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load_in_math_allenai_math

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two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.75 km and 1.10 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.75 + 1.10 = 2.75 km = 2750 m . required time = 2750 * 3 / 125 = 66 sec . answer : d"
a ) 48 , b ) 9 , c ) 7 , d ) 66 , e ) 15
d
subtract(divide(multiply(1.75, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(1.10, const_1000), divide(multiply(90, const_1000), const_3600)))
multiply(n2,const_1000)|multiply(n0,const_1000)|multiply(n3,const_1000)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#3,const_3600)|divide(#0,#4)|divide(#2,#5)|subtract(#6,#7)|
physics
allenai/math_qa
a batsman makes a score of 64 runs in the 16 th innings and thus increased his average by 3 . find his average after the 16 th inning ?
"let the average after the 16 th inning be p . so , the average after the 15 th inning will be ( p - 3 ) hence , 15 ( p - 30 ) + 64 = 16 p = > p = 19 . answer : d"
a ) 23 , b ) 28 , c ) 27 , d ) 19 , e ) 24
d
add(subtract(64, multiply(16, 3)), 3)
multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)|
general
allenai/math_qa
a train 90 m long is running at 20 kmph . in how much time will it pass a platform 80 m long ?
distance travelled = 90 + 80 m = 170 m speed = 20 * 5 / 8 = 25 / 2 m time = 170 * 2 / 25 = 13.6 seconds answer : d .
a ) 15.6 seconds , b ) 24.6 seconds , c ) 28.6 seconds , d ) 13.6 seconds , e ) 35.6 seconds
d
divide(add(90, 80), multiply(20, const_0_2778))
add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)|
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 g 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 ) g = 75 , d ) g = 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 bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability x that out of the two , one is white and one is blue ?
"the required probability x = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
d
divide(multiply(3, 5), divide(multiply(add(3, 5), add(5, const_2)), const_2))
add(n0,n1)|add(n1,const_2)|multiply(n0,n1)|multiply(#0,#1)|divide(#3,const_2)|divide(#2,#4)|
probability
allenai/math_qa
in measuring the sides of a rectangle , one side is taken 8 % in excess , and the other 7 % in deficit . find the error percent in the area calculated from these measurements .
"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 27 / 25 ) x ( 40 / 43 ) y = ( 913 / 909 ) ( xy ) error in measurement = ( 913 / 909 ) xy - xy = ( 4 / 909 ) xy error percentage = [ ( 4 / 909 ) xy ( 1 / xy ) 100 ] % = ( 11 / 25 ) % = 0.44 % . answer is c ."
a ) 0.11 % , b ) 0.7 % , c ) 0.44 % , d ) 0.6 % , e ) 0.8 %
c
subtract(subtract(8, 7), divide(multiply(8, 7), const_100))
multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)|
geometry
allenai/math_qa
if an average hard drive had a capacity of 0.1 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
"0.1 * 2 ^ 10 = 0.1 * 1024 = 102.4 the answer is d ."
a ) 256 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536
d
multiply(add(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(0.1, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), 0.1), const_10)
multiply(n0,const_2)|multiply(#0,const_2)|multiply(#1,const_2)|multiply(#2,const_2)|multiply(#3,const_2)|multiply(#4,const_2)|multiply(#5,const_2)|multiply(#6,const_2)|multiply(#7,const_2)|multiply(#8,const_2)|add(n0,#9)|multiply(#10,const_10)|
general
allenai/math_qa
the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 900 . what is the banker ' s discount ?
"explanation : td = ( bg Γ— 100 ) / tr = ( 900 Γ— 100 ) / ( 6 Γ— 12 ) = rs . 1250 bg = bd – td = > 900 = bd - 1250 = > bd = 2150 answer : option d"
a ) 1240 , b ) 1120 , c ) 1190 , d ) 2150 , e ) none of these
d
add(900, divide(multiply(900, const_100), multiply(12, 6)))
multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|add(n2,#2)|
gain
allenai/math_qa
train a leaves the station traveling at 30 miles per hour . two hours later train Π² leaves the same station traveling in the same direction at 36 miles per hour . how many miles from the station was train a overtaken by train b ?
"after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 6 miles per hour . the time to catch up is 60 / 6 = 10 hours . in 10 hours , train a travels another 30 * 10 = 300 miles for a total of 360 miles . the answer is b ."
a ) 320 , b ) 360 , c ) 400 , d ) 440 , e ) 480
b
multiply(divide(multiply(30, const_2), subtract(36, 30)), 36)
multiply(n0,const_2)|subtract(n1,n0)|divide(#0,#1)|multiply(n1,#2)|
physics
allenai/math_qa
on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent w of thatbeforejuly 1 last year ?
"the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before w = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
b
multiply(10, 10)
multiply(n1,n1)|
general
allenai/math_qa
a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 5 a rupee . find his net profit or loss percent ?
"the total number of mangoes bought by the shopkeeper be 30 . if he buys 6 a rupee , his cp = 5 he selling at 5 a rupee , his sp = 6 profit = sp - cp = 6 - 5 = 1 profit percent = 1 / 5 * 100 = 20 % answer : c"
a ) 34 % , b ) 33 % , c ) 20 % , d ) 35 % , e ) 30 %
c
divide(multiply(5, const_100), 6)
multiply(n1,const_100)|divide(#0,n0)|
gain
allenai/math_qa
the sum of all two digit numbers divisible by 9 is
required numbers are 18,27 . . . . . 99 this is an a . p . in which a = 18 , d = 9 and l = 99 . let the number of terms in it be n . then t = 99 so a + ( n - 1 ) d = 99 . 18 + ( n - 1 ) * 9 = 99 , 18 + 9 n - 9 = 99 9 + 9 n = 99 9 n = 99 - 9 n = 90 / 9 then n = 10 . required sum = n / 2 ( a + l ) = 10 / 2 ( 18 + 99 ) = 585 answer is b .
a ) 910 , b ) 585 , c ) 785 , d ) 685 , e ) 885
b
add(add(add(add(add(add(add(add(add(add(9, 9), add(add(9, 9), 9)), add(add(add(9, 9), 9), 9)), add(add(add(add(9, 9), 9), 9), 9)), add(add(add(add(add(9, 9), 9), 9), 9), 9)), add(add(add(add(add(add(9, 9), 9), 9), 9), 9), 9)), add(add(add(add(add(add(add(9, 9), 9), 9), 9), 9), 9), 9)), add(add(add(add(add(add(add(add(9, 9), 9), 9), 9), 9), 9), 9), 9)), add(add(add(add(add(add(add(add(add(9, 9), 9), 9), 9), 9), 9), 9), 9), 9)), add(add(add(add(add(add(add(add(add(add(9, 9), 9), 9), 9), 9), 9), 9), 9), 9), 9))
add(n0,n0)|add(n0,#0)|add(#0,#1)|add(n0,#1)|add(#2,#3)|add(n0,#3)|add(#4,#5)|add(n0,#5)|add(#6,#7)|add(n0,#7)|add(#8,#9)|add(n0,#9)|add(#10,#11)|add(n0,#11)|add(#12,#13)|add(n0,#13)|add(#14,#15)|add(n0,#15)|add(#16,#17)
general
allenai/math_qa
a , b and c can do a piece of work in 7 days , 21 days and 28 days respectively . how long will they taken , if all the three work together ?
"1 / 7 + 1 / 21 + 1 / 28 = 19 / 84 = > 84 / 19 = > 4 8 / 19 days answer : b"
a ) 2 , b ) 4 8 / 19 , c ) 5 , d ) 67 , e ) 9
b
inverse(add(inverse(28), add(inverse(7), inverse(21))))
inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4)|
physics
allenai/math_qa
the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 675 feet squared , what is the difference between the length and the width of the roof ?
"let the width = x x * 3 x = 675 x ^ 2 = 225 x = 15 length = 3 * 15 = 45 difference = 45 - 15 = 30 b is the answer"
a ) 38 . , b ) 30 . , c ) 42 . , d ) 44 . , e ) 46 .
b
subtract(multiply(sqrt(divide(675, 3)), 3), sqrt(divide(675, 3)))
divide(n1,n0)|sqrt(#0)|multiply(#1,n0)|subtract(#2,#1)|
geometry
allenai/math_qa
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount had been offered ?
"giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 Γ— ( 100 + 23.5 ) / ( 100 βˆ’ 5 ) = 100 Γ— 247 / 190 = 130 hence , required % profit = 130 – 100 = 30 % answer c"
a ) 28.5 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these
c
subtract(divide(multiply(add(const_100, 23.5), const_100), subtract(const_100, 5)), const_100)
add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)|
gain
allenai/math_qa
last year elaine spent 20 % of her annual earnings on rent . this year she earned 25 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
"for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 25 % more , or $ 125 . she would ' ve spent 30 % of this on rent , or $ 37.5 do $ 37.5 / $ 20 this will give you 187.5 % e is the correct answer ."
a ) 182.5 , b ) 184.5 , c ) 167.5 , d ) 172.5 , e ) 187.5
e
multiply(divide(multiply(add(divide(25, const_100), const_1), 30), 20), const_100)
divide(n1,const_100)|add(#0,const_1)|multiply(n2,#1)|divide(#2,n0)|multiply(#3,const_100)|
gain
allenai/math_qa
if there are 200 questions in a 3 hr examination . among these questions are 20 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
"x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 180 x + 20 * 2 x = 180 x = 180 / 220 x = 0.818182 time taken for type a problem = 20 * 2 * 0.818182 = 32.72727 min answer : d"
a ) 72 min , b ) 62 min , c ) 70 min , d ) 32.72727 min , e ) 76 min
d
multiply(multiply(const_2, divide(multiply(3, const_60), add(subtract(200, 20), multiply(const_2, 20)))), 20)
multiply(n1,const_60)|multiply(n2,const_2)|subtract(n0,n2)|add(#1,#2)|divide(#0,#3)|multiply(#4,const_2)|multiply(n2,#5)|
general
allenai/math_qa
a couple spent $ 132 in total while dining out and paid this amount using a credit card . the $ 132 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
"let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 132 x = 100 the correct answer is a ."
a ) $ 100 , b ) $ 104 , c ) $ 108 , d ) $ 112 , e ) $ 116
a
divide(multiply(divide(multiply(132, const_100), add(const_100, 20)), const_100), add(const_100, 10))
add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|divide(#2,#0)|multiply(#3,const_100)|divide(#4,#1)|
general
allenai/math_qa
in x game of billiards , x can give y 20 points in 60 and he can give z 50 points in 60 . how many points can y give z in x game of 100 ?
"x scores 60 while y score 40 and z scores 10 . the number of points that z scores when y scores 100 = ( 100 * 50 ) / 40 = 25 . in x game of 100 points , y gives ( 100 - 25 ) = 75 points to c . e"
a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 75
e
subtract(multiply(subtract(60, 20), const_3), multiply(subtract(60, 50), const_3))
subtract(n1,n0)|subtract(n1,n2)|multiply(#0,const_3)|multiply(#1,const_3)|subtract(#2,#3)|
general
allenai/math_qa
57 + 58 = 115 . how many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5 ?
"since 2 + 3 = 5 & 7 + 8 = 15 any combination with these no be will give u desirable result . . . so total no in 100 will be 20 & that ' s why in 1000 , it will be 20 x 15 = 300 . answer : c"
a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
c
divide(1500, 5)
divide(n4,n5)|
general
allenai/math_qa
sum of two numbers prime to each other is 14 and their l . c . m . is 45 . what are the numbers ?
"as two numbers are prime , satisfies all but option c will make the product of numbers i . e 45 answer : c"
a ) 6 and 5 , b ) 8 and 5 , c ) 9 and 5 , d ) 8 and 5 , e ) 3 and 5
c
add(45, 14)
add(n0,n1)|
physics
allenai/math_qa
the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years b in which the population would be doubled assuming there is no emigration or immigration is
"suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
a ) 20 , b ) 25 , c ) b = 30 , d ) b = 35 , e ) b = 40
d
divide(subtract(const_100, multiply(const_10, const_3)), multiply(divide(subtract(39.4, 19.4), 1000), const_100))
multiply(const_10,const_3)|subtract(n1,n2)|divide(#1,n0)|subtract(const_100,#0)|multiply(#2,const_100)|divide(#3,#4)|
general
allenai/math_qa
a book is bought for $ 32 and sold for $ 56 . what is the profit in percentage ?
56 / 32 = 1.75 the answer is c .
a ) 15 , b ) 35 , c ) 75 , d ) 25 , e ) 85
c
multiply(divide(subtract(56, 32), 32), const_100)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)
gain
allenai/math_qa
what is the remainder when 14452 Γ— 15652 Γ— 16781 is divided by 5 ?
only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 2 * 2 * 1 = will give units digit as 4 so , whatever be the number , if it ends in 4 , the remainder after dividing with 5 will be 4 . optione
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
e
reminder(multiply(multiply(14452, 15652), 16781), 5)
multiply(n0,n1)|multiply(n2,#0)|reminder(#1,n3)
general
allenai/math_qa
when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 5 of the remaining balance , what will be the final balance in her bank account ?
"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 5 of 300 = 60 total amount in her account = 360 answer b"
a ) 300 , b ) 360 , c ) 400 , d ) 500 , e ) 575
b
multiply(subtract(divide(200, subtract(1, divide(const_3, 5))), 200), add(1, divide(1, 5)))
divide(n3,n4)|divide(const_3,n2)|add(n3,#0)|subtract(n3,#1)|divide(n0,#3)|subtract(#4,n0)|multiply(#2,#5)|
general
allenai/math_qa
the average monthly salary of 15 employees in an organisation is rs . 1800 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?
"manager ' s monthly salary = rs . ( 1950 * 16 - 1800 * 15 ) = rs . 4200 answer : c"
a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4200 , d ) rs . 3619 , e ) rs . 3610
c
subtract(multiply(add(1800, 150), add(15, const_1)), multiply(1800, 15))
add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|
general
allenai/math_qa
a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 40 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
explanation : he covered 5 km in 1 hour , so he might cover 40 km in 8 hours . but he took 10 hours . he would have saved 10 Γ’ € β€œ 8 = 2 hours . answer : a
a ) 2 , b ) 8 , c ) 1 , d ) 6 , e ) 5
a
subtract(10, divide(40, 5))
divide(n2,n0)|subtract(n3,#0)
physics
allenai/math_qa
a certain league has two divisions . the respective divisions had 11 and 13 teams qualify for the playoffs . each division held its own double - elimination tournament - - where a team is eliminated from the tournament upon losing two games - - in order to determine its champion . the 4 division champions then played in a single - elimination tournament - - where a team is eliminated upon losing one game - - in order to determine the overall league champion . assuming that there were no ties and no forfeits , what is the maximum number of games that could have been played in order to determine the overall league champion ?
overall , there can be 47 minuses . tus , it is d .
a ) 41 , b ) 42 , c ) 45 , d ) 47 , e ) 49
d
add(subtract(multiply(13, const_2), const_1), subtract(multiply(11, const_2), const_1))
multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,const_1)|subtract(#1,const_1)|add(#2,#3)
general
allenai/math_qa
if there are 4 peanuts in a box and mary puts 6 more peanuts inside , how many peanuts are in the box ?
6 + 4 = 10 correct answer is c ) 10
a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
c
add(4, 6)
add(n0,n1)
general
allenai/math_qa
if 144 / 0.144 = 14.4 / x , then the value of x is :
= 144 / 0.144 = 14.4 / x = 144 x 1000 / 144 = 14.4 / x = x = 14.4 / 1000 = 0.0144 answer is c .
a ) 0.0414 , b ) 0.144 , c ) 0.0144 , d ) 0.414 , e ) none of them
c
divide(multiply(14.4, 0.144), 144)
multiply(n1,n2)|divide(#0,n0)
general
allenai/math_qa
a man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
"let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 12 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 12 , d = 12 b - 12 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 12 b - 12 c = 4 b + 4 c , - - > b = 2 c , - - > d = 12 b - 6 b = 6 b . interval = \ frac { d } { b } = \ frac { 6 b } { b } = 6 answer : b ( 6 minutes ) ."
a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
b
divide(subtract(12, divide(12, divide(add(4, 12), subtract(12, 4)))), const_1)
add(n0,n1)|subtract(n0,n1)|divide(#0,#1)|divide(n0,#2)|subtract(n0,#3)|divide(#4,const_1)|
physics
allenai/math_qa
how many multiples of 10 are there between 81 and 358 ?
"10 * 9 = 90 10 * 35 = 350 total no of multiples = ( 35 - 9 ) + 1 = 27 answer d"
a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
d
add(divide(subtract(358, 81), 10), const_1)
subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)|
general
allenai/math_qa
speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7380 km and comes back to the starting point . the total time taken by him is :
"explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7380 / 18 + 7380 / 14 = 410 + 527.1 = 937.1 hours answer : option b"
a ) 914.2 hours , b ) 937.1 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours
b
add(divide(7380, add(16, 2)), divide(7380, subtract(16, 2)))
add(n0,n1)|subtract(n0,n1)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)|
physics
allenai/math_qa
jaya two digits age when appended with the two digits age of amitabh the 4 digits number formed is a perfect square . what is the the sum of the 4 digits no . ?
min no could be = 7 ( 1024 ) let jaya has two digits number = 10 and amitabh has two digits number = 24 after appending = 1024 which is perfect square of 32 and sum of four digits number 1024 = 7 answer : b
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
b
add(add(const_1, const_2), 4)
add(const_1,const_2)|add(n0,#0)
general
allenai/math_qa
a photograph is copied onto a sheet of paper 8.5 inches by 10 inches . a 1.5 inch margin is left all around . what area in square inches does the picture cover ?
area covered by photograph = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e
['a ) 76', 'b ) 65', 'c ) 59.5', 'd ) 49', 'e ) 38.5']
e
rectangle_area(subtract(10, const_3), subtract(8.5, const_3))
subtract(n1,const_3)|subtract(n0,const_3)|rectangle_area(#0,#1)
geometry
allenai/math_qa
if x is divided by 7 , the remainder is 5 . what is the remainder if 4 x is divided by 7 ?
x = 7 q + 5 4 x = 7 * 4 q + 20 4 x = 7 * 4 q + 7 * 2 + 6 4 x = 7 ( 4 q + 2 ) + 6 4 x = 7 k + 6 ( k = 4 q + 2 ) answer d
a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
d
divide(divide(add(add(multiply(4, 7), const_10), const_10), 4), const_2)
multiply(n0,n2)|add(#0,const_10)|add(#1,const_10)|divide(#2,n2)|divide(#3,const_2)
general
allenai/math_qa
there are 2 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
"using anagram method : 4 _ 3 _ 2 _ 1 r _ r _ b _ b so . . 4 ! / number of repeated letters ( 2 ! ) ( 2 ! ) = 6 ans : d"
a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 100
d
multiply(factorial(2), factorial(2))
factorial(n0)|factorial(n1)|multiply(#0,#1)|
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 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 8 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 + 8 - 5 = 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 d ."
a ) 1440 , b ) 2340 , c ) 3240 , d ) 4320 , e ) 5420
d
divide(multiply(30, power(9, 5)), subtract(add(12, 8), 5))
add(n4,n5)|power(n8,n6)|multiply(n0,#1)|subtract(#0,n2)|divide(#2,#3)|
physics
allenai/math_qa
how many multiples of 5 are there between 5 to 85 ?
"explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 . answer : a"
a ) 15 , b ) 18 , c ) 17 , d ) none of these , e ) can not be determined
a
add(divide(subtract(85, 5), 5), const_1)
subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)|
general
allenai/math_qa
what is the total cost of 2 sandwiches at $ 2.44 each and 4 sodas at $ 0.87 each ?
"answer = c 2 * 2.44 + 4 * 0.87 = 2 ( 2.50 - 0.06 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.12 - 0.52 = 9 - 0.64 = 8.36"
a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.36 , d ) $ 10.08 , e ) $ 11.85
c
add(multiply(2, 2.44), multiply(4, 0.87))
multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|
general
allenai/math_qa
how many of the positive factors of 24 are not factors of 26
"factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 26 - 1 , 2 , 13 , 26 comparing both , we have 6 factors of 24 which are not factors of 26 - 3 , 4 , 6 , 8 , 12,24 answer : e"
a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 6
e
divide(26, 24)
divide(n1,n0)|
other
allenai/math_qa
cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 1 hours , how many minutes did it take cole to drive to work ?
"first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 1 hrs therefore , 1 = d / 75 + d / 105 lcm of 75 and 105 = 525 1 = d / 75 + d / 105 = > 1 = 7 d / 525 + 5 d / 525 = > d = 525 / 12 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 12 x 75 ) = > t 1 = ( 7 x 60 ) / 12 - - in minutes = > t 1 = 35 minutes . a"
a ) 35 , b ) 50 , c ) 62 , d ) 75 , e ) 78
a
multiply(divide(multiply(105, 1), add(75, 105)), const_60)
add(n0,n1)|multiply(n1,n2)|divide(#1,#0)|multiply(#2,const_60)|
physics
allenai/math_qa
running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
"let the number of required bottles be x machine 6 : 10 time 1 : 4 = : : 270 : x therefore 6 x 1 x x = 10 x 4 x 270 = > x = ( 10 x 4 x 270 ) / ( 6 ) = > x = 1800 answer : option b"
a ) 648 , b ) 1800 , c ) 2700 , d ) 10800 , e ) none
b
multiply(multiply(divide(270, 6), 4), 10)
divide(n1,n0)|multiply(n3,#0)|multiply(n2,#1)|
gain
allenai/math_qa
a person buys an article at $ 1200 . at what price should he sell the article so as to make a profit of 40 % ?
c 1680 cost price = $ 1200 profit = 40 % of 1200 = $ 480 selling price = cost price + profit = 1200 + 480 = 1680
a ) 1670 , b ) 1600 , c ) 1680 , d ) 1900 , e ) 1230
c
add(1200, multiply(1200, divide(40, const_100)))
divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)
gain
allenai/math_qa
a can do a piece of work in 20 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
"10 / 20 + 10 / 30 + 10 / x = 1 x = 60 days answer : b"
a ) 24 days , b ) 60 days , c ) 86 days , d ) 45 days , e ) 17 days
b
divide(10, subtract(const_1, divide(add(10, 10), 20)))
add(n2,n2)|divide(#0,n0)|subtract(const_1,#1)|divide(n2,#2)|
physics
allenai/math_qa
the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 25 % ?
"let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 75 gain % = 11 / 64 * 100 = 17.1 % . answer : d"
a ) 37.5 % , b ) 37.6 % , c ) 38.5 % , d ) 17.1 % , e ) 37.2 %
d
multiply(subtract(divide(subtract(const_100, 25), 64), const_1), const_100)
subtract(const_100,n1)|divide(#0,n0)|subtract(#1,const_1)|multiply(#2,const_100)|
gain
allenai/math_qa
a sum of money is distributed among w , x , y , z in the proportion of 1 : 6 : 2 : 4 . if x gets $ 1500 more than y , what is the w ' s share ?
let the shares of w , x , y , z are 1 a , 6 a , 2 a , 4 a 6 a - 2 a = 1500 4 a = $ 1500 , a = 375 w ' s share = 1 a = $ 375 answer is c
a ) $ 1500 , b ) $ 150 , c ) $ 375 , d ) $ 200 , e ) $ 450
c
divide(divide(1500, subtract(divide(6, 2), const_1)), 2)
divide(n1,n2)|subtract(#0,const_1)|divide(n4,#1)|divide(#2,n2)
general
allenai/math_qa
speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
"sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 210 / 7.5 + 210 / 10.5 ] hours = 48 hours . answer d"
a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 48 hours , e ) none
d
add(divide(210, add(9, 1.5)), divide(210, subtract(9, 1.5)))
add(n0,n1)|subtract(n0,n1)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)|
physics
allenai/math_qa
find compound interest on rs . 5000 at 12 % per annum for 1 year , compounded half - yearly .
"principal = rs . 5000 , rate = 6 % per half year time = 1 year = 2 half - years amount = rs . { 5000 x ( 1 + 6 / 100 ) 2 ] = rs . [ 5000 x 53 / 50 x 53 / 50 ] = rs . 5618 c . i . = rs . ( 5618 – 5000 ) = rs . 618 answer b"
a ) rs . 600 , b ) rs . 618 , c ) rs . 525 , d ) rs . 620 , e ) none
b
subtract(add(add(5000, divide(multiply(5000, 12), const_100)), divide(multiply(add(5000, divide(multiply(5000, 12), const_100)), 12), const_100)), 5000)
multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)|multiply(n1,#2)|divide(#3,const_100)|add(#2,#4)|subtract(#5,n0)|
gain
allenai/math_qa
find the total average marks of all the students in 2 separate classes , if the average marks of students in the first class of 39 students is 45 and that of another class of 35 students is 70 .
sum of the marks for the class of 39 students = 39 * 45 = 1755 sum of the marks for the class of 35 students = 35 * 70 = 2450 sum of the marks for the class of 74 students = 1755 + 2450 = 4205 average marks of all the students = 4205 / 74 = 56.8 answer : d
a ) 55.8 , b ) 51.8 , c ) 53.8 , d ) 56.8 , e ) 52.8
d
subtract(add(subtract(subtract(add(add(multiply(45, const_1), const_4), const_12), const_4), const_0_25), const_1), const_1)
multiply(n2,const_1)|add(#0,const_4)|add(#1,const_12)|subtract(#2,const_4)|subtract(#3,const_0_25)|add(#4,const_1)|subtract(#5,const_1)
general
allenai/math_qa
how many even number in the range between 8 to 100 inclusive are not divisible by 3
"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 47 . for 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 15 . hence , only divisible by 2 but not 3 = 47 - 15 = 32 . hence , answer c"
a ) 15 , b ) 30 , c ) 32 , d ) 33 , e ) 46
c
subtract(divide(subtract(subtract(100, 8), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(100, const_2), multiply(3, const_4)), 3), 3), 3), const_2))
multiply(n2,const_4)|subtract(n1,n0)|subtract(n1,const_2)|subtract(#1,const_2)|subtract(#2,#0)|divide(#3,const_2)|subtract(#4,n2)|subtract(#6,n2)|divide(#7,n2)|divide(#8,const_2)|subtract(#5,#9)|
general
allenai/math_qa
the average of first six multiples of 4 is :
"solution average = 4 ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 84 / 6 = 14 answer a"
a ) 14 , b ) 9 , c ) 12 , d ) 15 , e ) 17
a
add(4, const_1)
add(n0,const_1)|
general
allenai/math_qa
# p is defined as 2 p + 20 for any number p . what is p , if # ( # ( # p ) ) = 4 ?
# p = 2 p + 20 - - - > # ( # p ) = 2 ( 2 p + 20 ) + 20 = 4 p + 60 and thus # ( 4 p + 60 ) = 2 ( 4 p + 60 ) + 20 = 8 p + 140 = 4 - - - > 8 p = - 136 - - - > p = - 17 , d is the correct answer .
a ) – 108 , b ) – 44 , c ) 10 , d ) - 17 , e ) 18
d
divide(add(add(add(multiply(multiply(20, 2), 2), multiply(20, 2)), 20), 4), multiply(4, 2))
multiply(n1,n0)|multiply(n2,n0)|multiply(n0,#0)|add(#2,#0)|add(n1,#3)|add(n2,#4)|divide(#5,#1)|
general
allenai/math_qa
if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability w that n is divisible by 3 ?
prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .
a ) 1 / 3 , b ) ΒΌ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
d
divide(add(3, const_2), multiply(const_4, const_4))
add(n0,const_2)|multiply(const_4,const_4)|divide(#0,#1)
general
allenai/math_qa
a man bought 40 shares of rs . 60 at 6 discount , the rate of dividend being 12 1 / 2 % the rate of interest obtained is
"explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 6 = rs . 54 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 Γ— 25 / 2 Γ— 100 = rs . 7.5 total dividend = ( 40 Γ— 7.5 ) ie , he got a dividend of ( 40 Γ— 7.5 ) for an investment of rs . ( 40 Γ— 54 ) interest obtained = 40 Γ— 7.5 Γ— 100 / 40 Γ— 54 = 13.89 % answer : option a"
a ) 13.89 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
a
divide(multiply(multiply(40, 60), divide(12, const_100)), multiply(40, subtract(60, 6)))
divide(n3,const_100)|multiply(n0,n1)|subtract(n1,n2)|multiply(#0,#1)|multiply(n0,#2)|divide(#3,#4)|
gain
allenai/math_qa
working together at their respective constant rates , machine a and machine b can produce 900 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 900 unit total would it produce ?
"1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 900 units in 24 hrs , so it can produce 900 * 8 / 24 = 300 units is 8 hrs . 300 is 30 % of 900 . a is the answer"
a ) 30 , b ) 33 , c ) 50 , d ) 67 , e ) 75
a
multiply(divide(multiply(subtract(divide(multiply(multiply(const_4, const_4), const_100), 8), divide(multiply(multiply(const_4, const_4), const_100), add(8, divide(multiply(8, 50), const_100)))), 8), multiply(multiply(const_4, const_4), const_100)), const_100)
multiply(const_4,const_4)|multiply(n1,n2)|divide(#1,const_100)|multiply(#0,const_100)|add(n1,#2)|divide(#3,n1)|divide(#3,#4)|subtract(#5,#6)|multiply(n1,#7)|divide(#8,#3)|multiply(#9,const_100)|
gain
allenai/math_qa
( 12345679 x 72 ) = ?
"explanation : 12345679 x 72 = 12345679 x ( 70 + 2 ) = 12345679 x 70 + 12345679 x 2 = 864197530 + 24691358 = 888888888 answer : option b"
a ) 88888888 , b ) 888888888 , c ) 898989898 , d ) 9999999998 , e ) none
b
multiply(12345679, power(add(const_4, const_1), const_4))
add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)|
general
allenai/math_qa
a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 5 of th area of the garden . what is the radius of the circular garden ?
"as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 5 ( pir ^ 2 ) pir ^ 2 = 10 pir r = 10 answer : c"
a ) 1 , b ) 2 , c ) 10 , d ) 8 , e ) 16
c
multiply(const_2, sqrt(power(5, const_2)))
power(n1,const_2)|sqrt(#0)|multiply(#1,const_2)|
geometry
allenai/math_qa
today joelle opened an interest - bearing savings account and deposited $ 6000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
interest for 1 st year = 6000 * 5 / 100 = 300 interest for 2 nd year = 6300 * 5 / 100 = 315 total = 6000 + 300 + 315 = 6615 answer : d
a ) $ 6715 , b ) $ 5615 , c ) $ 6415 , d ) $ 6615 , e ) $ 6315
d
multiply(6000, power(add(const_1, divide(5, const_100)), const_2))
divide(n1,const_100)|add(#0,const_1)|power(#1,const_2)|multiply(n0,#2)
gain
allenai/math_qa
in a group of 28 junior high school students , 7 take french , 9 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
"e 8 add 7 + 9 + 4 to get 20 . then subtract 21 from the total students β‡’ 28 – 20 = 8 . answer is e"
a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 8
e
subtract(28, add(7, 9))
add(n1,n2)|subtract(n0,#0)|
other
allenai/math_qa
a can finish a work in 9 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
"b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 9 * 1 / 3 ) = 3 days . correct option : a"
a ) 3 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
a
divide(multiply(multiply(divide(const_1, 15), 10), 9), const_2)
divide(const_1,n1)|multiply(n2,#0)|multiply(n0,#1)|divide(#2,const_2)|
physics
allenai/math_qa
b takes 12 more days than a to finish a task . b and a start this task and a leaves the task 12 days before the task is finished . b completes 60 % of the overall task . how long would b have taken to finish the task if he had worked independently ?
detailed solution let us say a and b split their share of the task and started doing their respective shares simultaneously . let ’ s say a takes a days to finish the task . therefore , b takes a + 12 days to finish the entire task . a has to finish 40 % of the task , since b is doing the rest . so a will only take 2 a / 5 number of days . b only has to finish 60 % of the task , so b will take ( 3 ( a + 12 ) / 5 ) number of days . but as we know , b starts working along with a and finishes 12 days after a stops working . so , ( 3 ( a + 12 ) / 5 ) = ( ( 2 a ) / 5 + 12 ) 3 a + 36 = 2 a + 60 a = 24 ; b = 36 days . answer choice b
a ) 48 days , b ) 36 days , c ) 28 days , d ) 32 days , e ) 22 days
b
add(divide(multiply(12, const_10), add(const_4, const_1)), 12)
add(const_1,const_4)|multiply(n0,const_10)|divide(#1,#0)|add(n0,#2)
physics
allenai/math_qa
the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least Β½ foot when they are inside the traffic lane , what should be the limit l on the height of vehicles that are allowed to use the tunnel ?
"let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer l is 8 - . 5 = 7.5 . . . choose ( b ) !"
a ) 5 Β½ ft , b ) 7 Β½ ft , c ) 8 Β½ ft , d ) 9 Β½ ft , e ) 10 ft
b
subtract(divide(12, const_2), divide(const_1, const_2))
divide(n0,const_2)|divide(const_1,const_2)|subtract(#0,#1)|
physics
allenai/math_qa
a train 360 m long is running at a speed of 42 km / hr . in what time will it pass a bridge 140 m long ?
"speed = 42 * 5 / 18 = 35 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 35 = 43 sec answer : e"
a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 27 sec , e ) 43 sec
e
divide(360, multiply(subtract(42, 140), const_0_2778))
subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)|
physics
allenai/math_qa
150 is what percent of 60 ?
"60 * x = 150 - - > x = 2.5 - - > 2.5 expressed as percent is 250 % . answer : a ."
a ) 250 % , b ) 20 % , c ) 50 % , d ) 200 % , e ) 500 %
a
multiply(divide(150, 60), const_100)
divide(n0,n1)|multiply(#0,const_100)|
gain
allenai/math_qa
car a runs at the speed of 35 km / hr & reaches its destination in 9 hr . car b runs at the speed of 43 km / h & reaches its destination in 10 h . what is the respective ratio of distances covered by car a & car b ?
"sol . distance travelled by car a = 35 Γ— 9 = 315 km distance travelled by car b = 43 Γ— 10 = 430 km ratio = 315 / 430 = 63 : 86 e"
a ) 65 : 69 , b ) 56 : 45 , c ) 89 : 71 , d ) 68 : 23 , e ) 63 : 86
e
divide(multiply(35, 9), multiply(43, 10))
multiply(n0,n1)|multiply(n2,n3)|divide(#0,#1)|
physics
allenai/math_qa
in what time will a train 100 meters long cross an electric pole , if its speed is 36 km / hr
"first convert speed into m / sec speed = 36 * ( 5 / 18 ) = 10 m / sec time = distance / speed = 100 / 10 = 10 seconds answer : b"
a ) 8.5 seconds , b ) 10 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
b
divide(100, multiply(36, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
allenai/math_qa
working alone , john finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . john alone cleans the entire house in 6 hours . how many hours will it take nick and john to clean the entire house if they work together ?
answer is 3.6 hours . john does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6
e
inverse(add(inverse(6), inverse(multiply(divide(const_3, const_2), 6))))
divide(const_3,const_2)|inverse(n0)|multiply(n0,#0)|inverse(#2)|add(#1,#3)|inverse(#4)
physics
allenai/math_qa
find the value of 3 / 11 Γ— [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) … … … … . ( 1 + 1 / 120 ) ] is ?
"3 / 11 Γ— [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 Γ— [ 4 / 3 + 5 / 4 Γ— . . . . . . . . 121 / 120 ] 3 / 11 Γ— 4 / 3 Γ— 5 / 4 Γ— . . . . 121 / 120 121 / 11 = 11 . a )"
a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 16
a
divide(add(120, 1), 11)
add(n2,n10)|divide(#0,n1)|
general
allenai/math_qa
a certain bag contains 60 balls β€” 22 white , 18 green , 5 yellow , 6 red , and 9 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 5 ) / 60 = 45 / 60 = 0.75 . answer : d .
a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.75 , e ) 0.91
d
divide(add(add(22, 18), 5), 60)
add(n1,n2)|add(n3,#0)|divide(#1,n0)
other
allenai/math_qa
if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction .
"let the original fraction be x / y . then ( 115 % of x ) / ( 92 % of y ) = 15 / 16 = > ( 115 x / 92 y ) = 15 / 16 = ( ( 15 / 16 ) * ( 92 / 115 ) ) = 3 / 4 answer is a ."
a ) 3 / 4 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 , e ) none of them
a
divide(multiply(subtract(const_100, 8), 15), multiply(add(const_100, 15), 16))
add(n0,const_100)|subtract(const_100,n1)|multiply(n2,#1)|multiply(n3,#0)|divide(#2,#3)|
general
allenai/math_qa
the median annual household income in a certain community of 21 households is $ 50000 . if the mean w income of a household increases by 10 % per year over the next 2 years , what will the median income in the community be in 2 years ?
answer is e , because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean w is increase by 10 % . it could be the case that small number of higher end incomes increased a little or many low end incomes increased - it can not be identified .
a ) $ 50000 , b ) $ 60000 , c ) $ 60500 , d ) $ 65000 , e ) can not be determined
e
log(subtract(divide(10, 2), 10))
divide(n2,n3)|subtract(#0,n2)|log(#1)
general
allenai/math_qa
a lemonade stand sold only small and large cups of lemonade on tuesday . 2 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
"a simpler way i guess would be to think that in total 5 cups were sold . out of which 2 are small and 3 are large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 2 * 6 = 12 and 3 * 7 = 21 . total revenue was 12 + 21 = 33 and large cup sales as found above is 21 therefore answer is 21 / 33 i . e 7 / 11 b"
a ) ( a ) 7 / 16 , b ) ( b ) 7 / 11 , c ) ( c ) 10 / 21 , d ) ( d ) 17 / 35 , e ) ( e ) 1 / 2
b
divide(multiply(subtract(const_10, multiply(divide(2, 5), const_10)), multiply(divide(7, 6), multiply(divide(2, 5), const_10))), add(multiply(multiply(divide(2, 5), const_10), multiply(divide(2, 5), const_10)), multiply(subtract(const_10, multiply(divide(2, 5), const_10)), multiply(divide(7, 6), multiply(divide(2, 5), const_10)))))
divide(n2,n3)|divide(n0,n1)|multiply(#1,const_10)|multiply(#0,#2)|multiply(#2,#2)|subtract(const_10,#2)|multiply(#3,#5)|add(#4,#6)|divide(#6,#7)|
general
allenai/math_qa
if x is less than y by 40 % then y exceed x by :
"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 40 % ) = > 40 / ( 100 - 40 ) * 100 = 66.66 % answer : d"
a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these
d
multiply(subtract(divide(const_100, subtract(const_100, 40)), const_1), const_100)
subtract(const_100,n0)|divide(const_100,#0)|subtract(#1,const_1)|multiply(#2,const_100)|
general
allenai/math_qa
the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is
"solution clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer d"
a ) 276 , b ) 299 , c ) 312 , d ) 322 , e ) none
d
multiply(23, 14)
multiply(n0,n2)|
other
allenai/math_qa
if 20 % of a = b , then b % of 20 is the same as :
"20 % of a = b b % of 20 = = = = 4 % of a . answer : a"
a ) 4 % of a , b ) 8 % of a , c ) 12 % of a , d ) 9 % of a , e ) 1 % of a
a
divide(20, 20)
divide(n1,n0)|
gain
allenai/math_qa
ms . lopez deposits $ 140 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
using formula - a = p ( 1 + r / n ) ^ nt given p = 140 n = 2 t = 1 r = 0.2 substituting value in formula a = 140 ( 1 + 0.2 / 2 ) ^ 2 a = 169.40 $ = c
a ) $ 118.00 , b ) $ 120.00 , c ) $ 169.40 , d ) $ 122.00 , e ) $ 140.00
c
multiply(140, power(add(const_1, divide(divide(20, const_100), const_2)), const_2))
divide(n1,const_100)|divide(#0,const_2)|add(#1,const_1)|power(#2,const_2)|multiply(n0,#3)
gain
allenai/math_qa
a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 20 gallons of gasoline ?
"so 12.2 * 20 = 244 . . imo option d is correct answer . ."
a ) 190 , b ) 284.6 , c ) 300 , d ) 244 , e ) 312
d
multiply(12.2, 20)
multiply(n0,n2)|
general
allenai/math_qa
if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 278 pounds . what is jake ’ s present weight , in pounds ?
"consider sister weight now as x jakes weight ( 2 times + 8 ) = 2 x + 8 ( 2 x + 8 ) + ( x ) = 278 x = 90 jake ' s weight is . . . . 188 correct answer is e"
a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188
e
add(multiply(divide(subtract(278, 8), const_3), const_2), 8)
subtract(n1,n0)|divide(#0,const_3)|multiply(#1,const_2)|add(n0,#2)|
general
allenai/math_qa
john ' s bank ' s saving amount is decreased 12 % due to loan payment and current balance is rs . 44000 . find the actual balance before deduction ?
12 % decreased 88 % balance = 44000 100 % = 44000 / 88 * 100 = 50000 answer : b
a ) 8000 , b ) 50000 , c ) 9000 , d ) 9500 , e ) 10000
b
add(divide(multiply(44000, 12), const_100), 44000)
multiply(n0,n1)|divide(#0,const_100)|add(n1,#1)
gain
allenai/math_qa
the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 12 and 13 . the larger of the two numbers is :
"clearly , the numbers are ( 23 * 12 ) and ( 23 * 13 ) . larger number = ( 23 * 13 ) = 299 . answer : a"
a ) 299 , b ) 278 , c ) 322 , d ) 231 , e ) 121
a
multiply(23, 13)
multiply(n0,n2)|
other
allenai/math_qa
a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 290 m long ?
"explanation : speed = 45 km / hr = 45 Γ— ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 290 = 650 meter time taken to cross the platform = 650 / ( 25 / 2 ) = 650 Γ— 2 / 25 = 52 seconds answer : option e"
a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 52 sec
e
multiply(divide(add(divide(290, const_1000), divide(360, const_1000)), 45), const_3600)
divide(n2,const_1000)|divide(n0,const_1000)|add(#0,#1)|divide(#2,n1)|multiply(#3,const_3600)|
physics
allenai/math_qa
a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 684 , what is the reduced price for kg ?
"684 * ( 20 / 100 ) = 136 - - - - 4 ? - - - - 1 = > rs . 34 answer : c"
a ) 72 , b ) 27 , c ) 34 , d ) 28 , e ) 20
c
divide(divide(multiply(684, 20), const_100), 4)
multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)|
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 , 60 km / hr respectively . b starts six hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
"the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )"
a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5
d
subtract(40, 30)
subtract(n1,n0)|
physics
allenai/math_qa
if all of the telephone extensions in a certain company must be even numbers , and if each of the extensions uses all 4 of the digits 1 , 2 , 3 , and 8 , what is the greatest number of 4 - digit extensions that the company can have ?
since the phone number must be even , the unit ' s digit can be either 2 or 8 . when the unit ' s digit is 2 - - > number of possibilities is 3 ! = 6 when the unit ' s digit is 8 - - > number of possibilities is 3 ! = 6 largest number of extensions = 6 + 6 = 12 answer : c
a ) 4 , b ) 6 , c ) 12 , d ) 16 , e ) 24
c
multiply(4, const_3)
multiply(n0,const_3)
general
allenai/math_qa
according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 360 6 ounces servings of orange juice ?
"its a . total juice rquired = 360 * 6 = 2160 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 2160 / 48 = 45 . answer a"
a ) a ) 45 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
a
divide(divide(multiply(360, 6), 12), const_4)
multiply(n3,n4)|divide(#0,n2)|divide(#1,const_4)|
general
allenai/math_qa
a portion of the 80 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 50 % solution of chemicals resulted . what part of the original solution was replaced ?
"this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.8 ( 1 - x ) + 0.2 * x = 0.5 - - > x = 1 / 2 . answer : b ."
a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
b
divide(subtract(80, 50), subtract(80, 20))
subtract(n0,n2)|subtract(n0,n1)|divide(#0,#1)|
gain
allenai/math_qa
the area of a square is equal to five times the area of a rectangle of dimensions 60 cm * 12 cm . what is the perimeter of the square ?
"area of the square = s * s = 5 ( 60 * 12 ) = > s = 60 = 60 cm perimeter of the square = 4 * 60 = 240 cm . answer : e"
a ) 289 cm , b ) 800 cm , c ) 829 cm , d ) 288 cm , e ) 240 cm
e
multiply(sqrt(multiply(rectangle_area(60, 12), divide(12, const_2))), const_4)
divide(n1,const_2)|rectangle_area(n0,n1)|multiply(#0,#1)|sqrt(#2)|multiply(#3,const_4)|
geometry
allenai/math_qa
in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 5 hours a day , the number of men required is :
"explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 5 : 8 : : 12 : x = > 8 x 5 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 5 ) = > x = 24 answer : a"
a ) 24 , b ) 5 , c ) 6 , d ) 8 , e ) 9
a
divide(divide(multiply(multiply(12, 8), 10), 5), 8)
multiply(n0,n1)|multiply(n2,#0)|divide(#1,n4)|divide(#2,n1)|
physics
allenai/math_qa
if two integers x , y ( x > y ) are selected from - 6 to 6 ( inclusive ) , how many cases are there ?
"there are 13 integers from - 6 to 6 inclusive . 13 c 2 = 78 . the answer is c ."
a ) 70 , b ) 74 , c ) 78 , d ) 82 , e ) 86
c
add(add(add(add(add(add(add(6, 6), add(6, const_2)), add(6, const_1)), 6), 6), const_2), const_1)
add(n0,n1)|add(n1,const_2)|add(n1,const_1)|add(#0,#1)|add(#3,#2)|add(#4,n1)|add(#5,n0)|add(#6,const_2)|add(#7,const_1)|
general
allenai/math_qa
the h . c . f . of two numbers is 59 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is :
: explanation : clearly , the numbers are ( 59 x 13 ) and ( 59 x 16 ) . { \ color { blue } \ therefore } larger number = ( 59 x 16 ) = 944 . answer : b ) 944
a ) 678 , b ) 944 , c ) 456 , d ) 323 , e ) 899
b
multiply(59, 16)
multiply(n0,n2)
other
allenai/math_qa
john had a stock of 620 books in his bookshop . he sold 50 on monday , 82 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
"let n be the total number of books sold . hence n = 50 + 82 + 64 + 78 + 135 = 280 let m be the books not sold m = 620 - n = 620 - 280 = 340 percentage books not sold / total number of books = 340 / 620 = 0.55 = 54.84 % correct answer a"
a ) 54.84 % , b ) 36.5 % , c ) 46.5 % , d ) 56.5 % , e ) 66.5 %
a
multiply(divide(subtract(620, add(add(add(50, 82), add(60, 48)), 40)), 620), const_100)
add(n1,n2)|add(n3,n4)|add(#0,#1)|add(n5,#2)|subtract(n0,#3)|divide(#4,n0)|multiply(#5,const_100)|
gain
allenai/math_qa
on a scale of map , 0.6 cm represent 6.6 km . if the distance between the points on the map is 80.5 cm , the actual distance between these points is :
solution let the actual distance be x km . then , more distance on the map , more is the actual distance ( direct proportion ) ∴ 0.6 : 80.5 : : 6.6 : x ⇔ 0.6 x = 80.5 Γ— 6.6 ⇔ x = ⇔ x = 80.5 x 6.6 / 0.6 = x = 885.5 . answer d
a ) 9 km , b ) 72.5 km , c ) 190.75 km , d ) 885.5 km , e ) none of these
d
divide(multiply(80.5, 6.6), 0.6)
multiply(n1,n2)|divide(#0,n0)
physics
allenai/math_qa
if the average of 8 x and 8 y is greater than 120 , and x is twice y , what is the least integer value of x ?
"substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 8 x and 4 x is greater than 120 . average of 8 x and 4 x is 6 x . so , 6 x > 120 x > 20 answer : a"
a ) 20 , b ) 25 , c ) 30 , d ) 32 , e ) 42
a
multiply(8, const_2)
multiply(n0,const_2)|
general
allenai/math_qa
two trains are moving in opposite directions with speed of 210 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
explanation : relative speed = 210 + 90 = 300 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 300 hr = 1 / 150 hr = 3600 / 150 seconds = 24 seconds answer : option e
a ) 56 , b ) 48 , c ) 47 , d ) 26 , e ) 24
e
multiply(divide(add(1.1, 0.9), add(210, 90)), const_3600)
add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)
physics
allenai/math_qa
roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 4 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
"distance = relative speed * time = ( 4 + 3 ) * 4 = 28 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : a"
a ) 28 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 16 km
a
multiply(add(4, 3), 4)
add(n0,n1)|multiply(n2,#0)|
physics
allenai/math_qa
in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 24,947 . approximately what was the percent increase ?
"the percent increase is ( 24947 - 8902 ) / 8902 = 16045 / 8902 = 1.80 so the approximate answer is e"
a ) 45 % , b ) 125 % , c ) 145 % , d ) 150 % , e ) 180 %
e
divide(subtract(24,947, 8,902), 8,902)
subtract(n3,n1)|divide(#0,n1)|
general
allenai/math_qa
a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
"for 40 hrs = 40 * 16 = 640 excess = 976 - 640 = 336 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 336 / 28 = 12 total hrs = 40 + 12 = 52 answer b"
a ) 51 , b ) 52 , c ) 59 , d ) 55 , e ) 56
b
add(40, divide(subtract(976, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))
add(n3,const_100)|multiply(n0,n1)|multiply(n0,#0)|subtract(n4,#1)|divide(#2,const_100)|divide(#3,#4)|add(n1,#5)|
general
allenai/math_qa
if x is a positive integer , then the least value of x for which x ! is divisible by 100,000 is ? can someone please explain intuitively what the question is asking ?
in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d .
a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30
d
multiply(divide(const_10, const_2), const_4)
divide(const_10,const_2)|multiply(#0,const_4)
general
allenai/math_qa
a man is 18 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
"explanation : let ' s son age is x , then father age is x + 18 . = > 2 ( x + 2 ) = ( x + 18 + 2 ) = > 2 x + 4 = x + 20 = > x = 16 years option e"
a ) 21 years , b ) 22 years , c ) 23 years , d ) 12 years , e ) 16 years
e
divide(subtract(18, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))
multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)|
general
allenai/math_qa