at even place of the number , is either 0 or a number divisible by 11 . ( 1 + 3 + 5 + 8 ) - ( 2 + k + 7 ) = 17 - 9 - k = 8 - k therefore if k = 8 , then the value become zero . k = 8 is the least value so that 123 k 578 is divisible by 11 . answer : option a | a ) 8 , b ) 7 , c ) 5 , d ) 6 , e ) 4 | a | divide(divide(divide(lcm(123, 578), 578), const_4), const_4) | lcm(n0,n1)|divide(#0,n1)|divide(#1,const_4)|divide(#2,const_4) | general | allenai/math_qa |
in a public show 62 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ? | "75 % of 600 = 62 / 100 Γ 600 = 372 therefore , the number of vacant seats = 600 - 372 = 228 . answer : e" | a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 228 | e | divide(multiply(600, subtract(const_100, 62)), const_100) | subtract(const_100,n0)|multiply(n1,#0)|divide(#1,const_100)| | gain | allenai/math_qa |
a certain article of clothing was discounted during a special sale to 4 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ? | "say the original retail price of the item was $ 200 . the price after the first sale = 4 / 5 * $ 200 = $ 160 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 160 - 100 ) / 150 = 1 / 3 = 40 % . answer : c ." | a ) 50 % , b ) 33.33 % , c ) 40 % , d ) 16.66 % , e ) 12.5 % | c | multiply(subtract(divide(4, 5), multiply(divide(4, 5), divide(1, 2))), const_100) | divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)|subtract(#0,#2)|multiply(#3,const_100)| | gain | allenai/math_qa |
solve below question 2 x + 1 = - 21 | "2 x + 1 = - 21 x = - 11 a" | a ) - 11 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7 | a | divide(negate(add(21, 1)), 2) | add(n1,n2)|negate(#0)|divide(#1,n0)| | general | allenai/math_qa |
a corporation that had $ 10 billion in profits for the year paid out $ 200 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 ) | "required answer = [ employee benefit / profit ] * 100 = [ ( 200 million ) / ( 10 billion ) ] * 100 = [ ( 200 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 20 / 1000 ) * 100 = 2 % so answer is ( d )" | a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 % | d | multiply(divide(multiply(200, power(10, add(const_3, const_3))), multiply(10, power(10, 9))), const_100) | add(const_3,const_3)|power(n3,n4)|multiply(n0,#1)|power(n3,#0)|multiply(n1,#3)|divide(#4,#2)|multiply(#5,const_100)| | general | allenai/math_qa |
according to a recent student poll , 3 / 4 out of 20 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ? | "15 students are interested , 5 are not interested prob = 1 - 5 c 2 / 20 c 2 = 1 - ( 5 * 4 / ( 20 * 19 ) ) = 1 - 1 / 19 = 18 / 19 answer : c" | a ) 1 / 14 , b ) 4 / 49 , c ) 18 / 19 , d ) 45 / 49 , e ) 13 / 14 | c | divide(subtract(choose(20, const_2), choose(subtract(20, multiply(20, divide(3, 4))), const_2)), choose(20, const_2)) | choose(n2,const_2)|divide(n0,n1)|multiply(n2,#1)|subtract(n2,#2)|choose(#3,const_2)|subtract(#0,#4)|divide(#5,#0)| | gain | allenai/math_qa |
the average marks of a class of 30 students is 30 and that of another class of 50 students is 60 . find the average marks of all the students ? | "sum of the marks for the class of 30 students = 30 * 30 = 900 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 900 + 3000 = 3900 average marks of all the students = 3900 / 80 = 48.75 answer : d" | a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 48.75 , e ) 42.5 | d | divide(add(multiply(30, 30), multiply(50, 60)), add(30, 50)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)| | general | allenai/math_qa |
a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ? | "the total surface area is 2 ( 2 * 4 + 4 * 5 + 2 * 5 ) = 76 square feet the total cost is 76 * $ 20 = $ 1520 the answer is a ." | a ) $ 1520 , b ) $ 1640 , c ) $ 1780 , d ) $ 1850 , e ) $ 1960 | a | multiply(surface_rectangular_prism(4, 5, 2), 20) | surface_rectangular_prism(n0,n1,n2)|multiply(n3,#0)| | geometry | allenai/math_qa |
a dog takes 5 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is : | "explanation : dog : hare = ( 5 * 5 ) leaps of hare : 8 leaps of hare = 25 : 8 answer : b" | a ) 25 : 10 , b ) 25 : 8 , c ) 25 : 9 , d ) 8 : 25 , e ) 24 : 8 | b | divide(multiply(5, 5), 8) | multiply(n0,n2)|divide(#0,n1)| | other | allenai/math_qa |
the average age of applicants for a new job is 32 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ? | "minimum age = average - 1 standard deviation = 32 - 8 = 24 maximum age = average + 1 standard deviation = 32 + 8 = 40 maximum number of different ages of the applicants = 30 - 24 + 1 = 7 answer c" | a ) 8 , b ) 77 , c ) 7 , d ) 18 , e ) 34 | c | add(subtract(add(32, 8), subtract(32, 8)), const_1) | add(n0,n1)|subtract(n0,n1)|subtract(#0,#1)|add(#2,const_1)| | general | allenai/math_qa |
a certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ? | "1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 3 candidates for the math dep . , which gives as 3 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 3 * 45 = 135 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans d" | a ) 42 , b ) 70 , c ) 140 , d ) 135 , e ) 315 | d | multiply(multiply(10, 3), 3) | multiply(n3,n5)|multiply(n1,#0)| | other | allenai/math_qa |
the ratio , by volume , of bleach to detergent to water in a certain solution is 4 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ? | b : d : w = 4 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 4 / 40 ) = ( 1 / 30 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be c | ['a ) 80', 'b ) 70', 'c ) 60', 'd ) 40', 'e ) 50'] | c | multiply(divide(300, 100), divide(40, const_2)) | divide(n3,n2)|divide(n1,const_2)|multiply(#0,#1) | other | allenai/math_qa |
if 10 % of 30 % of 50 % of a number is 90 , then what is the number ? | "let the number be a given , 10 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 1 / 10 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 6000 . answer : b" | a ) 4000 , b ) 6000 , c ) 4400 , d ) 4500 , e ) none of these | b | divide(90, multiply(multiply(divide(50, const_100), divide(30, const_100)), divide(10, const_100))) | divide(n0,const_100)|divide(n2,const_100)|divide(n1,const_100)|multiply(#1,#2)|multiply(#0,#3)|divide(n3,#4)| | gain | allenai/math_qa |
if the number is divided by 3 , it reduced by 48 . the number is | "explanation : let the number be x . then , x - ( x / 3 ) = 48 = > 2 x / 3 = 48 = > x = 72 answer : option d" | a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 72 , e ) e ) 36 | d | divide(multiply(48, 3), subtract(3, const_1)) | multiply(n0,n1)|subtract(n0,const_1)|divide(#0,#1)| | general | allenai/math_qa |
jacob is 12 years old . he is 4 times as old as his brother . how old will jacob be when he is twice as old ? | "j = 12 ; j = 4 b ; b = 12 / 4 = 3 ; twice as old so b = 3 ( now ) + ( 3 ) = 6 ; jacob is 12 + 6 = 18 answer : e" | a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 18 | e | multiply(12, 4) | multiply(n0,n1)| | general | allenai/math_qa |
a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 165 m long ? | ": speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 165 = 525 m required time = 525 * 2 / 25 = 42 sec answer : e" | a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 42 | e | divide(360, multiply(subtract(45, 165), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics | allenai/math_qa |
if 4 men can paint 60 m long wall in 3 days , then 5 men can paint 50 m long wall in | the length of wall painted by one man in one day = 60 / 4 Γ£ β 3 = 5 m no . of days required to paint 50 m wall by 5 men = 50 / 5 Γ£ β 5 = 2 day . b | a ) 3 days , b ) 2 days , c ) 5 days , d ) 6 days , e ) 1 day | b | divide(50, multiply(divide(divide(60, 3), 4), 5)) | divide(n1,n2)|divide(#0,n0)|multiply(n3,#1)|divide(n4,#2) | physics | allenai/math_qa |
carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 2 inches long , how wide is jordan ' s rectangle , in inches ? | "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 2 w = 120 = > w = 60 answer d" | a ) 65 , b ) 63 , c ) 52 , d ) 60 , e ) 68 | d | divide(rectangle_area(5, 24), 2) | rectangle_area(n0,n1)|divide(#0,n2)| | geometry | allenai/math_qa |
the cost price of a radio is rs . 2400 and it was sold for rs . 2100 , find the loss % ? | "2400 - - - - 300 100 - - - - ? = > 12.5 % answer : a" | a ) 12.5 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 12.8 % | a | multiply(divide(subtract(2400, 2100), 2400), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain | allenai/math_qa |
a train running at the speed of 60 km / hr crosses a pole in 18 sec . what is the length of the train ? | "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 18 = 300 m answer : c" | a ) 118 , b ) 150 , c ) 300 , d ) 258 , e ) 191 | c | multiply(divide(multiply(60, const_1000), const_3600), 18) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics | allenai/math_qa |
a trader bought a car at 10 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ? | "original price = 100 cp = 80 s = 80 * ( 140 / 100 ) = 126 100 - 126 = 26 % answer : d" | a ) 118 , b ) 110 , c ) 112 , d ) 126 , e ) 115 | d | multiply(subtract(divide(divide(multiply(subtract(const_100, 10), add(const_100, 40)), const_100), const_100), const_1), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,const_1)|multiply(#5,const_100)| | gain | allenai/math_qa |
on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 44 centimeters assuming that 1 - inch is 2.54 centimeters ? | "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 44 cm . : 44 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 44 / ( 3.81 ) = 277 answer will be b ." | a ) 174.2 , b ) 277 , c ) 288.1 , d ) 296 , e ) 282.4 | b | multiply(divide(44, 2.54), divide(24, 1.5)) | divide(n2,n4)|divide(n1,n0)|multiply(#0,#1)| | physics | allenai/math_qa |
if p ( a ) = 2 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events . | "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 2 / 5 . 2 / 5 p ( a n b ) = 4 / 25 . b" | a ) 7 / 25 , b ) 4 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17 | b | multiply(divide(2, 5), divide(2, 5)) | divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)| | general | allenai/math_qa |
in a covering a certain distance , the speeds of a and b are in the ratio of 3 : 4 . a takes 30 minutes more than b to reach the destination . the time taken by a to reach the destination is ? | ratio of speeds = 3 : 4 ratio of times taken = 4 : 3 suppose a takes 4 x hrs and b takes 3 x hrs to reach the destination . then , 4 x - 3 x = 30 / 60 = > x = 1 / 2 time taken by a = 4 x hrs = 4 * 1 / 2 = 2 hrs . answer : c | a ) 8 hrs , b ) 9 hrs , c ) 2 hrs , d ) 2 hrs , e ) 9 hrs | c | multiply(4, divide(30, const_60)) | divide(n2,const_60)|multiply(n1,#0) | physics | allenai/math_qa |
the average age of 38 students in a group is 14 years . when teacher Γ’ β¬ β’ s age is included to it , the average increases by one . what is the teacher Γ’ β¬ β’ s age in years ? | "sol . age of the teacher = ( 39 Γ£ β 15 Γ’ β¬ β 38 Γ£ β 14 ) years = 53 years . answer c" | a ) 31 , b ) 36 , c ) 53 , d ) 58 , e ) none | c | add(38, const_1) | add(n0,const_1)| | general | allenai/math_qa |
in a club with 310 peopl , 138 play tennis , 255 play baseball , and 94 people play both sports . how many people do not pla a sport ? | take 94 off the baseball players - - > 161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 answer is e | ['a ) 9', 'b ) 8', 'c ) 4', 'd ) 10', 'e ) 11'] | e | subtract(subtract(310, 138), subtract(255, 94)) | subtract(n0,n1)|subtract(n2,n3)|subtract(#0,#1) | other | allenai/math_qa |
sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 06 : 00 and starts climbing at a constant pace . ken starts climbing only at 08 : 00 , when sari is already 800 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ? | both sari and ken climb in the same direction . speed of sari = 800 / 2 = 400 meters / hr ( since she covers 800 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 800 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 800 + 50 ) / ( 500 - 400 ) = 8.5 hrs starting from 8 : 00 , in 8.5 hrs , the time will be 16 : 30 answer ( a ) | a ) 16.3 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30 | a | add(divide(add(800, 50), subtract(500, divide(800, const_2))), 8) | add(n4,n6)|divide(n4,const_2)|subtract(n5,#1)|divide(#0,#2)|add(n2,#3) | physics | allenai/math_qa |
a man sitting in a train which is traveling at 56 kmph observes that a goods train , traveling in opposite direction , takes 15 seconds to pass him . if the goods train is 410 m long , find its speed | "explanation : relative speed = 410 / 15 m / sec = ( ( 410 / 15 ) Γ ( 18 / 5 ) ) kmph = 98 kmph . speed of goods train = ( 98 - 56 ) kmph = 42 kmph answer : option d" | a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 42 kmph , e ) 72 kmph | d | subtract(multiply(divide(410, 15), const_3_6), 56) | divide(n2,n1)|multiply(#0,const_3_6)|subtract(#1,n0)| | physics | allenai/math_qa |
if 15 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ? | explanation : let the required no of hectares be x . then men - - - hectares - - - days 15 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 15 * 30 / 24 * 80 x = 240 answer : b | a ) 127 , b ) 240 , c ) 287 , d ) 450 , e ) 281 | b | divide(multiply(36, 30), divide(multiply(15, 24), 80)) | multiply(n3,n4)|multiply(n0,n2)|divide(#1,n1)|divide(#0,#2) | physics | allenai/math_qa |
a number is doubled and 8 is added . if the resultant is trebled , it becomes 84 . what is that number ? | "solution let the number be x . then , 3 ( 2 x + 8 ) βΉ = βΊ 84 βΉ = βΊ 2 x + 8 = 28 βΉ = βΊ 2 x = 20 x = 10 . answer a" | a ) 10 , b ) 6 , c ) 8 , d ) none of these , e ) can not be determined | a | divide(subtract(84, multiply(const_3, 8)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | general | allenai/math_qa |
2 x + y = 13 | y | < = 13 for how many ordered pairs ( x , y ) that are solutions of the system above are x and y both integers ? | hi - the questions says | y | < = 13 so the values of y will range from 0 to 13 . so the values of y will be 0,1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 , 12,13 . so 14 ( e ) is the answer . remember sign does n ' t matter for y as y will always be positive . | a ) 7 , b ) 10 , c ) 12 , d ) 13 , e ) 14 | e | add(divide(add(13, 13), const_2), const_1) | add(n1,n1)|divide(#0,const_2)|add(#1,const_1) | general | allenai/math_qa |
evaluate : 11 + sqrt ( - 4 + 6 Γ 4 Γ· 3 ) = ? | "according to order of operations , inner brackets first where 6 Γ 4 Γ· 3 is first calculated since it has a multiplication and a division . 6 Γ 4 Γ· 3 = 24 Γ· 3 = 8 hence 11 + sqrt ( - 4 + 6 Γ 4 Γ· 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer d ) 13" | a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | d | add(11, sqrt(subtract(divide(multiply(6, 4), 3), 4))) | multiply(n1,n2)|divide(#0,n4)|subtract(#1,n1)|sqrt(#2)|add(n0,#3)| | general | allenai/math_qa |
in a bag containing 5 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of the balls that initiallyin the bag wereequally possible ? | "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . β΄ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b" | a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 4 , d ) 5 / 6 , e ) 6 / 7 | b | divide(add(1, add(divide(1, const_2), add(divide(1, add(1, 5)), divide(5, add(1, 5))))), add(1, 5)) | add(n0,n1)|divide(n1,const_2)|divide(n1,#0)|divide(n0,#0)|add(#2,#3)|add(#4,#1)|add(n1,#5)|divide(#6,#0)| | probability | allenai/math_qa |
of 60 applicants for a job , 28 had at least 4 years ' experience , 36 had degrees , and 6 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ? | "60 - 6 = 54 54 - 28 - 36 = - 10 then 10 are in the intersection between 4 years experience and degree . answer : a" | a ) 10 , b ) 13 , c ) 9 , d ) 7 , e ) 5 | a | add(subtract(add(28, 36), subtract(60, 6)), subtract(36, 28)) | add(n1,n3)|subtract(n0,n4)|subtract(n3,n1)|subtract(#0,#1)|add(#3,#2)| | general | allenai/math_qa |
50 % of a number is added to 120 , the result is the same number . find the number ? | "( 50 / 100 ) * x + 120 = x x = 240 answer : a" | a ) 240 , b ) 288 , c ) 1687 , d ) 997 , e ) 121 | a | divide(120, divide(120, const_100)) | divide(n1,const_100)|divide(n1,#0)| | gain | allenai/math_qa |
a shop sells 1 chocolate at the rate rupee 1 each . you can exchange 3 warppers for one chocolate . if you have rs . 15 , what is the maximum number of chocolates you can get ? | rs . 15 = 15 chocolates 15 wrappers = 5 chocolates 5 wrappers = 1 chocolate ( u have 2 wrappers with you . . ) count this wrapper with already existing wrappers = 15 + 5 + 1 + 1 = 22 chocolates . . answer : b | a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | b | add(add(add(divide(15, 3), 1), 1), 15) | divide(n3,n2)|add(n0,#0)|add(n0,#1)|add(n3,#2) | gain | allenai/math_qa |
in 1982 and 1983 , company b β s operating expenses were $ 13.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b β s profit ( revenues minus operating expenses ) from 1982 to 1983 ? | "profit in 1982 = 15.6 - 13 = 2.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 2.6 ) / 2.6 * 100 % = 46 1 / 6 % answer b" | a ) 3 % , b ) 46 1 / 6 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 % | b | subtract(const_100, divide(multiply(subtract(15.0, 13.0), const_100), subtract(18.8, 15.6))) | subtract(n3,n2)|subtract(n5,n4)|multiply(#0,const_100)|divide(#2,#1)|subtract(const_100,#3)| | general | allenai/math_qa |
the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1000 resolutions ? | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1000 resolutions . = 1000 * 2 * 22 / 7 * 22.4 = 104800 cm = 1408 m answer : d" | a ) 1077 m , b ) 804 m , c ) 978 m , d ) 1048 m , e ) 878 v | 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), 1000), 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 seller of used cars has 15 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ? | "ifno caris selected more than once then the number of clients = 15 / 3 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option e" | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15 | e | multiply(divide(15, 3), const_3) | divide(n0,n1)|multiply(#0,const_3)| | general | allenai/math_qa |
a bowl was half full of water . 4 cups of water were then added to the bowl , filling the bowl to 70 % of its capacity . how many cups of water are now in the bowl ? | lets say total volume of the container = v initial water content is half of total volume = v / 2 then 4 cups of water were added . current water content = ( v / 2 ) + 4 cups = ( 70 / 100 ) v = > v = 20 cups = > current water content is equivalent to = v / 2 + 4 cups = 20 / 2 + 4 = 14 cups ; answer : a | a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | a | multiply(divide(70, const_100), divide(multiply(4, const_100), multiply(subtract(divide(70, const_100), divide(divide(const_100, const_2), const_100)), const_100))) | divide(n1,const_100)|divide(const_100,const_2)|multiply(n0,const_100)|divide(#1,const_100)|subtract(#0,#3)|multiply(#4,const_100)|divide(#2,#5)|multiply(#0,#6) | gain | allenai/math_qa |
if m and n are positive integers and m ^ 2 + n ^ 2 = 89 , what is the value of m ^ 3 + n ^ 3 ? | "you need to integers which squared are equal 89 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 stop . the integers ca n ' t be greater than 8 or we will score above 89 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 the only pair that matches is 8 ^ 2 + 5 ^ 2 = 89 . so 8 ^ 3 + 5 ^ 3 = 637 . answer e . )" | a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 637 | e | gcd(89, const_4) | gcd(n2,const_4)| | general | allenai/math_qa |
jerry went to a shop and bought things worth rs . 30 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ? | "total cost of the items he purchased = rs . 30 given that out of this rs . 30 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % β΄ ( 30 β 30 / 100 β x ) 6 / 100 = 30 / 100 β 6 ( 30 β 0.3 β x ) = 30 β ( 30 β 0.3 β x ) = 5 β x = 30 β 0.3 β 5 = 24.7 e )" | a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 24.7 | e | subtract(30, add(multiply(divide(30, const_100), divide(const_100, 6)), divide(30, const_100))) | divide(n1,const_100)|divide(const_100,n2)|multiply(#0,#1)|add(#0,#2)|subtract(n0,#3)| | gain | allenai/math_qa |
in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 9 , 0 ) , ( 0 , - 3.5 ) , ( - 9 , 0 ) ? | "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 9 + 9 = 18 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 18 * 7 = 63 a is the answer" | a ) 63 , b ) 88 , c ) 112 , d ) 116 , e ) 120 | a | rhombus_area(multiply(9, const_2), multiply(3.5, const_2)) | multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1)| | geometry | allenai/math_qa |
canister c is 1 / 2 full of water and canister d , which has twice the capacity of canister c , is 1 / 3 full of water . if the water in canister d is poured in canister c until canister c is completely full of water , canister d will still contain what fraction of its capacity of water ? | say canister c has a capacity of 6 liters . it ' s half full , thus there can be poured 3 liters of water . canister b is 12 liters and there are 4 liters of water . we can pour 3 liters from d to c and 1 liter will still be left in d , which is 1 / 12 of its total capacity . answer : c . | a ) 0 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4 | c | subtract(divide(1, 3), multiply(divide(1, 2), divide(1, 2))) | divide(n0,n3)|divide(n0,n1)|multiply(#1,#1)|subtract(#0,#2) | general | allenai/math_qa |
a third of arun Γ’ β¬ β’ s marks in mathematics exceed a half of his marks in english by 10 . if he got 230 marks in two subjects together how many marks did he got in english ? | "let arun Γ’ β¬ β’ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 10 2 x - 3 y = 60 Γ’ β¬ Β¦ Γ’ β¬ Β¦ > ( 1 ) x + y = 230 Γ’ β¬ Β¦ Γ’ β¬ Β¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 150 and y = 80 answer is d ." | a ) 140,90 , b ) 180,60 , c ) 160,90 , d ) 150,80 , e ) none of them | d | add(divide(subtract(230, 10), add(const_1, divide(const_1, const_2))), 10) | divide(const_1,const_2)|subtract(n1,n0)|add(#0,const_1)|divide(#1,#2)|add(n0,#3)| | general | allenai/math_qa |
last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.8 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 0.8 ( x ) + 0.5 ( 1 - x ) = 0.75 0.3 x = 0.75 - 0.5 x = 0.25 / 0.3 x = 5 / 6 therefore the answer is d : 5 / 6 ." | a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16 | d | divide(subtract(0.75, 0.5), subtract(0.8, 0.5)) | subtract(n2,n0)|subtract(n1,n0)|divide(#0,#1)| | gain | allenai/math_qa |
3 containers a , b and c are having mixtures of milk and water in the ratio of 1 : 5 and 3 : 5 and 5 : 7 respectively . if the capacities of the containers are in the ratio of all the 3 containers are in the ratio 5 : 4 : 5 , find the ratio of milk to water , if the mixtures of all the 3 containers are mixed together . | assume that there are 500400 and 500 liters respectively in the 3 containers . then , we have , 83.33 , 150 and 208.33 liters of milk in each of the three containers . thus , the total milk is 441.66 liters . hence , the amount of water in the mixture is 1400 - 441.66 = 958.33 liters . hence , the ratio of milk to water is 441.66 : 958.33 = > 53 : 115 ( using division by . 3333 ) the calculation thought process should be ( 441 * 2 + 2 ) : ( 958 * 3 + 1 ) = 1325 : 2875 dividing by 25 = > 53 : 115 . answer a 53 : 115 | a ) 53 : 115 , b ) 55 : 115 , c ) 115 : 55 , d ) 5 : 115 , e ) 115 : 53 | a | divide(add(add(multiply(divide(1, add(1, 5)), 5), multiply(divide(3, add(3, 5)), 4)), multiply(divide(5, add(5, 7)), 5)), subtract(add(add(5, 4), 5), add(add(multiply(divide(1, add(1, 5)), 5), multiply(divide(3, add(3, 5)), 4)), multiply(divide(5, add(5, 7)), 5)))) | add(n1,n2)|add(n0,n2)|add(n2,n6)|add(n2,n9)|add(n2,#3)|divide(n1,#0)|divide(n0,#1)|divide(n2,#2)|multiply(n2,#5)|multiply(n9,#6)|multiply(n2,#7)|add(#8,#9)|add(#11,#10)|subtract(#4,#12)|divide(#12,#13) | other | allenai/math_qa |
sum of the squares of 3 no . is 156 and the sum of their products taken two at a time is 50 . find the sum ? | ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 156 + 2 * 50 a + b + c = Γ’ Λ Ε‘ 256 = 16 answer b | a ) 18 , b ) 16 , c ) 19 , d ) 21 , e ) 15 | b | sqrt(add(156, multiply(50, const_2))) | multiply(n2,const_2)|add(n1,#0)|sqrt(#1) | general | allenai/math_qa |
what is the value of β 16 % ? | "explanation : br > β 16 % = β 14 / β 100 = 4 / 10 = 40 / 100 = 40 % correct answer is c ) 40 %" | a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 % | c | circle_area(divide(16, multiply(const_2, const_pi))) | multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)| | gain | allenai/math_qa |
there are 2000 students in a school and among them 10 % of them attends chess class . 50 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ? | "10 % of 2000 gives 200 . so 200 attends chess and 50 % of 200 gives 100 so 100 enrolled for swimming answer : c" | a ) 1 , b ) 10 , c ) 100 , d ) 50 , e ) 20 | c | divide(multiply(divide(multiply(10, 2000), const_100), 50), const_100) | multiply(n0,n1)|divide(#0,const_100)|multiply(n2,#1)|divide(#2,const_100)| | gain | allenai/math_qa |
company p had 15 percent more employees in december than it had in january . if company p had 480 employees in december , how many employees did it have in january ? | "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 480 j = 480 / 1.15 j = 48,000 / 115 = 417 thus b is the correct answer ." | a ) 391 , b ) 417 , c ) 410 , d ) 423 , e ) 445 | b | divide(480, add(const_1, divide(15, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | gain | allenai/math_qa |
a worker earns $ 24 on the first day and spends $ 18 on the second day . the worker earns $ 24 on the third day and spends $ 18 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 48 ? | every two days , the net total is $ 6 . after 8 days , the worker will have $ 24 . on day 9 , the worker will receive $ 24 for a net total of $ 48 . the answer is c . | a ) 6 , b ) 7 , c ) 9 , d ) 12 , e ) 16 | c | add(multiply(divide(24, subtract(24, 18)), const_2), const_1) | subtract(n0,n1)|divide(n0,#0)|multiply(#1,const_2)|add(#2,const_1) | physics | allenai/math_qa |
if a farmer sells 5 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 10 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ? | say farmer has n goat and he is good for d days . : - we have 3 equations given in question : - ( n - 5 ) * d + 4 = ( n + 10 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 10 d - 3 n = 30 4 n - 5 d = 20 = > n = 20 ans b it is ! | a ) 12 , b ) 20 , c ) 48 , d ) 55 , e ) 60 | b | multiply(subtract(multiply(3, 4), 10), 10) | multiply(n1,n3)|subtract(#0,n2)|multiply(n2,#1) | general | allenai/math_qa |
in the fifth grade at parkway elementary school there are 420 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? | "total students = 420 boys = 320 , girls = 100 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 100 - 35 = 65 . correct option : d" | a ) 69 . , b ) 73 . , c ) 81 , d ) 65 , e ) 108 | d | subtract(subtract(420, 320), subtract(250, divide(multiply(250, 86), const_100))) | multiply(n2,n3)|subtract(n0,n1)|divide(#0,const_100)|subtract(n2,#2)|subtract(#1,#3)| | gain | allenai/math_qa |
how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ? | "d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec answer a" | a ) 16.8 , b ) 17.8 , c ) 15.9 , d ) 13.2 , e ) 12.4 | a | divide(add(110, 170), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics | allenai/math_qa |
ram , who is half as efficient as krish , will take 27 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ? | number of days taken by ram to complete task = 27 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 27 days is 27 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 27 w / 3 w = 9 days answer c | a ) 16 days , b ) 12 days , c ) 9 days , d ) 6 days , e ) 18 days | c | inverse(add(divide(const_1, 27), divide(const_1, divide(27, const_2)))) | divide(const_1,n0)|divide(n0,const_2)|divide(const_1,#1)|add(#0,#2)|inverse(#3) | physics | allenai/math_qa |
there are 14 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ? | "the total number of stations = 16 from 16 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 16 p β ways . 16 p β = 16 * 15 = 240 . answer : e" | a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 240 | e | multiply(add(14, const_1), add(add(14, const_1), const_1)) | add(n0,const_1)|add(#0,const_1)|multiply(#0,#1)| | physics | allenai/math_qa |
a man can row downstream at 16 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ? | "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 16 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 26 = > x = 13 , y = 3 . answer : a" | a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9 | a | divide(divide(add(16, 10), const_2), const_2) | add(n0,n1)|divide(#0,const_2)|divide(#1,const_2)| | physics | allenai/math_qa |
if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 3 = 1 / ( 2 * ( 10 ) ^ 3 ) , then m = | "1 / 5 ^ m * 1 / 4 ^ 3 = 2 * 1 / 2 ^ 3 * 5 ^ 3 * 8 2 ^ 3 * 5 ^ 3 * 8 / 4 ^ 3 = 5 ^ m or 5 ^ 3 = 5 ^ m m = 3 b" | a ) 4 , b ) 3 , c ) 1 , d ) 6 , e ) 8 | b | subtract(add(multiply(divide(1, 4), 2), multiply(divide(1, 5), 2)), divide(5, 2)) | divide(n0,n3)|divide(n0,n1)|divide(n1,n6)|multiply(n6,#0)|multiply(n6,#1)|add(#3,#4)|subtract(#5,#2)| | general | allenai/math_qa |
16.036 divided by 0.04 gives : | = 16.036 / 0.04 = 1603.6 / 4 = 400.9 answer is d . | a ) 40.09 , b ) 4.06 , c ) 40.06 , d ) 400.9 , e ) 400.6 | d | divide(16.036, 0.04) | divide(n0,n1) | general | allenai/math_qa |
robert ate 12 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ? | 12 - 3 = 9 . answer is c | a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2 | c | subtract(12, 3) | subtract(n0,n1)| | general | allenai/math_qa |
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