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in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7500 , what was the number of valid votes that the other candidate got ? | "explanation : total number of votes = 7500 given that 20 % of percentage votes were invalid = > valid votes = 80 % total valid votes = 7500 × ( 80 / 100 ) 1 st candidate got 55 % of the total valid votes . hence the 2 nd candidate should have got 45 % of the total valid votes = > valid votes that 2 nd candidate got = total valid votes × ( 45 / 100 ) = 7500 × ( 80 / 100 ) × ( 45 / 100 ) = 75 × 45 × 45 = 75 × 4 × 9 = 300 × 9 = 2700 answer : option b" | a ) 2800 , b ) 2700 , c ) 2100 , d ) 2500 , e ) none of these | b | multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 7500) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(n2,#4)| | gain | allenai/math_qa |
a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 12 miles per gallon , and from town b to town c , the car averaged 11 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ? | "ans is b given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 12 ) + ( x / 11 ) ) = 15.3 ( formula avg speed = total distance / total time )" | a ) 13 , b ) 13.5 , c ) 14 , d ) 14.5 , e ) 15.3 | b | divide(add(multiply(11, const_10), divide(multiply(11, const_10), const_2)), add(divide(multiply(11, const_10), 12), divide(divide(multiply(11, const_10), const_2), 11))) | multiply(n1,const_10)|divide(#0,const_2)|divide(#0,n0)|add(#1,#0)|divide(#1,n1)|add(#2,#4)|divide(#3,#5)| | general | allenai/math_qa |
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ? | "let the total number of workers be x . then , 8000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 2000 x = 36000 = x = 18 . answer : c" | a ) a ) 23 , b ) b ) 21 , c ) c ) 18 , d ) d ) 56 , e ) e ) 12 | c | add(6, divide(multiply(6, subtract(12000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | general | allenai/math_qa |
the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 6 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ? | "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 6 = 74 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 74 + 4 = 78 d" | a ) 45 , b ) 65 , c ) 75 , d ) 78 , e ) 90 | d | subtract(multiply(80, const_4), subtract(multiply(79, const_4), add(const_3.0, subtract(multiply(80, const_4), multiply(84, 6))))) | multiply(n1,const_4)|multiply(n3,const_4)|multiply(n0,const_3)|subtract(#0,#2)|add(n2,#3)|subtract(#1,#4)|subtract(#0,#5)| | general | allenai/math_qa |
in the first 10 overs of a cricket game , the run rate was only 4.8 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ? | "required run rate = 282 - ( 4.8 x 10 ) = 234 234 / 40 = 5.85 b )" | a ) 4.25 , b ) 5.85 , c ) 6.25 , d ) 7 , e ) 7.5 | b | divide(subtract(282, multiply(10, 4.8)), 40) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain | allenai/math_qa |
yesterday ' s closing prices of 1980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ? | lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer . | a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694 | b | subtract(1980, divide(1980, add(divide(add(const_100, 20), const_100), const_1))) | add(n1,const_100)|divide(#0,const_100)|add(#1,const_1)|divide(n0,#2)|subtract(n0,#3) | gain | allenai/math_qa |
you hold some gold in a vault as an investment . over the past year the price of gold increases by 30 % . in order to keep your gold in the vault , you must pay 2 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year . | "( 100 % + 30 % ) * ( 100 % - 2 % ) = 130 * 0.98 = 127.4 % an increase of 27.4 % your gold holdings have increased in value by 27.4 % . the answer is b" | a ) 27.5 % , b ) 27.4 % , c ) 27.6 % , d ) 27.7 % , e ) 28.4 % | b | subtract(30, divide(30, 2)) | divide(n0,n1)|subtract(n0,#0)| | gain | allenai/math_qa |
if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 3 a ) / ( c - a ) = | "let ' s say c = 2 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 2 answer d ( hopefully ) ) )" | a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5 | d | multiply(subtract(5, 3), 3) | subtract(n1,n2)|multiply(n2,#0)| | general | allenai/math_qa |
500 x 223 + 500 x 77 = ? | "= 8796 x ( 223 + 77 ) ( by distributive law ) = 500 x 300 = 150000 answer is c" | a ) 2736900 , b ) 2738800 , c ) 150000 , d ) 2716740 , e ) none of them | c | multiply(500, power(223, 500)) | power(n1,n2)|multiply(n0,#0)| | general | allenai/math_qa |
in what time will a train 140 m long cross an electric pole , it its speed be 144 km / hr ? | "speed = 144 * 5 / 18 = 40 m / sec time taken = 140 / 40 = 3.5 sec . answer : a" | a ) 3.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) 6 sec | a | divide(140, multiply(144, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics | allenai/math_qa |
which greatest possible length can be used to measure exactly 15 meter 75 cm , 11 meter 25 cm and 7 meter 65 cm | "explanation : convert first all terms into cm . i . e . 1575 cm , 1125 cm , 765 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 255 . option b" | a ) 45 cm , b ) 255 cm , c ) 244 cm , d ) 55 cm , e ) 280 cm | b | floor(divide(add(multiply(15, const_100), 75), add(multiply(11, const_100), 25))) | multiply(n0,const_100)|multiply(n2,const_100)|add(n1,#0)|add(n3,#1)|divide(#2,#3)|floor(#4)| | physics | allenai/math_qa |
find the area of trapezium whose parallel sides are 30 cm and 12 cm long , and the distance between them is 16 cm ? | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 30 + 12 ) * ( 16 ) = 336 cm 2 answer : d" | a ) 288 cm 2 , b ) 277 cm 2 , c ) 285 cm 2 , d ) 336 cm 2 , e ) 340 cm 2 | d | quadrilateral_area(16, 12, 30) | quadrilateral_area(n2,n1,n0)| | physics | allenai/math_qa |
length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? | "let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m b" | a ) 50 m , b ) 60 m , c ) 65 m , d ) 75 m , e ) 80 m | b | divide(add(divide(5300, 26.50), multiply(const_2, 20)), const_4) | divide(n2,n1)|multiply(n0,const_2)|add(#0,#1)|divide(#2,const_4)| | physics | allenai/math_qa |
the number of employees in obelix menhir co . is a prime number and is less than 300 . the ratio of the number of employees who are graduates and above , to that of employees who are not , can possibly be : - | explanation : going through the given options , option 1 : - 101 : 88 = > 189 . [ divisible by 3 ] option 2 : - 87 : 100 = > 187 . [ divisible by 11 ] option 3 : - 85 : 98 = > 183 . [ divisible by 3 ] option 4 : - 97 : 84 = > 181 . [ prime number ] hence , only 181 is the prime number i . e the total number of employee in the company and the required ratio is 97 : 84 . answer : e | a ) 101 : 88 , b ) 87 : 100 , c ) 110 : 111 , d ) 85 : 98 , e ) 97 : 84 | e | divide(subtract(const_100, divide(300, const_100)), subtract(subtract(const_100, divide(300, const_100)), add(const_10, divide(300, const_100)))) | divide(n0,const_100)|add(#0,const_10)|subtract(const_100,#0)|subtract(#2,#1)|divide(#2,#3) | general | allenai/math_qa |
find the average of all the numbers between 6 and 34 which are divisible by 5 ? | "average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = 20 . answer : b" | a ) 32 , b ) 20 , c ) 28 , d ) 11 , e ) 18 | b | divide(add(add(6, const_4), subtract(34, const_4)), const_2) | add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)| | general | allenai/math_qa |
a zeebra chases a tiger 5 hours after the tiger runs . zeebra takes 6 hours to reach the tiger . if the average speed of the zeebra is 55 kmph , what s the average speed of the tiger ? | tiger take 11 hours and zeebra take 6 hours . . . then distance chased by them is 55 * 6 . so speed of tiger is ( 55 * 6 ) / 11 = 30 kmph . answer is c | a ) 35 kmph , b ) 32 kmph , c ) 30 kmph , d ) 31 kmph , e ) 20 kmph | c | divide(multiply(55, 6), add(5, 6)) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0) | physics | allenai/math_qa |
what least value should be replaced by * in 2631 * 4 so the number become divisible by 3 | "explanation : trick : number is divisible by 3 , if sum of all digits is divisible by 3 , so ( 2 + 6 + 3 + 1 + * + 4 ) = 16 + * should be divisible by 9 , 16 + 2 will be divisible by 2 , so that least number is 2 . answer : option d" | a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7 | d | subtract(4, subtract(4, 4)) | subtract(n1,n1)|subtract(n1,#0)| | general | allenai/math_qa |
a , b and c started a partnership business by investing rs . 24000 , rs . 32000 , rs . 36000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ? | "a : b : c = 24000 : 32000 : 36000 = 6 : 8 : 9 let total profit = p then p ã — 9 / 23 = 36000 p = ( 36000 ã — 23 ) / 9 = 92000 answer is d ." | a ) 70000 , b ) 60000 , c ) 80000 , d ) 92000 , e ) 50000 | d | add(add(multiply(divide(24000, 36000), 36000), multiply(divide(32000, 36000), 36000)), 36000) | divide(n0,n2)|divide(n1,n2)|multiply(n3,#0)|multiply(n3,#1)|add(#2,#3)|add(n3,#4)| | gain | allenai/math_qa |
if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 2 other contributions made before john ' s , what is the size of his donation ? | "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 2 people . so $ 50 . but , he also has to put in the average for himself ( the threeth person ) , so add $ 75 . so $ 125 is your answer . answer a" | a ) $ 125 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450 | a | add(subtract(multiply(add(2, const_1), 75), multiply(add(2, const_1), 50)), 50) | add(n2,const_1)|multiply(n1,#0)|multiply(n0,#0)|subtract(#1,#2)|add(n0,#3)| | general | allenai/math_qa |
running at the same constant rate , 16 identical machines can produce a total of 32 shirt per minute . at this rate , how many shirt could 8 such machines produce in 10 minutes ? | "let ' s take the approach that uses the answer choices to eliminate wasted time . 32 / 16 = 2 shirt per minute per machine . 8 machines = 16 per minute . 10 minutes worth = 160 shirt . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d ." | a ) 911 , b ) 100 , c ) 101 , d ) 160 , e ) 785 | d | multiply(multiply(divide(32, 16), 10), 8) | divide(n1,n0)|multiply(n3,#0)|multiply(n2,#1)| | gain | allenai/math_qa |
a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 80 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ? | "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 3 hours to travel 240 km , so c leaves 5 hours after a . the answer is d ." | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | d | subtract(40, 30) | subtract(n1,n0)| | physics | allenai/math_qa |
for how many values of n , is | | | n - 5 | - 10 | - 5 | = 2 ? ( those ls are mods ) | i think its 8 | | | n - 5 | - 10 | - 5 | = 2 let | n - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so ' a ' has four solutions 13 , 7 , 17 and 3 for a = 13 ; x has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d | a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8 | d | power(2, const_3) | power(n3,const_3) | general | allenai/math_qa |
a runs twice as fast as b and gives b a start of 60 m . how long should the racecourse be so that a and b might reach in the same time ? | ratio of speeds of a and b is 2 : 1 b is 60 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 60 m is 60 / 1 = 60 m so the total time taken by a and b to reach = 2 * 60 = 120 m answer : a | a ) 120 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above | a | multiply(60, const_2) | multiply(n0,const_2) | physics | allenai/math_qa |
what is the unit digit in the product ( 3 ^ 68 x 6 ^ 59 x 7 ^ 71 ) ? | "unit digit in 3 ^ 4 = 1 = > unit digit in ( 3 ^ 4 ) ^ 16 = 1 therefore , unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) ^ 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 = 1 = > unit digit in ( 7 ^ 4 ) ^ 17 is 1 unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) ^ 17 x 7 ^ 3 ] = ( ( 1 x 3 ) = 3 therefore , required digit = unit digit in ( 3 x 6 x 3 ) = 4 answer is c" | a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) none of them | c | subtract(multiply(multiply(3, 6), 3), subtract(multiply(multiply(3, 6), 3), const_4)) | multiply(n0,n2)|multiply(n0,#0)|subtract(#1,const_4)|subtract(#1,#2)| | general | allenai/math_qa |
in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 100 bricks in the wall , how many bricks does the bottom row contain ? | "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 100 5 x - 10 = 100 5 x = 90 x = 18 answer : a" | a ) 18 , b ) 16 , c ) 17 , d ) 15 , e ) 19 | a | divide(subtract(subtract(subtract(subtract(100, const_1), const_2), const_3), const_4), 5) | subtract(n1,const_1)|subtract(#0,const_2)|subtract(#1,const_3)|subtract(#2,const_4)|divide(#3,n0)| | general | allenai/math_qa |
imagine an analog clock set to 12 o ' clock . note that the hour and minute hands overlap . how many times each day do both the hour and minute hands overlap ? how would you determine the exact times of the day that this occurs ? | 22 times in a day . 12,1 hours 60 / 11 minutes , 2 hours 120 / 11 minutes , . . . so on till 12 ( 11 hours 660 / 11 minutes ) answer : c | a ) 11 , b ) 12 , c ) 22 , d ) 24 , e ) 44 | c | multiply(subtract(12, const_1), const_2) | subtract(n0,const_1)|multiply(#0,const_2) | physics | allenai/math_qa |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , the how old is b ? | "explanation : 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 = 42 ⇒ 5 x = 40 ⇒ x = 8 . hence , b ' s age = 2 x = 16 years . answer : a" | a ) 16 , b ) 9 , c ) 8 , d ) 11 , e ) 10 | a | divide(multiply(subtract(42, 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 |
if a = 105 and a ^ 3 = 21 × 25 × 45 × b , what is the value of b ? | "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × b = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x b = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b b = 7 ^ 2 = 49 answer d" | a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54 | d | divide(power(105, 3), multiply(multiply(21, 25), 45)) | multiply(n2,n3)|power(n0,n1)|multiply(n4,#0)|divide(#1,#2)| | general | allenai/math_qa |
jack and christina are standing 360 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 5 feet per second and christina walks in a straight line toward jack at a constant speed of 7 feet per second . lindy runs at a constant speed of 12 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ? | "the relative speed of jack and christina is 5 + 7 = 12 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 360 / 12 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 12 * 30 = 360 feet . answer : d ." | a ) 270 , b ) 300 , c ) 330 , d ) 360 , e ) 390 | d | multiply(divide(360, add(5, 7)), 12) | add(n1,n2)|divide(n0,#0)|multiply(n3,#1)| | physics | allenai/math_qa |
if the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline , by how much % should he reduce the quantity of gasoline that he buys ? | explanatory answer let the price of 1 litre of gasoline be $ x and let ron initially buy ' y ' litres of gasoline . therefore , he would have spent $ xy on gasoline . when the price of gasoline increases by 25 % , the new price per litre of gasoline is 1.25 x . ron intends to increase the amount he spends on gasoline by 15 % . i . e . , he is willing to spend xy + 15 % of xy = 1.15 xy let the new quantity of gasoline that he can get be ' q ' . then , 1.25 x * q = 1.15 xy or q = 1.15 xy / 1.25 x = 0.92 y . as the new quantity that he can buy is 0.92 y , he gets 0.08 y lesser than what he used to get earlier . or a reduction of 8 % . the correct choice is ( c ) | a ) 10 % , b ) 12.5 % , c ) 8 % , d ) 12 % , e ) 6.66 % | c | multiply(subtract(const_1, divide(add(const_1, divide(15, const_100)), add(const_1, divide(25, const_100)))), const_100) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|divide(#2,#3)|subtract(const_1,#4)|multiply(#5,const_100) | general | allenai/math_qa |
the volumes of two cones are in the ratio 1 : 40 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ? | "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 40 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 8 / 5 i . e . h 1 : h 2 = 8 : 5 answer : a" | a ) 8 : 5 , b ) 8 : 9 , c ) 2 : 2 , d ) 8 : 2 , e ) 2 : 8 | a | divide(divide(1, 40), power(divide(1, 2), 2)) | divide(n0,n1)|divide(n0,n3)|power(#1,n3)|divide(#0,#2)| | geometry | allenai/math_qa |
if the price of a certain computer increased 30 percent from d dollars to 351 dollars , then 2 d = | "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 270 i . e . 2 d = 2 * 270 = 540 answer : option a" | a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700 | a | multiply(divide(351, divide(add(const_100, 30), const_100)), 2) | add(n0,const_100)|divide(#0,const_100)|divide(n1,#1)|multiply(n2,#2)| | general | allenai/math_qa |
a and b are two partially filled buckets of water . if 4 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 5 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ? | "let a contains a , b contains b liters so , ( a - 4 ) / ( b + 4 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 5 ) / ( a + 5 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 47 / 5 ans : ( a )" | a ) 47 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23 | a | divide(multiply(add(add(4, const_3), const_2), divide(4, const_2)), add(const_2, divide(const_1, const_2))) | add(n0,const_3)|divide(n0,const_2)|divide(const_1,const_2)|add(#0,const_2)|add(#2,const_2)|multiply(#3,#1)|divide(#5,#4)| | general | allenai/math_qa |
the number which exceeds 16 % of it by 126 is : | "solution solution let the number be x . x - 16 % of x = 126 x - 16 / 100 x = 126 x - 4 / 25 x = 126 21 / 25 x = 126 x = ( 126 x 25 / 21 ) = 150 answer a" | a ) 150 , b ) 52 , c ) 58 , d ) 60 , e ) 62 | a | divide(multiply(126, const_100), subtract(const_100, 16)) | multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)| | gain | allenai/math_qa |
a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ? | "lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2500 so 200 * x + 230 * x = 2500 = > 430 x = 2500 = > x is approximately equal to 6 . so total people is 2 * 6 = 12 we are not taking 12 as answer because say 11 th person has minimum of 180 weight then 200 * 6 + 230 * 6 = 2580 ( which is more than 2500 ) answer e ." | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | e | multiply(divide(multiply(const_10, 200), add(200, 230)), const_2) | add(n1,n2)|multiply(n1,const_10)|divide(#1,#0)|multiply(#2,const_2)| | general | allenai/math_qa |
a train 150 meters long completely crosses a 320 meters long bridge in 40 seconds . what is the speed of the train is ? | "s = ( 150 + 320 ) / 40 = 470 / 40 * 18 / 5 = 42 answer : b" | a ) 32 , b ) 42 , c ) 54 , d ) 66 , e ) 09 | b | divide(divide(add(150, 320), const_1000), divide(40, const_3600)) | add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)| | physics | allenai/math_qa |
a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 340 million , approximately what was the percent increase in sales ? | "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 340 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 340 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 340 ) / 340 ] x 100 65 / 340 x 100 ≈ 13 % . the answer is e ." | a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 13 % | e | multiply(divide(subtract(385, 340), 340), const_100) | subtract(n0,n1)|divide(#0,n1)|multiply(#1,const_100)| | general | allenai/math_qa |
convert 500 miles into meters ? | "1 mile = 1609.34 meters 500 mile = 500 * 1609.34 = 804670 meters answer is c" | a ) 784596 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 864520 | c | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 500), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)| | physics | allenai/math_qa |
an agent , gets a commission of 5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth | "explanation : let the total sale be rs . x . then , 5 % . of x = 12.50 < = > ( 5 / 100 * x ) = 125 / 10 < = > x = 250 . answer : d" | a ) 333 , b ) 500 , c ) 887 , d ) 250 , e ) 132 | d | divide(12.50, divide(5, const_100)) | divide(n0,const_100)|divide(n1,#0)| | gain | allenai/math_qa |
a baseball card decreased in value 30 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ? | "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.7 = 70 after second year price = 70 * 0.9 = 63 final decrease = [ ( 100 - 63 ) / 100 ] * 100 = 37 % correct answer - b" | a ) 28 % , b ) 37 % , c ) 32 % , d ) 36 % , e ) 72 % | b | subtract(const_100, multiply(multiply(subtract(const_1, divide(10, const_100)), subtract(const_1, divide(30, const_100))), const_100)) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)| | gain | allenai/math_qa |
the average of 13 numbers is 60 . average of the first 7 of them is 56 and that of the last 7 is 61 . find the 8 th number ? | "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 56 = 392 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 392 - 780 = 39 . answer : a" | a ) 39 , b ) 83 , c ) 45 , d ) 53 , e ) 64 | a | subtract(multiply(8, 61), subtract(multiply(13, 60), multiply(56, 7))) | multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)| | general | allenai/math_qa |
tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 54000 after completion of one year . what will be jose ' s share of profit ? | sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 54000 = 30000 e | a ) 20000 , b ) 24000 , c ) 34000 , d ) 35000 , e ) 30000 | e | multiply(54000, subtract(const_1, divide(multiply(30000, multiply(const_2, multiply(const_2, const_3))), add(multiply(45000, subtract(multiply(const_2, multiply(const_2, const_3)), 2)), multiply(30000, multiply(const_2, multiply(const_2, const_3))))))) | multiply(const_2,const_3)|multiply(#0,const_2)|multiply(n0,#1)|subtract(#1,n1)|multiply(n2,#3)|add(#4,#2)|divide(#2,#5)|subtract(const_1,#6)|multiply(n3,#7) | gain | allenai/math_qa |
a train 150 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 150 * 3 / 55 = 8 sec . answer : e" | a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 8 | e | divide(150, multiply(add(60, 6), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics | allenai/math_qa |
a person has 12004 coins of silver . how much would he need to add so that he can distribute equally among his 7 children in whole numbers ? | he would need to add one coin more so 12005 is fully divisible by 7 and each would get 1715 coins . so the correct answer is a | a ) 1 coin , b ) 2 coins , c ) 3 coins , d ) 4 coins , e ) coins | a | subtract(multiply(add(floor(divide(12004, 7)), const_1), 7), 12004) | divide(n0,n1)|floor(#0)|add(#1,const_1)|multiply(n1,#2)|subtract(#3,n0) | general | allenai/math_qa |
when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum r of all possible 2 - digit remainders for x / y ? | "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . r = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b" | a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784 | b | divide(59.32, subtract(2, floor(2))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | general | allenai/math_qa |
what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 % p . a . ? | "amount = [ 25000 * ( 1 + 12 / 100 ) 3 ] = 25000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 35123.20 - 25000 ) = rs . 10123.20 answer : c" | a ) rs . 10123.77 , b ) rs . 10123.21 , c ) rs . 10123.20 , d ) rs . 10123.28 , e ) rs . 10123.21 | c | subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(12, const_100)), 3)), multiply(multiply(const_4, const_100), const_100)) | divide(n2,const_100)|multiply(const_100,const_4)|add(#0,const_1)|multiply(#1,const_100)|power(#2,n1)|multiply(#3,#4)|subtract(#5,#3)| | gain | allenai/math_qa |
a family pays $ 900 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ? | "assuming the medical expenses are $ 1000 or more , the family pays $ 900 + $ 400 = $ 1300 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 700 when the medical expenses are $ 1700 . the answer is e ." | a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,500 , e ) $ 1,700 | e | subtract(1,000, 900) | subtract(n2,n0)| | general | allenai/math_qa |
a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 4 cubic feet . if a large block has twice the width , twice the depth , and twice the length of a normal block , what is the volume of cheese in a large block in cubic feet ? | volume of cube = lbh = 4 new cube l , b , h are increases of 2 l , 2 b , 2 h new volume of cube = 2 l * 2 b * 2 h = 8 * lbh = 8 * 4 = 32 answer : d | ['a ) 16', 'b ) 20', 'c ) 36', 'd ) 32', 'e ) 28'] | d | multiply(multiply(multiply(const_2, const_2), const_2), 4) | multiply(const_2,const_2)|multiply(#0,const_2)|multiply(n0,#1) | geometry | allenai/math_qa |
what is the sum of all remainders obtained when the first 130 natural numbers are divided by 9 ? | "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 412 . answer : d ." | a ) 397 , b ) 401 , c ) 403 , d ) 412 , e ) 399 | d | add(const_3, multiply(divide(subtract(130, reminder(130, 9)), 9), add(add(add(const_1, const_2), const_3), add(add(const_1, const_4), add(const_4, add(add(const_1, const_2), const_3)))))) | add(const_1,const_2)|add(const_1,const_4)|reminder(n0,n1)|add(#0,const_3)|subtract(n0,#2)|add(#3,const_4)|divide(#4,n1)|add(#1,#5)|add(#3,#7)|multiply(#8,#6)|add(#9,const_3)| | general | allenai/math_qa |
find the average of all the numbers between 6 and 34 which are divisible by 6 . | "solution average = ( ( 12 + 18 + 24 + 30 ) / 5 ) = 84 / 4 = 21 . answer e" | a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 21 | e | divide(add(add(6, const_4), subtract(34, const_4)), const_2) | add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)| | general | allenai/math_qa |
a shopkeeper cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 20 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 10 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage . | anyways , one can infer that he ' steals ' 20 % from suppliers and then charges 10 % extra to customers so basically 1.2 * 1.1 = 1.32 given that 1 is start point , we get 32 % more hence answer is b | a ) 20 % , b ) 32 % , c ) 23.365 % , d ) 22.109 % , e ) 2 % | b | subtract(multiply(add(20, const_100), divide(add(10, const_100), const_100)), const_100) | add(n0,const_100)|add(n1,const_100)|divide(#1,const_100)|multiply(#0,#2)|subtract(#3,const_100) | gain | allenai/math_qa |
the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 9 percent , what was the annual interest rate last year ? | "9 = 1.1 * x x = 8.18 % answer c )" | a ) 1 % , b ) 1.1 % , c ) 8.18 % , d ) 10 % , e ) 10.8 % | c | divide(multiply(9, const_100), add(9, const_100)) | add(n1,const_100)|multiply(n1,const_100)|divide(#1,#0)| | gain | allenai/math_qa |
in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 14 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ? | "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,14 = 14 / 100 x = 80 * 14 / 100 x = 11.2 11.2 / 10 = 1,12 = 112 % , answer b" | a ) 80 % , b ) 112 % , c ) 120 % , d ) 124.2 % , e ) 138 % | b | multiply(divide(multiply(14, subtract(const_1, divide(20, const_100))), 10), const_100) | divide(n3,const_100)|subtract(const_1,#0)|multiply(n4,#1)|divide(#2,n1)|multiply(#3,const_100)| | gain | allenai/math_qa |
before 2 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ? | a - 2 = 4 ( b - 2 ) - - > a - 4 b = - 6 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 14 - - > a = 3 ( 18 ) = 50 a - b = 50 - 14 = 36 answer : a | a ) 36 , b ) 42 , c ) 54 , d ) 60 , e ) 64 | a | subtract(subtract(multiply(4, add(subtract(multiply(4, 3), 4), subtract(multiply(4, 2), 2))), subtract(multiply(4, 2), 2)), add(subtract(multiply(4, 3), 4), subtract(multiply(4, 2), 2))) | multiply(n1,n2)|multiply(n0,n1)|subtract(#0,n1)|subtract(#1,n0)|add(#2,#3)|multiply(n1,#4)|subtract(#5,#3)|subtract(#6,#4)| | general | allenai/math_qa |
the average age of one class strength 32 students is 16 yrs . if the staff ' s age is also included , the average increases by one year . find the age of the staff | total age of students = > 32 × 16 = 512 yrs total age inclusive staff = 33 × ( 16 + 1 ) = 561 = > staff ' s age 561 - 512 = 49 yrs answer c | a ) 50 , b ) 52 , c ) 49 , d ) 32 , e ) 35 | c | subtract(multiply(add(32, const_1), add(16, const_1)), multiply(32, 16)) | add(n0,const_1)|add(n1,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2) | general | allenai/math_qa |
a can do a piece of work in 20 days , b can do a piece of work in 12 days , both are working together for 3 days after a left the job , then how many days b requires to complete the remaining work ? | first take lcm of ( 20,12 ) = 60 ; total work = 60 ; a ' s one day work = 60 / 20 = 3 ; b ' s one day work = 60 / 12 = 5 ; one day work of both a + b = 3 + 5 = 8 ; total work completed in 3 days = 8 * 3 = 24 ; remaining work is = 60 - 24 = 36 ; remaining work completed by b in = 36 / 12 = 3 days . answer = c | a ) 6 days , b ) 5 days , c ) 3 days , d ) 7 days , e ) 12 days | c | floor(add(inverse(multiply(subtract(inverse(add(divide(const_1, 20), divide(const_1, 12))), 3), divide(const_1, 12))), const_1)) | divide(const_1,n1)|divide(const_1,n0)|add(#1,#0)|inverse(#2)|subtract(#3,n2)|multiply(#0,#4)|inverse(#5)|add(#6,const_1)|floor(#7) | physics | allenai/math_qa |
three cubes of metal whose edges are 9 , 12 and 21 cm respectively , are melted and one new cube is made . find the edge of the new cube ? | "93 + 123 + 213 = a 3 = > a = 22.7 answer : b" | a ) 28 , b ) 22.7 , c ) 66 , d ) 18 , e ) 99 | b | power(add(add(volume_cube(9), volume_cube(12)), volume_cube(21)), const_0_33) | volume_cube(n0)|volume_cube(n1)|volume_cube(n2)|add(#0,#1)|add(#3,#2)|power(#4,const_0_33)| | physics | allenai/math_qa |
a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose their own dress ? | answer : b | a ) 22 , b ) 87 , c ) 29 , d ) 26 , e ) 191 | b | divide(choose(const_2, const_1), factorial(3)) | choose(const_2,const_1)|factorial(n0)|divide(#0,#1)| | probability | allenai/math_qa |
john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 15 , what was the price before the first discount ? | "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 15 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 15 solve for x x = $ 26.66 correct answer d" | a ) $ 45.10 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 26.66 , e ) $ 65.23 | d | divide(multiply(multiply(const_100, const_100), 15), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25))) | multiply(const_100,const_100)|subtract(const_100,n0)|multiply(n2,#0)|multiply(#1,const_100)|multiply(n0,#1)|subtract(#3,#4)|divide(#2,#5)| | gain | allenai/math_qa |
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces ) | "25 / 4 ÷ 4 = 25 / 16 pounds in each container 25 / 16 pounds * 16 ounces / pound = 25 ounces in each container the answer is b ." | a ) 22 , b ) 25 , c ) 28 , d ) 31 , e ) 34 | b | divide(multiply(divide(25, 4), 16), 4) | divide(n0,n1)|multiply(n4,#0)|divide(#1,n2)| | general | allenai/math_qa |
find the principle on a certain sum of money at 7 % per annum for 2 2 / 5 years if the amount being rs . 1120 ? | "1120 = p [ 1 + ( 7 * 12 / 5 ) / 100 ] p = 958.90 answer : b" | a ) 939.6 , b ) 958.9 , c ) 927.78 , d ) 926.82 , e ) 902.1 | b | divide(1120, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 7), const_100), const_1)) | multiply(n1,n3)|add(n1,#0)|divide(#1,n3)|multiply(n0,#2)|divide(#3,const_100)|add(#4,const_1)|divide(n4,#5)| | general | allenai/math_qa |
a jar full of whisky contains 30 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ? | "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 1 / 3 . hence , a is the correct answer ." | a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5 | a | divide(subtract(30, 26), subtract(30, 19)) | subtract(n0,n2)|subtract(n0,n1)|divide(#0,#1)| | gain | allenai/math_qa |
two trains of length 60 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ? | "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 60 + 280 = 400 m . the time required = d / s = 340 / 20 = 20 sec . answer : c" | a ) 10 sec , b ) 32 sec , c ) 17 sec , d ) 20 sec , e ) 89 sec | c | divide(add(60, 280), multiply(add(42, 30), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | physics | allenai/math_qa |
a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 60 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ? | "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 60 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 30 cents . fraction of spirit is 1 / 2 . 30 = k * ( 1 / 2 ) k = 60 cost per liter = 60 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 60 * ( 1 / 3 ) * 3 = 50 cents e . 60 cents" | a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 60 | e | multiply(multiply(60, divide(1, add(1, 2))), add(1, 2)) | add(n0,n4)|divide(n0,#0)|multiply(n2,#1)|multiply(#0,#2)| | geometry | allenai/math_qa |
the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum q of all the digits of the integers from 0 to 99 inclusive ? | "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just q = 900 : the answer is c ." | a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100 | c | multiply(divide(multiply(9, add(9, 1)), 2), multiply(2, const_10)) | add(n6,n3)|multiply(const_10,n7)|multiply(n6,#0)|divide(#2,n7)|multiply(#3,#1)| | general | allenai/math_qa |
the population of a village is 12000 . it increases annually at the rate of 24 % p . a . what will be its population after 2 years ? | "formula : ( after = 100 denominator ago = 100 numerator ) 12000 × 124 / 100 × 124 / 100 = 18451 b" | a ) 14567 , b ) 18451 , c ) 18789 , d ) 18786 , e ) 14400 | b | multiply(12000, power(add(const_1, divide(24, const_100)), 2)) | divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | gain | allenai/math_qa |
by selling an article at rs . 250 , a profit of 25 % is made . find its cost price ? | "sp = 250 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 250 * [ 100 / ( 100 + 25 ) ] = 250 * [ 100 / 125 ] = rs . 200 answer : e" | a ) s . 486 , b ) s . 455 , c ) s . 220 , d ) s . 480 , e ) s . 200 | e | divide(multiply(250, const_100), add(const_100, 25)) | add(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)| | gain | allenai/math_qa |
find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 12 cm | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 12 ) = 228 cm 2 answer : e" | a ) 178 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 228 cm 2 | e | quadrilateral_area(12, 18, 20) | quadrilateral_area(n2,n1,n0)| | physics | allenai/math_qa |
if the average ( arithmetic mean ) of 2 x , 4 x , and 8 x is 140 , what is the value of x ? | "am of 2 x , 4 x and 8 x = 2 x + 4 x + 8 x / 3 = 14 x / 3 given that 14 x / 3 = 140 x = 30 answer is b" | a ) 20 , b ) 30 , c ) 15 , d ) 33 , e ) 31 | b | subtract(multiply(4, const_2), multiply(2, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general | allenai/math_qa |
the diagonals of two squares are in the ratio of 3 : 7 then find the ratio of its areas ? | "let the diagonals of the squares be 3 x and 7 x ratio of their areas = 1 / 2 ( 3 x ) ^ 2 : 1 / 2 ( 7 x ) ^ 2 = 9 x ^ 2 : 49 x ^ 2 = 9 : 49 answer is c" | a ) 7 : 37 , b ) 6 : 46 , c ) 9 : 49 , d ) 8 : 68 , e ) 6 : 61 | c | divide(const_4, power(7, 3)) | power(n1,n0)|divide(const_4,#0)| | geometry | allenai/math_qa |
a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 120 miles at 60 mph ? | "total time for travelling 120 miles @ 60 mph = 120 / 60 = 2 hour = 120 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 120 minutes it will use = 3 gallons . thus , full tank = 3 + 8 = 11 gallons - - - > 3 / 11 = 27 % of the fuel used . d is the correct answer ." | a ) 15 % , b ) 20 % , c ) 25 % , d ) 27 % , e ) 40 % | d | divide(divide(multiply(40, 60), multiply(120, 60)), add(divide(multiply(40, 60), multiply(120, 60)), 8)) | multiply(n0,n1)|multiply(n3,n4)|divide(#0,#1)|add(n2,#2)|divide(#2,#3)| | physics | allenai/math_qa |
if xy > 0 , 1 / x + 1 / y = 6 , and 1 / xy = 12 , then ( x + y ) / 6 = ? | "( 1 / x + 1 / y ) = 6 canbe solved as { ( x + y ) / xy } = 12 . substituting for 1 / xy = 12 , we get x + y = 6 / 12 = = > ( x + y ) / 6 = 6 / ( 12 * 6 ) = 1 / 12 . a" | a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6 | a | divide(divide(6, 12), 12) | divide(n3,n5)|divide(#0,n5)| | general | allenai/math_qa |
a man buys a cycle for rs . 2300 and sells it at a loss of 30 % . what is the selling price of the cycle ? | "s . p . = 70 % of rs . 2300 = rs . 70 x 2300 / 100 = rs . 1610 answer : option b" | a ) s . 1690 , b ) s . 1610 , c ) s . 1890 , d ) s . 1602 , e ) s . 1092 | b | divide(multiply(subtract(const_100, 30), 2300), const_100) | subtract(const_100,n1)|multiply(n0,#0)|divide(#1,const_100)| | gain | allenai/math_qa |
a and b invests rs . 3000 and rs . 5000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ? | ( 3 * 6 + 6 * 6 ) : ( 5 * 12 ) 54 : 60 = > 9 : 10 answer : e | a ) 8 : 8 , b ) 9 : 8 , c ) 9 : 7 , d ) 9 : 5 , e ) 9 : 10 | e | divide(add(multiply(3000, 6), multiply(multiply(3000, const_2), 6)), multiply(5000, add(6, 6))) | add(n2,n2)|multiply(n0,n2)|multiply(n0,const_2)|multiply(n2,#2)|multiply(n1,#0)|add(#1,#3)|divide(#5,#4) | gain | allenai/math_qa |
if ( n + 2 ) ! / n ! = 110 , n = ? | "( n + 2 ) ! / n ! = 110 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 110 from here , we might just test the answer choices . since ( 11 ) ( 10 ) = 110 , we can see that n = 9 b" | a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | b | subtract(add(const_4, const_4), const_1) | add(const_4,const_4)|subtract(#0,const_1)| | general | allenai/math_qa |
what is the least number . which should be added to 0.0320 to make it a perfect square ? | 0.0320 + 0.0004 = 0.0324 ( 0.18 ) ^ 2 answer : b | a ) 0.0005 , b ) 0.0004 , c ) 0.0006 , d ) 0.0002 , e ) 0.0001 | b | subtract(multiply(divide(add(add(const_12, const_4), const_2), const_100), divide(add(add(const_12, const_4), const_2), const_100)), 0.032) | add(const_12,const_4)|add(#0,const_2)|divide(#1,const_100)|multiply(#2,#2)|subtract(#3,n0) | general | allenai/math_qa |
calculate the value of y : 5 y ^ 2 - 8 y + 55 = 59 | using the elimination method substitute options for x and find the correct option . answer : c | a ) 7 , b ) 1 , c ) 2 , d ) 9 , e ) 8 | c | divide(add(sqrt(subtract(power(8, const_2), multiply(multiply(5, subtract(55, 59)), const_4))), 8), multiply(5, 2)) | multiply(n0,n1)|power(n2,const_2)|subtract(n3,n4)|multiply(n0,#2)|multiply(#3,const_4)|subtract(#1,#4)|sqrt(#5)|add(n2,#6)|divide(#7,#0) | general | allenai/math_qa |
one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 75,000 as total savings , how much has he saved in public provident fund ? | "let savings in n . s . c and p . p . f . be rs . x and rs . ( 175000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 175000 - x ) = x / 3 + x / 2 = 87500 = 5 x / 6 = 87500 = x = 87500 x 6 / 5 = 105000 savings in public provident fund = rs . ( 175000 - 105000 ) = rs . 70000 answer is d ." | a ) 80000 , b ) 60000 , c ) 50000 , d ) 70000 , e ) 90000 | d | multiply(add(multiply(multiply(const_100, const_10), const_100), subtract(multiply(multiply(const_100, const_10), const_100), multiply(multiply(const_2, const_100), const_100))), divide(1, add(divide(const_3, const_2), 1))) | divide(const_3,const_2)|multiply(const_10,const_100)|multiply(const_100,const_2)|add(n0,#0)|multiply(#1,const_100)|multiply(#2,const_100)|divide(n0,#3)|subtract(#4,#5)|add(#4,#7)|multiply(#8,#6)| | general | allenai/math_qa |
at what rate percent on simple interest will rs . 750 amount to rs . 975 in 5 years ? | "225 = ( 750 * 5 * r ) / 100 r = 6 % . answer : e" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | e | multiply(divide(divide(subtract(975, 750), 750), 5), const_100) | subtract(n1,n0)|divide(#0,n0)|divide(#1,n2)|multiply(#2,const_100)| | gain | allenai/math_qa |
a can do a work in 9 days and b can do the same work in 18 days . if they work together , in how many days will they complete the work ? | one day ' s work of a and b = 1 / 9 + 1 / 8 = ( 2 + 1 ) / 18 = 1 / 6 so , the time taken to complete the work is 6 days . answer : a | a ) 6 days , b ) 7 days , c ) 5 days , d ) 3 days , e ) 2 days | a | divide(const_1, add(divide(const_1, 9), divide(const_1, 18))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2) | physics | allenai/math_qa |
in the coordinate plane , points ( x , 3 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 3 / 5 , then x + y = | "line k passes through the origin and has slope 3 / 5 means that its equation is y = 3 / 5 * x . thus : ( x , 3 ) = ( 3 , 5 ) and ( 5 , y ) = ( 3 , 5 ) - - > x + y = 3 + 5 = 8 . answer : b" | a ) 9 , b ) 8 , c ) 7 , d ) 5 , e ) 6 | b | multiply(multiply(5, 5), divide(3, 5)) | divide(n0,n3)|multiply(n1,n3)|multiply(#0,#1)| | general | allenai/math_qa |
a customer purchased a package of ground beef at a cost of $ 1.95 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 35 percent less than the package of ground beef . what was the cost per pound of the steak ? | "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.95 . let x be the price per pound for the steak . then 0.65 x = 195 x = 195 / 0.65 = $ 3.00 the answer is c ." | a ) $ 2.50 , b ) $ 2.75 , c ) $ 3.00 , d ) $ 3.25 , e ) $ 3.50 | c | divide(1.95, add(multiply(const_0_25, const_2), multiply(const_0_33, const_1))) | multiply(const_0_25,const_2)|multiply(const_0_33,const_1)|add(#0,#1)|divide(n0,#2)| | general | allenai/math_qa |
in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 188 votes . find the total number of valid votes ? | "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 188 = > 4 x / 10 = 188 = > 4 x = 1880 = > x = 470 . answer : d" | a ) 430 , b ) 438 , c ) 436 , d ) 470 , e ) 422 | d | divide(188, divide(subtract(70, subtract(const_100, 70)), const_100)) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)| | gain | allenai/math_qa |
the average of first 13 natural numbers is ? | "sum of 13 natural no . = 182 / 2 = 91 average = 91 / 13 = 7 answer : c" | a ) 5.2 , b ) 5.5 , c ) 7 , d ) 9 , e ) 10 | c | add(13, const_1) | add(n0,const_1)| | general | allenai/math_qa |
if ( n + 2 ) ! / n ! = 90 , n = ? | "( n + 2 ) ! / n ! = 90 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 132 from here , we might just test the answer choices . since ( 10 ) ( 9 ) = 90 , we can see that n = 8 b" | a ) 2 / 131 , b ) 8 , c ) 10 , d ) 11 , e ) 12 | b | subtract(add(const_4, const_4), const_1) | add(const_4,const_4)|subtract(#0,const_1)| | general | allenai/math_qa |
a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ? | "i think d - 31 / 45 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 4 x so old = x , new = 3 x now 1 / 3 of x are occupied and 1 / 5 of 3 x are occupied which simplifies to ( 3 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 3 / 5 of x occupied in the new ward . add them up to get 14 / 15 of x there are 3 x beds in new tower so ratio is : ( 14 / 15 ) x / 3 x = 14 / 45 of x subtract that from 45 / 45 of x and you get the number of un - occupied beds to total capacity of new tower = 31 / 45 d" | a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 31 / 45 , e ) 11 / 15 | d | multiply(add(multiply(4, 3), 1), multiply(divide(1, 3), divide(1, 5))) | divide(n1,n2)|divide(n1,n4)|multiply(n0,n2)|add(n1,#2)|multiply(#0,#1)|multiply(#3,#4)| | general | allenai/math_qa |
a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches ) | "the tank is emptied at this rate : 9 + 6 - 3 = 12 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 12 = 4320 minutes . the answer is c ." | a ) 2110 , b ) 3210 , c ) 4320 , d ) 5430 , e ) 6540 | c | divide(multiply(30, power(9, 3)), subtract(add(9, 6), 3)) | add(n4,n5)|power(n8,n2)|multiply(n0,#1)|subtract(#0,n2)|divide(#2,#3)| | physics | allenai/math_qa |
in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 65 , what is the greatest possible value of b x a ? | "i also was confused when i was looking forabove number : d as far as i understood , 65 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 65 x 1 ( a = 6 , b = 5 respectively we have = 30 ) . this is the greatest possible value of b x a . imo e ." | a ) 0 , b ) 10 , c ) 15 , d ) 20 , e ) 30 | e | multiply(add(const_3, const_4), add(const_2, const_3)) | add(const_3,const_4)|add(const_2,const_3)|multiply(#0,#1)| | general | allenai/math_qa |
a secret can be told only 2 persons in 5 minutes . the same person tells to 2 more persons and so on . how long will take to tell it to 768 persons ? | at start one person will tell to 2 persons , it will take 5 min , now that 1 + 2 = 3 persons will tell this to next 6 persons , then 1 + 2 + 6 = 9 persons will tell to next 18 persons , then 1 + 2 + 6 + 18 = 27 persons to 54 similarly 1 + 2 + 6 + 18 + 54 = 81 persons will tell this to 162 persons similarly 1 + 2 + 6 + 18 + 54 + 162 = 243 persons will tell this to 486 persons , upto this step total persons who have listened this secret = 2 + 6 + 18 + 54 + 162 + 486 = 728 , and total time taken upto this step = 5 * 6 = 30 min , now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min answer : e | a ) 25 min , b ) 32 min , c ) 33 min , d ) 34 min , e ) 35 min | e | multiply(add(2, 5), 5) | add(n0,n1)|multiply(n1,#0) | physics | allenai/math_qa |
a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 36 , what is the total amount ? | "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 36 39 - - - ? = > 156 answer : e" | a ) 115 , b ) 116 , c ) 117 , d ) 118 , e ) 156 | e | add(add(multiply(divide(const_100, 45), 36), multiply(divide(50, 45), 36)), 36) | divide(const_100,n0)|divide(n1,n0)|multiply(n2,#0)|multiply(n2,#1)|add(#2,#3)|add(n2,#4)| | general | allenai/math_qa |
a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ? | max no . of crates = 5 . max weight = 120 kg max . weight carried = 5 * 120 = 600 kg = c | a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 375 | c | multiply(5, 120) | multiply(n2,n3) | general | allenai/math_qa |
on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 320,000 ? | "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 320 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 320,000 = 6 years total 30 years ." | a ) 30 , b ) 16 , c ) 18 , d ) 20 , e ) 24 | a | divide(log(divide(multiply(const_3, const_10), add(const_4, const_1))), log(power(divide(multiply(const_2, const_10), add(const_4, const_1)), divide(const_1, 12)))) | add(const_1,const_4)|divide(const_1,n1)|multiply(const_10,const_3)|multiply(const_10,const_2)|divide(#2,#0)|divide(#3,#0)|log(#4)|power(#5,#1)|log(#7)|divide(#6,#8)| | general | allenai/math_qa |
if 4 men can reap 40 acres of land in 15 days , how many acres of land can 16 men reap in 30 days ? | "4 men 40 acres 15 days 16 men ? 30 days 40 * 16 / 4 * 30 / 15 40 * 4 * 2 40 * 8 = 320 answer : a" | a ) 320 , b ) 240 , c ) 369 , d ) 489 , e ) 125 | a | multiply(40, multiply(divide(16, 4), divide(30, 15))) | divide(n3,n0)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2)| | physics | allenai/math_qa |
there are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed . | "explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a" | a ) 26 , b ) 32 , c ) 35 , d ) 30 , e ) 45 | a | divide(add(408, 216), multiply(multiply(multiply(const_2, const_2), const_2), const_3)) | add(n0,n1)|multiply(const_2,const_2)|multiply(#1,const_2)|multiply(#2,const_3)|divide(#0,#3)| | general | allenai/math_qa |
last week vartan spent 15 percent of his wages on recreation . this week , his wages are 10 percent less than last week ʼ s wages and he spent 30 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ? | say vartan ' s wages last week were $ 100 , so he spent 0.15 * 100 = $ 15 on recreation ; this week ' s wages is 0.9 * 100 = $ 90 , so he spends 0.3 * 90 = $ 27 on recreation ; 27 / 15 = 1.8 , hence the amount he spends on recreation this week is 180 % of the amount he spent on recreation last week : 15 * 1.8 = 27 . answer : c . | a ) 100 % , b ) 160 % , c ) 180 % , d ) 200 % , e ) 220 % | c | divide(multiply(30, subtract(const_100, 10)), 15) | subtract(const_100,n1)|multiply(n2,#0)|divide(#1,n0) | general | allenai/math_qa |
if the sum of two numbers is 60 and the h . c . f and l . c . m of these numbers are 3 and 120 respectively , then the sum of the reciprocal of the numbers is equal to : | "let the numbers be a and b . then , a + b = 60 and ab = 3 * 120 = 360 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 60 / 360 = 1 / 6 . answer : c" | a ) 2 / 9 , b ) 4 / 5 , c ) 1 / 6 , d ) 6 / 6 , e ) 3 / 9 | c | divide(add(3, 120), multiply(3, 120)) | add(n1,n2)|multiply(n1,n2)|divide(#0,#1)| | general | allenai/math_qa |
of the total amount that jill spent on a shopping trip , excluding taxes , she spent 20 percent on clothing , 50 percent on food , and 30 percent on other items . if jill paid a 10 percent tax on the clothing , 15 percent tax on the food , and no tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ? | "assume she has $ 200 to spend . tax clothing = 20 % = $ 40 = $ 10.00 food = 50 % = $ 100 = $ 15.00 items = 30 % = $ 60 = $ 0.00 total tax = $ 25.00 % of total amount = 25 / 200 * 100 = 12.25 % answer e" | a ) 12.45 , b ) 12.5 , c ) 12.65 , d ) 12.35 , e ) 12.25 | e | multiply(divide(add(multiply(20, divide(10, const_100)), multiply(30, divide(15, const_100))), const_100), const_100) | divide(n3,const_100)|divide(n4,const_100)|multiply(n0,#0)|multiply(n2,#1)|add(#2,#3)|divide(#4,const_100)|multiply(#5,const_100)| | general | allenai/math_qa |
a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 15 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ? | "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 15 - 2 cmb = 100 b - cb - mb - 2 cmb = 25 hence the probability = 25 / 100 = 1 / 4 . c" | a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 4 , d ) 7 / 10 , e ) 9 / 10 | c | divide(subtract(100, subtract(add(50, 40), 15)), 100) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)|divide(#2,n0)| | other | allenai/math_qa |
average of 5 numbers is 12 . if one number is excluded the average becomes 10 . the excluded number is | explanation : number is ( 5 * 12 ) - ( 4 * 10 ) = 60 - 40 = 20 answer : option b | a ) 35 , b ) 20 , c ) 40 , d ) 30 , e ) 67 | b | subtract(multiply(5, 12), multiply(10, const_4)) | multiply(n0,n1)|multiply(n2,const_4)|subtract(#0,#1) | general | allenai/math_qa |
a box contains 1 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? | "my complicated version of your simple approach let the 5 black balls be bbbbb and 1 red balls be r they can be arranged in 6 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 5 ! x 1 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 4 black ( bbbb ) and 1 red ( r ) they can be arranged in ( 5 ! ) / ( 4 ! x 1 ! ) hence required probability = [ ( 6 ! ) / ( 5 ! x 1 ! ) ] / [ ( 5 ! ) / ( 4 ! x 1 ! ) ] = 6 / 5 c" | a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3 | c | divide(add(1, 5), 5) | add(n0,n1)|divide(#0,n1)| | probability | allenai/math_qa |
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