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mlfoundations-dev
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load_in_math_allenai_math

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5
967
Rationale
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options
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correct
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5 values
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_source
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1 value
a number is doubled and 9 is added . if resultant is trebled , it becomes 69 . what is that number
"explanation : = > 3 ( 2 x + 9 ) = 69 = > 2 x + 9 = 23 = > x = 7 answer : option a"
a ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 15
a
divide(subtract(69, multiply(const_3, 9)), multiply(const_3, const_2))
multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)|
general
allenai/math_qa
the monthly rent of a shop of dimension 20 feet × 15 feet is rs . 3600 . what is the annual rent per square foot of the shop ?
"sol . monthly rent per square feet = 3600 / ( 20 * 15 ) = 12 & annual rent per square feet = 12 * 12 = 144 answer : b"
a ) 43 , b ) 144 , c ) 68 , d ) 87 , e ) 92
b
multiply(add(const_10, const_2), divide(3600, rectangle_area(20, 15)))
add(const_10,const_2)|rectangle_area(n0,n1)|divide(n2,#1)|multiply(#0,#2)|
geometry
allenai/math_qa
john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 40,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 40,000 ( 1 + 0.04 / 4 ) ^ 4 - 40,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 40,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 40,000 ( 1.0201 + 1 ) = 80804 . hence answer is e .
a ) 50000 , b ) 55000 , c ) 60000 , d ) 70000 , e ) 80804
e
divide(subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(divide(4, const_100), const_4)), const_4)), multiply(multiply(const_4, const_100), const_100)), subtract(power(add(const_1, divide(divide(2, const_100), const_2)), const_2), const_1))
divide(n2,const_100)|divide(n0,const_100)|multiply(const_100,const_4)|divide(#0,const_4)|divide(#1,const_2)|multiply(#2,const_100)|add(#3,const_1)|add(#4,const_1)|power(#6,const_4)|power(#7,const_2)|multiply(#5,#8)|subtract(#9,const_1)|subtract(#10,#5)|divide(#12,#11)
gain
allenai/math_qa
machine x and machine b are each used to manufacture 660 sprockets . it takes machine x 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine x . how many sprockets per hour does machine x produces ?
i think the correct answer is a . machine x produces at a speed of x sp / hour and b at a speed of b sp / hour . so , 660 / x = ( 660 / b ) + 10 and x = 1,1 x - - - > 1,1 * 660 = 660 + 11 x - - - > a = 6 , so answer a is correct
a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
a
divide(660, multiply(add(const_1, divide(10, const_100)), const_100))
divide(n1,const_100)|add(#0,const_1)|multiply(#1,const_100)|divide(n0,#2)
general
allenai/math_qa
john and steve are speed walkers in a race . john is 16 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
"let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 16 + 2 - - - > 0.5 t = 18 - - - > t = 36 seconds . c is the correct answer ."
a ) 13 seconds , b ) 17 seconds , c ) 36 seconds , d ) 34 seconds , e ) 51 seconds
c
divide(add(divide(multiply(3.7, add(16, 2)), subtract(4.2, 3.7)), add(16, 2)), 4.2)
add(n0,n3)|subtract(n1,n2)|multiply(n2,#0)|divide(#2,#1)|add(#0,#3)|divide(#4,n1)|
physics
allenai/math_qa
a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 50 km / hr . what is the speed of the car in the second half of the trip ?
"let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 100 + ( d / 2 ) / v d / 150 = d / 2 v and so v = 75 km / hr the answer is c ."
a ) 55 , b ) 60 , c ) 75 , d ) 80 , e ) 90
c
divide(multiply(60, divide(multiply(50, 60), multiply(subtract(50, 60), 60))), divide(60, const_10))
divide(n0,const_10)|multiply(n0,n1)|subtract(n1,n0)|multiply(n0,#2)|divide(#1,#3)|multiply(n0,#4)|divide(#5,#0)|
general
allenai/math_qa
a box contains 6 white , 5 red and 8 white marbles . 5 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
explanation : total marbles in a box = 6 black + 5 red + 8 green marbles = 19 marbles 5 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 5 = 11628 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 6 c 5 + 5 c 5 + 8 c 5 = 6 + 1 + 56 = 63 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 63 / 11628 answer : e
a ) 19 / 11628 , b ) 36 / 11628 , c ) 613 / 11628 , d ) 6113 / 11628 , e ) 63 / 11628
e
divide(add(add(divide(factorial(6), factorial(5)), divide(factorial(5), factorial(5))), divide(factorial(8), multiply(factorial(subtract(8, 5)), factorial(5)))), divide(factorial(add(add(6, 5), 8)), multiply(factorial(5), factorial(subtract(add(add(6, 5), 8), 5)))))
add(n0,n1)|factorial(n0)|factorial(n1)|factorial(n2)|subtract(n2,n1)|add(n2,#0)|divide(#1,#2)|divide(#2,#2)|factorial(#4)|add(#6,#7)|factorial(#5)|multiply(#8,#2)|subtract(#5,n1)|divide(#3,#11)|factorial(#12)|add(#9,#13)|multiply(#2,#14)|divide(#10,#16)|divide(#15,#17)
other
allenai/math_qa
when a mobile is sold for rs . 24000 , the owner loses 40 % . at what price must that mobile be sold in order to gain 40 % ?
"60 : 24000 = 140 : x x = ( 24000 x 140 ) / 60 = 56000 . hence , s . p . = rs . 56,000 . answer : option b"
a ) 54,000 , b ) 56,000 , c ) 58,000 , d ) 60,000 , e ) 62,000
b
floor(multiply(divide(divide(divide(multiply(divide(multiply(24000, const_100), subtract(const_100, 40)), add(const_100, 40)), const_100), const_100), 40), const_2))
add(n1,const_100)|multiply(n0,const_100)|subtract(const_100,n1)|divide(#1,#2)|multiply(#0,#3)|divide(#4,const_100)|divide(#5,const_100)|divide(#6,n1)|multiply(#7,const_2)|floor(#8)|
gain
allenai/math_qa
a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
"there are 60 siblings in junior class and 60 their pair siblings in the senior class . we want to determine probability of choosing one sibling from junior class and its pair from senior . what is the probability of choosing any sibling from junior class ? 60 / 1000 ( as there are 60 of them ) . what is the probability of choosing pair of chosen sibling in senior class ? as in senior class there is only one pair of chosen sibling it would be 1 / 800 ( as there is only one sibling pair of chosen one ) . so the probability of that the 2 students selected will be a sibling pair is : 60 / 1000 ∗ 1 / 800 = 3 / 40000 answer : a ."
a ) 3 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
a
divide(1, const_3)
divide(n3,const_3)|
probability
allenai/math_qa
you collect baseball cards . suppose you start out with 13 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
"solution start with 13 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 13 + 1 which is 7 , so you ' re left with 13 - 7 = 6 . peter takes 1 baseball card from you : 6 - 1 = 5 baseball cards . paul triples the number of baseball cards you have : 5 ã — 3 = 15 baseball cards . so you have 15 at the end . correct answer : a"
a ) 15 , b ) 18 , c ) 19 , d ) 20 , e ) 21
a
multiply(subtract(subtract(subtract(13, const_4), const_4), 1), const_3)
subtract(n0,const_4)|subtract(#0,const_4)|subtract(#1,n1)|multiply(#2,const_3)|
general
allenai/math_qa
if - 11 and - 8 are negative integers , then - 11 * - 8 + 5 is
answer : e
a ) - 14 , b ) 14 , c ) 33 , d ) 83 , e ) 93
e
add(multiply(negate(11), negate(8)), 5)
negate(n0)|negate(n1)|multiply(#0,#1)|add(n4,#2)|
general
allenai/math_qa
two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 9 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
"rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 9 combined = 5 / 18 work done in 2 days = 5 / 9 work left = 4 / 9 rate * time = work left 1 / 8 * time = 4 / 9 time = 32 / 9 b"
a ) 7 / 4 , b ) 32 / 9 , c ) 15 / 4 , d ) 10 / 3 , e ) 17 / 5
b
max(divide(subtract(const_1, multiply(add(divide(const_1, add(const_4, const_2)), divide(const_1, 9)), const_2)), divide(const_1, 9)), const_3)
add(const_2,const_4)|divide(const_1,n0)|divide(const_1,#0)|add(#2,#1)|multiply(#3,const_2)|subtract(const_1,#4)|divide(#5,#1)|max(#6,const_3)|
physics
allenai/math_qa
a man can row upstream at 20 kmph and downstream at 60 kmph , and then find the speed of the man in still water ?
"us = 20 ds = 60 m = ( 20 + 60 ) / 2 = 40 answer : e"
a ) 32 kmph , b ) 34 kmph , c ) 30 kmph , d ) 45 kmph , e ) 40 kmph
e
divide(add(20, 60), const_2)
add(n0,n1)|divide(#0,const_2)|
physics
allenai/math_qa
if the annual increase in the population of a town is 4 % and the present number of people is 15625 , what will the population be in 3 years ?
"the required population is = 15625 ( 1 + 4 / 100 ) ^ 3 = 15625 * 26 / 25 * 26 / 25 * 26 / 25 = 17576 answer is d"
a ) 15265 , b ) 16458 , c ) 25600 , d ) 17576 , e ) 14785
d
multiply(multiply(divide(add(4, const_100), const_100), 15625), divide(add(4, const_100), const_100))
add(n0,const_100)|divide(#0,const_100)|multiply(n1,#1)|multiply(#1,#2)|
gain
allenai/math_qa
for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 25 true ?
answer d ( a + b ) ( a - b ) = 25 5 cases for ( a + b ) , ( a - b ) 25 , 1 5 , 5 answer d
a ) 1 , b ) 3 , c ) 5 , d ) 2 , e ) 9
d
divide(log(25), log(add(const_4, const_1)))
add(const_1,const_4)|log(n2)|log(#0)|divide(#1,#2)
general
allenai/math_qa
how many integers between 324,700 and 418,600 have tens digit 1 and units digit 3 ?
"the integers are : 324,713 324,813 etc . . . 418,513 the number of integers is 4186 - 3247 = 939 the answer is c ."
a ) 652 , b ) 827 , c ) 939 , d ) 1045 , e ) 1136
c
subtract(418,600, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2))
add(const_3,const_4)|multiply(const_100,const_2)|multiply(#0,const_10)|add(#1,#2)|add(#3,const_2)|subtract(n1,#4)|
general
allenai/math_qa
a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 61.50 , his capital is ?
"let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 61.50 32 x - 31 x = 6150 * 4 x = 24,600 . answer : c"
a ) 24,607 , b ) 24,609 , c ) 24,600 , d ) 24,602 , e ) 24,604
c
divide(61.50, divide(const_4, 4))
divide(const_4,n3)|divide(n4,#0)|
gain
allenai/math_qa
there are 24 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
"the total number of stations = 26 from 26 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 26 p 2 ways . 26 p 2 = 26 * 25 = 650 answer : c"
a ) 800 , b ) 820 , c ) 650 , d ) 870 , e ) 900
c
multiply(add(24, const_2), subtract(add(24, const_2), const_1))
add(n0,const_2)|subtract(#0,const_1)|multiply(#0,#1)|
physics
allenai/math_qa
if a trader sold two cars each at rs . 325475 and gains 10 % on the first and loses 10 % on the second , then his profit or loss percent on the whole is ?
"sp of each car is rs . 325475 , he gains 10 % on first car and losses 10 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 10 ) ( 10 ) / 100 % = 1.00 % answer : e"
a ) 1.44 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.00 %
e
divide(multiply(10, 10), const_100)
multiply(n1,n1)|divide(#0,const_100)|
gain
allenai/math_qa
1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ?
"1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ? 9 = 3 check the third eqn . answer : c"
a ) 1 , b ) 255 , c ) 3 , d ) 445 , e ) 235
c
divide(subtract(subtract(25, multiply(multiply(add(const_4, const_2), add(const_4, const_2)), const_10)), 1), const_2)
add(const_2,const_4)|multiply(#0,#0)|multiply(#1,const_10)|subtract(n5,#2)|subtract(#3,n0)|divide(#4,const_2)|
general
allenai/math_qa
in 10 years , a will be twice as old as b was 10 years ago . if a is now 8 years older than b the present age of b is
"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 8 = > 2 b - b - 8 = 30 b = 38 so the present age of b is 38 years answer : b"
a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41
b
add(add(multiply(const_2, 10), 10), 8)
multiply(n0,const_2)|add(n0,#0)|add(n2,#1)|
general
allenai/math_qa
fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.55 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
"let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.55 9.9 - 45 x + 36 x = 8.55 9 x = 1.35 x = 0.15 the answer is e ."
a ) 7 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
e
multiply(subtract(divide(22, const_100), divide(subtract(8.55, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100)
divide(n6,const_100)|multiply(n1,n5)|multiply(n0,n4)|multiply(#0,#1)|subtract(#2,#1)|subtract(n2,#3)|divide(#5,#4)|subtract(#0,#6)|multiply(#7,const_100)|
gain
allenai/math_qa
the number x of cars sold each week varies with the price y in dollars according to the equation x = 800000 – 50 y . what would be the total weekly revenue w , in dollars , from the sale of cars priced at $ 15000 ?
number of cars sold = x = 800000 - 50 y y = 15000 x = 800000 - 750000 = 50000 revenue from 50000 cars = 15000 * 50000 = 750000000 e
a ) 50000 , b ) 750000 , c ) 850000 , d ) 7 , 500000 , e ) w = 75000,000
e
divide(reminder(multiply(subtract(800000, multiply(50, 15000)), 15000), multiply(const_100, multiply(const_1000, const_1000))), const_100)
multiply(n1,n2)|multiply(const_1000,const_1000)|multiply(#1,const_100)|subtract(n0,#0)|multiply(n2,#3)|reminder(#4,#2)|divide(#5,const_100)
general
allenai/math_qa
a sum of money at simple interest amounts to rs . 2240 in 2 years and to rs . 2600 in 5 years . the sum is :
"s . i . for 3 years = rs . ( 2600 - 2240 ) = rs . 360 . s . i . for 1 year = rs . 360 / 3 = rs . 120 . s . i . for 2 years = rs . ( 120 x 2 ) = rs . 240 . principal = rs . ( 2240 - 240 ) = rs . 2000 . answer : option b"
a ) rs . 1500 , b ) rs . 2000 , c ) rs . 1000 , d ) rs . 1200 , e ) rs . 1800
b
subtract(2240, divide(multiply(subtract(2600, 2240), 2), 5))
subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)|
gain
allenai/math_qa
amit and ananthu can do a work in 15 days and 30 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
"amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 30 ananthu can do work in = 4 / 5 * 30 = 24 days so total days = 24 + 3 = 27 days answer : e"
a ) 28 days , b ) 20 days , c ) 23 days , d ) 25 days , e ) 27 days
e
add(divide(subtract(const_1, multiply(inverse(15), 3)), inverse(30)), 3)
inverse(n0)|inverse(n1)|multiply(#0,n2)|subtract(const_1,#2)|divide(#3,#1)|add(#4,n2)|
physics
allenai/math_qa
if the sum of two positive integers is 20 and the difference of their squares is 40 , what is the product of the two integers ?
"let the 2 positive numbers x and y x + y = 20 - - 1 x ^ 2 - y ^ 2 = 40 = > ( x + y ) ( x - y ) = 40 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 11 y = 9 product = 11 * 9 = 99 answer b"
a ) 108 , b ) 99 , c ) 128 , d ) 135 , e ) 143
b
multiply(divide(subtract(20, divide(40, 20)), divide(40, 20)), add(divide(subtract(20, divide(40, 20)), divide(40, 20)), divide(40, 20)))
divide(n1,n0)|subtract(n0,#0)|divide(#1,#0)|add(#2,#0)|multiply(#3,#2)|
general
allenai/math_qa
the price of lunch for 15 people was $ 209.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
"take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 209 is for 115 then we have to calculate for 100 for 115 209 for 100 x so by cross multiplication we get 115 x = 100 * 209 = > x = 100 * 209 / 110 by simplifying we get x as 190 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 190 / 15 = 12.66 so our answer is b )"
a ) $ 11.73 , b ) $ 12.66 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
b
multiply(multiply(divide(209.00, add(const_100, 15)), const_100), divide(const_1, 15))
add(n0,const_100)|divide(const_1,n0)|divide(n1,#0)|multiply(#2,const_100)|multiply(#1,#3)|
general
allenai/math_qa
in how many ways can a teacher write an answer key for a mini - quiz that contains 3 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
2 multiples - choice questions can be answered in = 4 x 4 = 16 ways 3 true - false questions can be answered in = 2 x 2 x 2 = 8 ways but out of the 8 ways , 2 ways [ ( true - true - true ) ( false - false - false ) ] will contain same answers thus 3 true - false questions can be answered in = 2 x 2 x 2 = 6 ways total ways to answer the quiz = 16 x 6 = 96 answer c
a ) 88 , b ) 90 , c ) 96 , d ) 98 , e ) 102
c
multiply(subtract(multiply(const_2, multiply(2, 2)), 2), multiply(const_4, const_4))
multiply(const_4,const_4)|multiply(n1,n1)|multiply(#1,const_2)|subtract(#2,n1)|multiply(#0,#3)
general
allenai/math_qa
annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 25 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
"annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 25 minutes , sam rides 5 km so sam will be 3 km ahead . it will take annie 60 minutes to catch sam . the answer is c ."
a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
c
multiply(divide(subtract(divide(12, multiply(subtract(15, 12), divide(40, const_60))), multiply(subtract(15, 12), divide(40, const_60))), subtract(15, 12)), const_60)
divide(n2,const_60)|subtract(n0,n1)|multiply(#0,#1)|divide(n1,#2)|subtract(#3,#2)|divide(#4,#1)|multiply(#5,const_60)|
physics
allenai/math_qa
in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 180 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 = 180 = > 4 x / 10 = 180 = > 4 x = 1800 = > x = 450 . answer : a"
a ) 450 , b ) 570 , c ) 480 , d ) 520 , e ) 550
a
divide(180, 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
three unbiased coins are tossed , what is the probability of getting at least 2 tails ?
"total cases are = 2 ^ 3 = 8 favoured cases = [ tth , tht , htt , ttt ] = 4 probability = 4 / 8 = 1 / 2 answer d"
a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 2 , e ) 1 / 10
d
negate_prob(divide(const_1, power(const_2, const_3)))
power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)|
probability
allenai/math_qa
150 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
"milk = 3 / 5 * 150 = 90 liters water = 50 liters 90 : ( 50 + p ) = 3 : 4 150 + 3 p = 360 = > p = 70 50 liters of water are to be added for the ratio become 3 : 4 . answer : c"
a ) 90 liters , b ) 20 liters , c ) 50 liters , d ) 20 liters , e ) 70 liters
c
multiply(divide(150, add(3, 2)), 2)
add(n1,n2)|divide(n0,#0)|multiply(n2,#1)|
general
allenai/math_qa
the average of 13 numbers is 60 . average of the first 6 of them is 57 and that of the last 8 is 61 . find the 8 th number ?
"sum of all the 13 numbers = 13 * 60 = 780 sum of the first 6 of them = 6 * 57 = 342 sum of the last 8 of them = 8 * 61 = 488 so , the 8 th number = 342 + 488 - 780 = 50 . answer : c"
a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54
c
subtract(multiply(8, 61), subtract(multiply(13, 60), multiply(57, 6)))
multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)|
general
allenai/math_qa
the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 54 . what is the difference between the two digits of that number ?
sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 54 ⇔ 9 ( x - y ) = 54 ⇔ x - y = 6 answer c
a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
c
divide(54, subtract(const_10, const_1))
subtract(const_10,const_1)|divide(n0,#0)
general
allenai/math_qa
subtracting 2 % of a from a is equivalent to multiplying a by how much ?
answer let a - 2 % of a = ab . ⇒ ( 98 x a ) / 100 = ab ∴ b = 0.98 correct option : a
a ) 0.98 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
a
divide(subtract(const_100, 2), const_100)
subtract(const_100,n0)|divide(#0,const_100)
general
allenai/math_qa
if the radius of a circle is decreased 20 % , what happens to the area ?
"area of square = pi * radius ^ 2 new radius = 4 / 5 * old radius so new area = ( 4 / 5 ) ^ 2 old area = > 16 / 25 of old area = > 64 % old area answer : c"
a ) 10 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
c
subtract(const_100, multiply(power(divide(20, const_100), const_2), const_100))
divide(n0,const_100)|power(#0,const_2)|multiply(#1,const_100)|subtract(const_100,#2)|
geometry
allenai/math_qa
a car gets 30 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 200 kilometers ?
"each 30 kilometers , 1 gallon is needed . we need to know how many 30 kilometers are there in 200 kilometers ? 200 ã · 30 = 6.7 ã — 1 gallon = 6.7 gallons correct answer is c ) 6.7 gallons"
a ) 3.5 gallons , b ) 2.7 gallons , c ) 6.7 gallons , d ) 4.5 gallons , e ) 7.5 gallons
c
divide(200, 30)
divide(n1,n0)|
physics
allenai/math_qa
in town x , 64 percent of the population are employed , and 55 percent of the population are employed males . what percent of the employed people in town x are females ?
"we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 55 are employed males , hence 9 % are employed females . ( employed females ) / ( total employed people ) = 9 / 64 = 14 % answer : a ."
a ) 14 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
a
multiply(divide(subtract(64, 55), 64), const_100)
subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|
gain
allenai/math_qa
if the sales tax be reduced from 4 ( 1 / 4 ) % to 1 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 4500 ?
explanation : required difference = ( 4 ( 1 / 4 ) of rs . 4500 ) - ( 1 ( 1 / 2 ) of rs . 4500 ) = ( 17 / 4 – 3 / 2 ) % of rs . 4500 = ( 11 / 4 ) x ( 1 / 100 ) x 4500 = rs . 123.75 answer c
a ) rs . 156.66 , b ) rs . 150.23 , c ) rs . 123.75 , d ) rs . 135.06 , e ) none of these
c
subtract(multiply(add(divide(add(4, divide(1, 4)), const_100), 1), divide(4500, add(divide(add(divide(1, 2), 1), const_100), 1))), 4500)
divide(n1,n0)|divide(n1,n5)|add(n0,#0)|add(n1,#1)|divide(#2,const_100)|divide(#3,const_100)|add(n1,#4)|add(n1,#5)|divide(n6,#7)|multiply(#6,#8)|subtract(#9,n6)
general
allenai/math_qa
three table runners have a combined area of 208 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 208 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 208 - 24 - 140 all three = 22 answer : a
['a ) 22 square inches', 'b ) 20 square inches', 'c ) 24 square inches', 'd ) 28 square inches', 'e ) 30 square inches']
a
divide(subtract(subtract(208, 24), multiply(175, divide(80, const_100))), const_2)
divide(n1,const_100)|subtract(n0,n3)|multiply(n2,#0)|subtract(#1,#2)|divide(#3,const_2)
geometry
allenai/math_qa
at a certain company , each employee has a salary grade s that is at least 1 and at most 6 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 6 receives how many more dollars per hour than an employee with a salary grade of 1 ?
"salary grade of 6 is p ( 6 ) = 9.50 + 0.25 ( 6 – 1 ) = 9.50 + 0.25 * 5 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 6 ) - p ( 1 ) = 9.50 + 0.25 * 5 - 9.50 = 1.25 . answer : c ."
a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
c
add(multiply(0.25, subtract(6, 1)), 0.25)
subtract(n1,n0)|multiply(n3,#0)|add(n3,#1)|
general
allenai/math_qa
simplify : 0.72 * 0.43 + 0.12 * 0.34
given exp . = 0.72 * 0.43 + ( 0.12 * 0.34 ) = 0.3096 + 0.0408 = 0.3504 answer is a
a ) 0.3504 , b ) 0.4209 , c ) 0.4889 , d ) 0.6412 , e ) 0.4612
a
add(multiply(0.72, 0.43), multiply(0.12, 0.34))
multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)
general
allenai/math_qa
30 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 3 : 4 ?
"let x be the amount of liquid q to be added . ( 2 / 5 ) * 30 + x = ( 4 / 7 ) * ( 30 + x ) 420 + 35 x = 600 + 20 x 15 x = 180 x = 12 the answer is c ."
a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
c
subtract(divide(multiply(divide(multiply(add(3, 4), divide(multiply(30, 3), add(3, 2))), 3), 4), add(3, 4)), divide(multiply(30, 2), add(3, 2)))
add(n3,n4)|add(n1,n2)|multiply(n0,n1)|multiply(n0,n2)|divide(#2,#1)|divide(#3,#1)|multiply(#0,#4)|divide(#6,n3)|multiply(n4,#7)|divide(#8,#0)|subtract(#9,#5)|
general
allenai/math_qa
a fellow borrowed a certain sum of money at 4 % per annum at simple interest and in 4 years the interest amounted to rs . 1260 less than the sum lent . what was the sum lent ?
"p - 1260 = ( p * 4 * 4 ) / 100 p = 1500 answer : c"
a ) 1050 , b ) 1220 , c ) 1500 , d ) 1060 , e ) 1110
c
divide(1260, subtract(const_1, divide(multiply(4, 4), const_100)))
multiply(n0,n0)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2)|
gain
allenai/math_qa
the sum of the first 50 positive even integers is 2550 . what is the sum of even integers from 102 to 200 inclusive ?
first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : 2550 + ( 100 * 50 ) = 7550 ; answer : b
a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
b
multiply(divide(add(200, 102), const_2), add(divide(subtract(200, 102), const_2), const_1))
add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)
general
allenai/math_qa
on multiplying a numberz by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
the only thing you actually know about the correct number z is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
d
multiply(add(subtract(add(multiply(const_100, const_4), multiply(const_100, const_4)), const_100), add(multiply(const_3, const_4), const_3)), 153)
multiply(const_3,const_4)|multiply(const_100,const_4)|add(#0,const_3)|add(#1,#1)|subtract(#3,const_100)|add(#2,#4)|multiply(n0,#5)
other
allenai/math_qa
an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many g meters long ?
"let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
b
subtract(15, add(multiply(const_4, 2), multiply(const_4, 1.5)))
multiply(n1,const_4)|multiply(n2,const_4)|add(#0,#1)|subtract(n0,#2)|
general
allenai/math_qa
. a car covers a distance of 390 km in 4 hours . find its speed ?
390 / 4 = 98 kmph answer : d
a ) 104 , b ) 55 , c ) 66 , d ) 98 , e ) 100
d
divide(390, 4)
divide(n0,n1)
physics
allenai/math_qa
if 3 cats can kill 3 rats in 3 minutes , how long will it take 100 cats to kill 100 rats ?
"it will take 3 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 3 minutes , so 100 cats can kill 100 rats in 3 minutes answer c"
a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes
c
multiply(3, const_1)
multiply(n0,const_1)|
physics
allenai/math_qa
in a jar there are balls in different colors : blue , red , green and yellow . the probability of drawing a blue ball is 1 / 8 . the probability of drawing a red ball is 2 / 5 . the probability of drawing a green ball is 7 / 10 . if a jar can not contain more than 50 balls , how many yellow balls are in the jar ?
answer of 1 st just add the given probabilities p ( blue ) + p ( red ) + p ( green ) i . e 1 / 8 + 2 / 5 + 3 / 10 = 5 + 16 + 12 / 40 now we know p ( blue ) + p ( red ) + p ( green ) + p ( yellow ) = 1 33 / 40 + p ( yellow ) = 1 p ( yellow ) = 33 / 40 i . e why yellow balls are 7 . d
a ) 12 , b ) 15 , c ) 23 , d ) 7 , e ) 5
d
subtract(50, add(add(divide(lcm(lcm(8, 5), 10), 8), multiply(divide(lcm(lcm(8, 5), 10), 5), 2)), multiply(divide(lcm(lcm(8, 5), 10), 10), 7)))
lcm(n1,n3)|lcm(n5,#0)|divide(#1,n1)|divide(#1,n3)|divide(#1,n5)|multiply(n2,#3)|multiply(n4,#4)|add(#2,#5)|add(#7,#6)|subtract(n6,#8)
general
allenai/math_qa
the population of a town increased from 1 , 24,300 to 1 , 62,400 in a decade . the average percent increase of population per year is :
"explanation : increase in 10 years = ( 162400 - 124300 ) = 87500 . increase % = ( 38100 / 162400 x 100 ) % = 23 % . required average = ( 23 / 10 ) % = 2.3 % . answer : option c"
a ) 4.37 % , b ) 4 % , c ) 2.3 % , d ) 3.75 % , e ) none
c
add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(1, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(1, const_3)), const_1000)), 1), const_10), const_100), const_4)
add(n2,const_3)|add(const_3,const_4)|multiply(const_10,const_1000)|multiply(#2,const_10)|multiply(#0,const_100)|multiply(#1,const_10)|add(#0,#5)|subtract(#3,const_1000)|multiply(#6,const_1000)|subtract(#7,const_1000)|subtract(#9,#4)|divide(#10,#8)|subtract(#11,n0)|divide(#12,const_10)|multiply(#13,const_100)|add(#14,const_4)|
general
allenai/math_qa
a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 2 km on foot . his total journey is
"explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 2 = x 5 x + 12 = 6 x x = 12 km answer : option c"
a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km
c
multiply(3, 2)
multiply(n3,n4)|
general
allenai/math_qa
what is the least value of x . so that 43 x 87 is divisible by 3 ?
"the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + 3 + x + 8 + 7 = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . c"
a ) 4 , b ) 5 , c ) 2 , d ) 6 , e ) 7
c
divide(divide(divide(lcm(43, 87), 87), const_4), const_4)
lcm(n0,n1)|divide(#0,n1)|divide(#1,const_4)|divide(#2,const_4)|
general
allenai/math_qa
the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 27 minutes is :
"explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 27 / 60 ) ) km = 11.25 km . answer : e"
a ) 9.25 , b ) 5.25 , c ) 7.25 , d ) 6.25 , e ) 11.25
e
multiply(divide(27, const_60), add(20, 5))
add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)|
physics
allenai/math_qa
1 = 5,2 = 10,3 = 253,4 = 254,5 = 255,6 = 256,7 = 257,8 = 258 then 10 = ?
"1 = 5,2 = 10,3 = 253,4 = 254,5 = 255,6 = 256,7 = 257,8 = 258 then 10 = ? 10 = 2 check the first eqn . answer : a"
a ) 2 , b ) 255 , c ) 345 , d ) 445 , e ) 235
a
divide(subtract(subtract(255,6, multiply(multiply(add(const_4, const_2), add(const_4, const_2)), const_10)), 1), const_2)
add(const_2,const_4)|multiply(#0,#0)|multiply(#1,const_10)|subtract(n5,#2)|subtract(#3,n0)|divide(#4,const_2)|
general
allenai/math_qa
two cars are driving toward each other . the first car is traveling at a speed of 100 km / h , which is 20 % slower than the second car ' s speed . if the distance between the cars is 1125 km , how many hours will it take until the two cars meet ?
"the speed of the first car is 100 km / h . the speed of the second car is 100 / 0.8 = 125 km / h . the two cars complete a total of 225 km each hour . the time it takes the cars to meet is 1125 / 225 = 5 hours . the answer is d ."
a ) 4 , b ) 4.5 , c ) 4.8 , d ) 5 , e ) 5.5
d
divide(add(multiply(100, const_4), multiply(divide(multiply(const_4, 100), add(const_1, const_4)), const_4)), add(100, divide(multiply(const_4, 100), add(const_1, const_4))))
add(const_1,const_4)|multiply(n0,const_4)|divide(#1,#0)|add(n0,#2)|multiply(#2,const_4)|add(#1,#4)|divide(#5,#3)|
physics
allenai/math_qa
alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1051 . find the cost of each ice - cream cup ?
"let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1051 96 + 225 + 490 + 6 x = 1051 6 x = 240 = > x = 40 . answer : b"
a ) 25 , b ) 40 , c ) 77 , d ) 99 , e ) 91
b
divide(subtract(subtract(subtract(1051, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)
multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3)|
general
allenai/math_qa
there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 76 . how tall is the fourth person ?
"let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 76 ) = 304 x = 72 and the fourth person has a height of 72 + 10 = 82 inches the answer is d ."
a ) 76 , b ) 78 , c ) 80 , d ) 82 , e ) 84
d
add(divide(subtract(multiply(76, 4), add(6, add(4, 6))), 4), add(4, 6))
add(n0,n2)|multiply(n0,n3)|add(n2,#0)|subtract(#1,#2)|divide(#3,n0)|add(#0,#4)|
general
allenai/math_qa
a man invests rs . 5,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
"explanation : interest on rs . 5000 at 5 % per annum = ( 5000 × 5 × 1 ) / 100 = rs . 250 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 5000 + x ) × 6 × 1 / 100 . = > 250 + 2 x / 25 = ( 5000 + x ) × 6 × 1 / 100 . = > 25000 + 8 x = ( 5000 + x ) × 6 . = > 25000 + 8 x = 30000 + 6 x . = > 2 x = 5000 . = > x = 2500 . answer : c"
a ) rs . 1200 , b ) rs . 1300 , c ) rs . 2500 , d ) rs . 2000 , e ) none of these
c
multiply(multiply(8, const_1000), divide(subtract(6, 5), subtract(8, 6)))
multiply(n2,const_1000)|subtract(n3,n1)|subtract(n2,n3)|divide(#1,#2)|multiply(#3,#0)|
gain
allenai/math_qa
if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 2 : 1 / 11 : 1 / 12 : 1 / 13 then find the total number of items the wholesaler distributes ?
"here , a : b : c : d = 1 / 2 : 1 / 11 : 1 / 12 : 1 / 13 1 ) l . c . m of 2 : 11 : 12 : 13 is 1716 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 2 ) x 1716 = 858 b = ( 1 / 11 ) x 1716 = 156 c = ( 1 / 12 ) x 1716 = 143 d = ( 1 / 13 ) x 1716 = 132 3 ) total number of toys = ( 858 x + 156 x + 143 x + 132 x ) = 1289 x minimum number of pens ( x ) = 1 therefore , total number of items = 1289 items . correct option : b"
a ) 289 , b ) 1289 , c ) 1389 , d ) 1281 , e ) 128
b
add(add(multiply(const_100, const_4), const_100), add(multiply(12, const_4), add(const_4, const_3)))
add(const_3,const_4)|multiply(const_100,const_4)|multiply(n5,const_4)|add(#1,const_100)|add(#0,#2)|add(#3,#4)|
general
allenai/math_qa
a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 30 x / 100 - 24 x / 100 = 840 = > 6 x / 100 = 840 = > x = 14000 . answer : c
a ) rs . 7000 , b ) rs . 9000 , c ) rs . 14000 , d ) rs . 17000 , e ) rs . 27000
c
divide(840, divide(multiply(subtract(15, 12), const_2), const_100))
subtract(n0,n1)|multiply(#0,const_2)|divide(#1,const_100)|divide(n2,#2)
gain
allenai/math_qa
in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ?
the triangle is symmetric about the x - axis . the part above the x - axis forms a triangle with a base of 8 and a height of 4 . the area of this part is ( 1 / 2 ) ( 8 ) ( 4 ) . we can double this to find the area of the whole triangle . the total area is ( 2 ) ( 1 / 2 ) ( 8 ) ( 4 ) = 32 . the answer is d .
['a ) 29', 'b ) 30', 'c ) 31', 'd ) 32', 'e ) 33']
d
multiply(triangle_area(add(7, 1), 4), const_2)
add(n0,n2)|triangle_area(n3,#0)|multiply(#1,const_2)
geometry
allenai/math_qa
a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 20 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
"wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 20 emlpoyee paid = . 8 * 240 = 192 $ answer c"
a ) $ 198 , b ) $ 216 , c ) $ 192 , d ) $ 230 , e ) $ 240
c
subtract(add(200, multiply(divide(200, const_100), 20)), multiply(divide(add(200, multiply(divide(200, const_100), 20)), const_100), 20))
divide(n1,const_100)|multiply(n0,#0)|add(n1,#1)|divide(#2,const_100)|multiply(n2,#3)|subtract(#2,#4)|
gain
allenai/math_qa
the maximum number of student amoung them 1204 pens and 840 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
"solution required number of student = h . c . f of 1204 and 840 = 28 . answer b"
a ) 91 , b ) 28 , c ) 56 , d ) 89 , e ) none of these
b
gcd(1204, 840)
gcd(n0,n1)|
general
allenai/math_qa
the total number of digits used in numbering the pages of a book having 366 pages is
"explanation : total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 267 ) = ( 9 + 180 + 801 ) = 990 . answer : b"
a ) 732 , b ) 990 , c ) 1098 , d ) 1305 , e ) 1605
b
subtract(subtract(multiply(366, const_3), subtract(const_100, const_1)), subtract(const_10, const_1))
multiply(n0,const_3)|subtract(const_100,const_1)|subtract(const_10,const_1)|subtract(#0,#1)|subtract(#3,#2)|
general
allenai/math_qa
what is the angle between the hands of a clock when time is 8 : 40 ?
"angle between two hands = 40 h - 11 / 2 m = 40 * 8 - 40 * 11 / 2 = 320 - 220 = 100 deg answer : e"
a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 100 deg
e
subtract(multiply(40, multiply(const_3, const_2)), 8)
multiply(const_2,const_3)|multiply(n1,#0)|subtract(#1,n0)|
geometry
allenai/math_qa
if the sides of a triangle are 28 cm , 24 cm and 15 cm , what is its area ?
"the triangle with sides 28 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : a"
a ) 180 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 886 cm 2
a
divide(multiply(24, 15), const_2)
multiply(n1,n2)|divide(#0,const_2)|
geometry
allenai/math_qa
shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5,000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12,000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15,000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16,000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60,000 chips ?
for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e
a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15
e
multiply(add(2, 3), 3)
add(n1,n6)|multiply(n6,#0)
general
allenai/math_qa
if shares of two persons in profits are rs . 400 and rs . 500 then ratio of their capitals is
"profit = time * capital so 400 : 500 = 4 : 5 answer : b"
a ) 3 : 4 , b ) 4 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
b
divide(400, 500)
divide(n0,n1)|
other
allenai/math_qa
the average of 5 numbers id 27 . if one number is excluded , the average becomes 25 . the excluded number is
solution excluded number = ( 27 x 5 ) - ( 25 x 4 ) = 135 - 100 = 35 . answer d
a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) none
d
subtract(multiply(27, 5), multiply(25, const_4))
multiply(n0,n1)|multiply(n2,const_4)|subtract(#0,#1)
general
allenai/math_qa
in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 63 as quotient . what is the correct quotient ?
"12 * 63 = 756 756 % 21 = 36 answer : b"
a ) 0 , b ) 36 , c ) 13 , d ) 20 , e ) 25
b
divide(multiply(12, 63), 21)
multiply(n1,n3)|divide(#0,n2)|
general
allenai/math_qa
there is enough provisions for 600 men in an army camp for 25 days . if there were 200 men less , how long will the provision last ?
exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 200 * d 2 d 2 = 600 * 25 / 200 = 75 days . answer : d
a ) 50 days , b ) 60 days , c ) 70 days , d ) 75 days , e ) 90 days
d
divide(multiply(600, 25), 200)
multiply(n0,n1)|divide(#0,n2)
physics
allenai/math_qa
one type of liquid contains 20 % of water and the second type of liquid contains 35 % of water . a glass is filled with 10 parts of 1 st liquid and 4 parts of 2 nd liquid . the percentage of water in the new mixture in the glass is ?
required percentage = ( 20 % of 10 + 35 % of 4 ) / 10 + 4 * 100 = 3.4 / 14 * 100 = 24.3 % answer is c
a ) 22.15 % , b ) 23.5 % , c ) 24.3 % , d ) 25 % , e ) 29.6 %
c
multiply(divide(const_100, add(10, 4)), add(divide(multiply(20, 10), const_100), divide(multiply(35, 4), const_100)))
add(n2,n4)|multiply(n0,n2)|multiply(n1,n4)|divide(#1,const_100)|divide(#2,const_100)|divide(const_100,#0)|add(#3,#4)|multiply(#6,#5)
gain
allenai/math_qa
the ratio of male to female in a class is 2 : 7 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two - third of the females in the class ?
here is my approach = > males = > 2 x and females = 7 x = > total = 9 x now 9 x = > 360 therefore 16 x / 3 = > 213 degree . p . s = > 16 x / 3 is nothing but total number of students with the given preference answer e
['a ) a ) 160 degree', 'b ) b ) 168 degree', 'c ) c ) 191 degree', 'd ) d ) 192 degree', 'e ) e ) 213 degree']
e
add(multiply(const_360, divide(divide(const_2, add(2, 7)), const_3)), multiply(const_360, multiply(divide(7, add(2, 7)), divide(const_2, const_3))))
add(n0,n1)|divide(const_2,const_3)|divide(const_2,#0)|divide(n1,#0)|divide(#2,const_3)|multiply(#3,#1)|multiply(#4,const_360)|multiply(#5,const_360)|add(#6,#7)
geometry
allenai/math_qa
x can finish a work in 36 days . y can finish the same work in 24 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
"work done by x in 1 day = 1 / 36 work done by y in 1 day = 1 / 24 work done by y in 12 days = 12 / 24 = 1 / 2 remaining work = 1 – 1 / 2 = 1 / 2 number of days in which x can finish the remaining work = ( 1 / 2 ) / ( 1 / 36 ) = 18 e"
a ) 12 , b ) 13 , c ) 16 , d ) 17 , e ) 18
e
divide(subtract(const_1, multiply(12, divide(const_1, 24))), divide(const_1, 36))
divide(const_1,n1)|divide(const_1,n0)|multiply(n2,#0)|subtract(const_1,#2)|divide(#3,#1)|
physics
allenai/math_qa
3 candidates in an election and received 3000 , 5000 and 20000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
"total number of votes polled = ( 3000 + 5000 + 20000 ) = 28000 so , required percentage = 11628 / 20400 * 100 = 71.42 % d"
a ) 45.12 % , b ) 50 % , c ) 57 % , d ) 71.42 % , e ) 65 %
d
multiply(divide(20000, add(add(3000, 5000), 20000)), const_100)
add(n1,n2)|add(n3,#0)|divide(n3,#1)|multiply(#2,const_100)|
gain
allenai/math_qa
in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.75 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
12 * 1.75 + 0.75 * 12 * 55 = 516 hence - d
a ) 320 $ , b ) 420 $ , c ) 490 $ , d ) 516 $ , e ) 680 $
d
multiply(multiply(0.75, 55), 12)
multiply(n1,n3)|multiply(n2,#0)|
general
allenai/math_qa
the sum of the ages of 4 children born at the intervals of 4 years each is 36 years . what is the age of the youngest child ?
"let x = the youngest child . each of the other four children will then be x + 4 , x + 8 , x + 12 we know that the sum of their ages is 36 . so , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 36 therefore the youngest child is 3 years old answer : a"
a ) 3 , b ) 18 , c ) 10 , d ) 99 , e ) 38
a
divide(subtract(divide(36, divide(4, 4)), multiply(subtract(4, const_1), 4)), 4)
divide(n0,n1)|subtract(n0,const_1)|divide(n2,#0)|multiply(n1,#1)|subtract(#2,#3)|divide(#4,n1)|
general
allenai/math_qa
find the average of all numbers between 5 and 45 which are divisible by 6
"explanation : average = ( 6 + 12 + 18 + 24 + 30 + 36 + 42 / 6 ) = 168 / 6 = 28 option c"
a ) 26 , b ) 24 , c ) 28 , d ) 30 , e ) 35
c
divide(add(add(add(multiply(6, const_3), add(6, multiply(6, const_2))), multiply(6, const_4)), multiply(add(const_4, const_1), 6)), 6)
add(const_1,const_4)|multiply(n2,const_2)|multiply(n2,const_3)|multiply(n2,const_4)|add(n2,#1)|multiply(n2,#0)|add(#4,#2)|add(#6,#3)|add(#7,#5)|divide(#8,n2)|
general
allenai/math_qa
the speed at which a girl can row a boat in still water is 30 kmph . if she rows downstream , where the speed of current is 6 kmph , what time will he take to cover 240 metres ?
speed of the boat downstream = 30 + 6 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 240 m = 240 / 10 = 24 seconds . answer : e
a ) 21 , b ) 22 , c ) 23 , d ) 20 , e ) 24
e
divide(multiply(240, const_3_6), add(30, 6))
add(n0,n1)|multiply(n2,const_3_6)|divide(#1,#0)
physics
allenai/math_qa
indu gave bindu rs . 4375 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
"4375 = d ( 100 / 4 ) 2 d = 7 answer : b"
a ) s . 10 , b ) s . 7 , c ) s . 5 , d ) s . 3 , e ) s . 4
b
subtract(subtract(multiply(4375, power(add(const_1, divide(4, const_100)), 2)), 4375), multiply(multiply(4375, divide(4, const_100)), 2))
divide(n2,const_100)|add(#0,const_1)|multiply(n0,#0)|multiply(n1,#2)|power(#1,n1)|multiply(n0,#4)|subtract(#5,n0)|subtract(#6,#3)|
gain
allenai/math_qa
after getting 2 successive discounts , a shirt with a list price of rs 150 is available at rs 105 . if the second discount is 12.55 , find the first discount .
"let the first discount be x % then , 87.5 % of ( 100 - x ) % of 150 = 105 = 87.5 / 100 * ( 100 - x ) / 100 * 450 = 150 = > 105 = > 100 - x = ( 105 * 100 * 100 ) / ( 150 * 87.5 ) = 80 x = ( 100 - 80 ) = 20 first discount = 20 % answer is e ."
a ) 22 % , b ) 18 % , c ) 24 % , d ) 17 % , e ) 20 %
e
divide(multiply(subtract(150, divide(multiply(105, const_100), subtract(const_100, 12.55))), const_100), 150)
multiply(n2,const_100)|subtract(const_100,n3)|divide(#0,#1)|subtract(n1,#2)|multiply(#3,const_100)|divide(#4,n1)|
gain
allenai/math_qa
a salesman ' s income consists of a commission and a base salary of $ 370 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
"total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 370 * 2 = $ 740 therefore , commission = $ 1430 - $ 740 = $ 690 for 2 weeks avg weekly commission = $ 345 answer b"
a ) $ 150 , b ) $ 345 , c ) $ 365 , d ) $ 715 , e ) $ 730
b
subtract(divide(subtract(multiply(500, 7), add(add(add(406, 413), add(436, 420)), 395)), const_2), 370)
add(n2,n3)|add(n4,n5)|multiply(n7,n8)|add(#0,#1)|add(n6,#3)|subtract(#2,#4)|divide(#5,const_2)|subtract(#6,n0)|
general
allenai/math_qa
if 2 x + y = 7 and x + 2 y = 5 , then ( 2 x + 2 y ) / 3 =
"2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 2 * 3 + 2 * 1 ) / 3 = ( 6 + 3 ) / 3 = 9 / 3 = 3 a"
a ) 3 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
a
divide(add(divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1)), subtract(7, multiply(2, divide(subtract(multiply(7, 2), 5), subtract(multiply(2, 2), const_1))))), 2)
multiply(n0,n1)|multiply(n0,n0)|subtract(#0,n3)|subtract(#1,const_1)|divide(#2,#3)|multiply(n0,#4)|subtract(n1,#5)|add(#4,#6)|divide(#7,n4)|
general
allenai/math_qa
if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) =
6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b
a ) 2925 , b ) 3456 , c ) 4581 , d ) 3683 , e ) 1308
b
multiply(power(4, 2), power(6, 3))
power(n1,n3)|power(n0,n4)|multiply(#0,#1)
general
allenai/math_qa
a pipe takes a hours to fill the tank . but because of a leakage it took 7 times of its original time . find the time taken by the leakage to empty the tank
pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 420 x = 70 min answer : e
a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min
e
multiply(const_10, multiply(const_1, 7))
multiply(n0,const_1)|multiply(#0,const_10)
physics
allenai/math_qa
3 log 3 ( - 5 ) = ?
"since - 5 is not in the domain of function log 3 ( x ) , 3 log 3 ( - 5 ) is undefined correct answer b"
a ) 1 , b ) undentified , c ) 3 , d ) 7 , e ) 5
b
divide(log(multiply(3, 3)), log(const_10))
log(const_10)|multiply(n0,n0)|log(#1)|divide(#2,#0)|
general
allenai/math_qa
a person travels equal distances with speeds of 3 km / hr , 6 km / hr , 9 km / hr . and takes a total time of 11 minutes . find the total distance ?
"let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 6 ) + ( x / 9 ) = 11 / 60 x = 0.3 total distance = 3 * 0.3 = 0.9 km = 900 meters correct option is c"
a ) 1 km , b ) 500 mts , c ) 900 mts , d ) 2 km , e ) 250 mts
c
multiply(multiply(divide(divide(11, const_60), add(add(divide(const_1, 3), divide(const_1, 6)), divide(const_1, 9))), const_3), const_1000)
divide(n3,const_60)|divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#1,#2)|add(#4,#3)|divide(#0,#5)|multiply(#6,const_3)|multiply(#7,const_1000)|
physics
allenai/math_qa
in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is ?
"explanation : total employees = \ inline \ frac { ( 25 - 10 ) \ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c"
a ) 11 , b ) 82 , c ) 10 , d ) 28 , e ) 23
c
subtract(20, 10)
subtract(n0,n2)|
general
allenai/math_qa
the l . c . m . of two numbers is 30 . the numbers are in the ratio 2 : 3 . then sum of the number is :
"let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 30 or x = 5 . the numbers are 10 and 15 . hence , required sum = ( 10 + 15 ) = 25 . answer : option a"
a ) 25 , b ) 32 , c ) 40 , d ) 53 , e ) 54
a
add(multiply(divide(30, multiply(2, 3)), 3), multiply(divide(30, multiply(2, 3)), 2))
multiply(n1,n2)|divide(n0,#0)|multiply(n2,#1)|multiply(n1,#1)|add(#2,#3)|
other
allenai/math_qa
in 130 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
"distance covered by b in 9 sec . = 130 / 45 x 9 m = 26 m . a beats b by 26 metres . answer : option d"
a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 26 m , e ) 12 m
d
multiply(divide(130, 45), subtract(45, 36))
divide(n0,n2)|subtract(n2,n1)|multiply(#0,#1)|
physics
allenai/math_qa
3 candidates in an election and received 5136 , 7636 and 11628 votes respectively . what % of the total votes did the winningcandidate got in that election ?
"total number of votes polled = ( 5136 + 7636 + 11628 ) = 24400 so , required percentage = 11628 / 24400 * 100 = 48 % b"
a ) 45 % , b ) 48 % , c ) 57 % , d ) 59 % , e ) 61 %
b
multiply(divide(11628, add(add(5136, 7636), 11628)), const_100)
add(n1,n2)|add(n3,#0)|divide(n3,#1)|multiply(#2,const_100)|
gain
allenai/math_qa
if x is a randomly chosen integer between 1 and 20 , inclusive , and y is a randomly chosen integer between 21 and 40 , inclusive , what is the probability that xy is a multiple of 4 ?
there are two ways that i see of getting a multiple of 4 1 ) x and / or y is a multiple of 4 2 ) x is a multiple of 2 and y is a multiple of 2 for 1 we have p ( option 1 ) = ( 5 / 20 ) ( 20 / 20 ) + ( 5 / 20 ) ( 20 / 20 ) - ( 5 / 20 ) ( 5 / 20 ) = 1 / 2 - 1 / 16 since 5 of the numbers in each range are divisible by 4 , and if either x or y is selected to be divisible by 4 the selection of the other variable does not matter . notice the last subtraction term which corrects the fact that we have counted the possibility of both being divisible by 4 twice ( e . g . p ( a union b ) = p ( a ) + p ( b ) - p ( a and b ) ) . notice at this point that the probability of option one is already 7 / 16 , the second largest available option . if we can come up with any other possibilities for getting xy divisble by 4 we must go with option e . of course this is the case because if we select a multiple of 2 that is not a multiple of 4 from both ranges of numbers , the product is divisible by 4 . we can formally compute this as : p ( option 2 ) = ( 5 / 20 ) * ( 5 / 20 ) = 1 / 16 since we do not wish to double count possibilities that fall into category 1 , we only count the probability of selecting even numbers from each set that are not divisible by 4 ( e . g . the other 5 even integers in each set ) . total probability is then p ( option 1 ) + p ( option 2 ) = 1 / 2
a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 8 , d ) 7 / 16 , e ) ½
e
subtract(1, add(multiply(multiply(divide(const_1, const_2), divide(const_1, const_2)), divide(const_1, const_2)), add(multiply(divide(const_1, const_2), divide(const_1, const_2)), multiply(multiply(divide(const_1, const_2), divide(const_1, const_2)), divide(const_1, const_2)))))
divide(const_1,const_2)|multiply(#0,#0)|multiply(#0,#1)|add(#1,#2)|add(#3,#2)|subtract(n0,#4)
general
allenai/math_qa
f and e are midpoints of ab and ad respectively . if the side of square abcd is 8 , what is the area of triangle cef ?
area of shaded figure = area of square - ( area of triangle aef + area of triangle fbc + area of triangle edc ) = 8 * 8 - ( 1 / 2 * 4 * 4 + 1 / 2 * 4 * 8 + 1 / 2 * 4 * 8 ) = 24 . answer e .
['a ) 8 √ 2', 'b ) 9 √ 3', 'c ) 18', 'd ) 16 √ 2', 'e ) 24']
e
subtract(subtract(subtract(square_area(8), triangle_area(divide(8, const_2), 8)), triangle_area(divide(8, const_2), 8)), triangle_area(divide(8, const_2), divide(8, const_2)))
divide(n0,const_2)|square_area(n0)|triangle_area(n0,#0)|triangle_area(#0,#0)|subtract(#1,#2)|subtract(#4,#2)|subtract(#5,#3)
geometry
allenai/math_qa
james and david work at a grocery shop with 6 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that james and david will both be chosen ?
"probability that james and david will both be chosen out of 6 workers = ( 2 / 6 ) * ( 1 / 5 ) = 1 / 15 answer e"
a ) 1 / 20 , b ) 1 / 22 , c ) 1 / 23 , d ) 1 / 25 , e ) 1 / 15
e
multiply(2, multiply(divide(const_1, 6), divide(const_1, subtract(6, const_1))))
divide(const_1,n0)|subtract(n0,const_1)|divide(const_1,#1)|multiply(#0,#2)|multiply(#3,n1)|
physics
allenai/math_qa
one fourth of one third of two fifth of a number is 35 . what will be 40 % of that number
"explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 35 then x = 35 * 30 = 1050 40 % of 1050 = 420 answer : option b"
a ) a ) 140 , b ) b ) 420 , c ) c ) 180 , d ) d ) 200 , e ) e ) 220
b
divide(multiply(divide(35, multiply(multiply(divide(const_1, const_4), divide(const_1, const_3)), divide(const_2, add(const_2, const_3)))), 40), const_100)
add(const_2,const_3)|divide(const_1,const_4)|divide(const_1,const_3)|divide(const_2,#0)|multiply(#1,#2)|multiply(#3,#4)|divide(n0,#5)|multiply(n1,#6)|divide(#7,const_100)|
gain
allenai/math_qa
rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 200 pages , of which 80 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
"for 200 - 80 - 20 = 100 pages only cost is 5 $ per page for the first time page is typed - 100 * 5 = 500 $ ; for 80 pages the cost is : first time 5 $ + 3 $ of the first revision - 80 * ( 5 + 3 ) = 640 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 500 + 640 + 220 = 1360 $ . answer : a ."
a ) $ 1360 , b ) $ 1620 , c ) $ 1650 , d ) $ 680 , e ) $ 770
a
add(add(multiply(200, 5), multiply(80, 3)), multiply(multiply(20, 3), const_2))
multiply(n0,n2)|multiply(n1,n3)|multiply(n1,n4)|add(#0,#1)|multiply(#2,const_2)|add(#3,#4)|
general
allenai/math_qa
what is the value of ( 12 + 22 + 32 + 42 + - - - - - + 102 )
"explanation : ( 12 + 22 + … . . + n 2 ) = ( 1 / 6 ) n ( n + 1 ) ( 2 n + 1 ) here , n = 10 therefore , ( 12 + 22 + … . . + 102 ) = ( 1 / 6 ) 10 ( 10 + 1 ) ( 2 x 10 + 1 ) = ( 1 / 6 ) x 10 x 11 x 21 = 385 answer : c"
a ) 295 , b ) 324 , c ) 385 , d ) 391 , e ) 399
c
power(12, negate(22))
negate(n1)|power(n0,#0)|
general
allenai/math_qa
the perimeter of a triangle is 39 cm and the inradius of the triangle is 1.5 cm . what is the area of the triangle ?
"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 1.5 * 39 / 2 = 29 cm 2 answer : e"
a ) 22 , b ) 35 , c ) 77 , d ) 54 , e ) 29
e
triangle_area(1.5, 39)
triangle_area(n0,n1)|
geometry
allenai/math_qa
a train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min . find the length of train ?
explanation : we know , speed = distance / time speed = 10 / 50 x 60 = 40 x 5 / 18 m / sec = 11.1 m / sec length of train = ( speed x time ) = ( 11.11 x 10 ) = 111.1 m answer is c
a ) 100.1 m , b ) 223.1 m , c ) 111.1 m , d ) 120.3 m , e ) 133.4 m
c
multiply(divide(multiply(const_1000, 10), multiply(const_60, 15)), 10)
multiply(n0,const_1000)|multiply(n2,const_60)|divide(#0,#1)|multiply(n0,#2)
physics
allenai/math_qa