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load_in_math_allenai_math

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of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
"of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; # of permutations of 3 digits in ppqr - 4 ! / 2 ! total : 9 * 8 * 7 * 4 ! / 2 ! = 6048 . answer : a ."
a ) 6048 , b ) 3648 , c ) 7248 , d ) 1448 , e ) 2168
a
multiply(multiply(subtract(const_10, const_1), subtract(const_10, const_2)), const_1)
subtract(const_10,const_1)|subtract(const_10,const_2)|multiply(#0,#1)|multiply(#2,const_1)|
general
allenai/math_qa
in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 11 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 11 ) = 36 / 20 = 9 / 5 . answer : d ."
a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 9 / 5 , e ) 3 / 2
d
divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 11))
add(n1,n2)|divide(n0,#0)|add(n3,#1)|subtract(n0,#1)|divide(#3,#2)|
general
allenai/math_qa
a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,055 . how much did she invest at 5 % ?
"et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1055 / 1000 ) - 1 = 0.055 = 5.5 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.055 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.055 - 0.01 x = - 0.005 x = - 0.005 / - 0.01 = 5 / 10 = 50 % so x = 50 % of the 1000 which is 500 answer : a"
a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
a
subtract(multiply(multiply(5, const_2), const_100), subtract(multiply(subtract(add(multiply(multiply(5, const_2), const_100), add(multiply(multiply(5, const_2), 5), const_4)), multiply(multiply(5, const_2), const_100)), const_100), multiply(5, multiply(multiply(5, const_2), const_100))))
multiply(n1,const_2)|multiply(#0,const_100)|multiply(n1,#0)|add(#2,const_4)|multiply(n1,#1)|add(#3,#1)|subtract(#5,#1)|multiply(#6,const_100)|subtract(#7,#4)|subtract(#1,#8)|
gain
allenai/math_qa
the arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
"mean = 17.5 two standard deviations is 2.5 + 2.5 = 5.0 there could be two calues for this . mean + two standard deviations = 22.5 mean - two standard deviations = 12.5 answer choice has 12.5 and so e is the answer ."
a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
e
subtract(17.5, multiply(2, 2.5))
multiply(n1,n2)|subtract(n0,#0)|
general
allenai/math_qa
the length of a room is 8 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
"area = 8 Γ— 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 8 Γ— 4.75 Γ— 900 = 8 Γ— 4275 = rs . 34200 answer is e ."
a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 34200
e
multiply(900, multiply(8, 4.75))
multiply(n0,n1)|multiply(n2,#0)|
physics
allenai/math_qa
a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the distance in km ?
explanation : speed = 2 v 1 v 2 / v 1 βˆ’ v 2 = 2 Γ— 3 Γ— 23 βˆ’ 2 = 12 km / h = hr distance = vt 1 ( 1 + v / v 1 ) = 12 Γ— 40 / 60 ( 1 + 12 / 3 ) = 40 km answer is c
a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 45
c
multiply(divide(add(multiply(2, divide(add(multiply(2, divide(40, const_60)), multiply(3, divide(40, const_60))), subtract(3, 2))), multiply(2, divide(40, const_60))), divide(40, const_60)), divide(add(multiply(2, divide(40, const_60)), multiply(3, divide(40, const_60))), subtract(3, 2)))
divide(n1,const_60)|subtract(n0,n2)|multiply(n2,#0)|multiply(n0,#0)|add(#2,#3)|divide(#4,#1)|multiply(n2,#5)|add(#6,#2)|divide(#7,#0)|multiply(#8,#5)
physics
allenai/math_qa
suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have
to arrange them as described i did as follows on my scratch paper ( see the file attached ) , where i counted 4 sides and bottom , hence 4 + 1 = 5 . e
['a ) 4', 'b ) 6', 'c ) 9', 'd ) 10', 'e ) 5']
e
add(add(const_4, const_1), const_1)
add(const_1,const_4)|add(#0,const_1)
geometry
allenai/math_qa
evaluate : 30 - 12 * 3 * 2 = ?
"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 30 - 12 * 3 * 2 = 30 - 8 = 22 correct answer e"
a ) 62 , b ) 52 , c ) 32 , d ) 12 , e ) 22
e
subtract(30, multiply(multiply(12, const_2.0), 2))
multiply(n1,const_2.0)|multiply(n3,#0)|subtract(n0,#1)|
general
allenai/math_qa
a train running at the speed of 40 km / hr crosses a pole in 27 seconds . what is the length of the train ?
"speed = ( 40 * 5 / 18 ) m / sec = ( 100 / 9 ) m / sec length of the train = ( speed x time ) = ( 100 / 9 * 29 ) m = 300 m . answer : b"
a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
b
multiply(divide(multiply(40, const_1000), const_3600), 27)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
physics
allenai/math_qa
the perimeter of a rectangle is equal to the perimeter of aright - angled triangle of height 12 cm . if the base of the triangle is equal to the breadth of the rectangle , what is the length of the rectangle ”
p = 2 ( l + b ) = l + b + h = l + b + 12 . data inadequate . answer d
['a ) 18 cm', 'b ) 24 cm', 'c ) 22 cm', 'd ) data inadequate', 'e ) none of these']
d
multiply(const_2, sqrt(add(const_1, power(12, const_2))))
power(n0,const_2)|add(#0,const_1)|sqrt(#1)|multiply(#2,const_2)
geometry
allenai/math_qa
what is the smallest no . which must be added to 8261955 so as to obtain a sum which is divisible by 11 ?
for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 8261955 , difference = ( 8 + 6 + 9 + 5 ) - ( 2 + 1 + 5 ) = 28 - 8 = 20 . the units digit is at odd place . so we add 2 to the number = > 8261955 + 2 = 8261957 now , ( 8 + 6 + 9 + 7 ) - ( 2 + 1 + 5 ) = 30 - 8 = 22 = > 22 is a multiple of 11 and hence 8261957 is also divisible by 11 b
a ) 8 , b ) 11 , c ) 13 , d ) 15 , e ) 16
b
divide(multiply(8261955, 11), 8261955)
multiply(n0,n1)|divide(#0,n0)
general
allenai/math_qa
the youngest of 4 children has siblings who are 4 , 5 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?
x + ( x + 4 ) + ( x + 5 ) + ( x + 7 ) = 84 4 x + 16 = 84 4 x = 68 x = 17 the answer is d .
a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
d
divide(subtract(multiply(4, 21), add(add(4, 5), 7)), 4)
add(n0,n2)|multiply(n0,n5)|add(n3,#0)|subtract(#1,#2)|divide(#3,n0)
general
allenai/math_qa
a chemist mixes one liter of pure water with x liters of a 30 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
"concentration of salt in pure solution = 0 concentration of salt in salt solution = 30 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 30 - 15 ) / ( 15 - 0 ) = 1 / 1 1 / x = 1 / 1 x = 1 answer : d"
a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
d
divide(15, subtract(30, 15))
subtract(n0,n1)|divide(n1,#0)|
gain
allenai/math_qa
how many litres of pure acid are there in 4 litres of a 35 % solution
explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 8 * 20 / 100 = 1.4 answer : option e
a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.4
e
multiply(divide(35, const_100), 4)
divide(n1,const_100)|multiply(n0,#0)|
gain
allenai/math_qa
a is 2 times as fast as b . a alone can do the work in 20 days . if a and b working together in how many days will the work be completed ?
"a can finish 1 work in 20 days b can finish 1 / 2 work in 20 days - since a is 2 faster than b this means b can finish 1 work in 20 * 2 days = 40 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 40 / ( 20 + 40 ) = 13 days so answer is b"
a ) 23 , b ) 13 , c ) 21 , d ) 24 , e ) 25
b
divide(const_1, add(divide(const_1, 20), divide(divide(const_1, 20), 2)))
divide(const_1,n1)|divide(#0,n0)|add(#0,#1)|divide(const_1,#2)|
physics
allenai/math_qa
a and b together have $ 1210 . if 4 / 15 of a ' s amount is equal to 2 / 5 of b ' s amount , how much amount does b have ?
4 / 15 a = 2 / 5 b a = 2 / 5 * 15 / 4 b a = 3 / 2 b a / b = 3 / 2 a : b = 3 : 2 b ' s share = 1210 * 2 / 5 = $ 484 answer is c
a ) $ 310 , b ) $ 395 , c ) $ 484 , d ) $ 512 , e ) $ 542
c
divide(1210, add(divide(divide(2, 5), divide(4, 15)), const_1))
divide(n3,n4)|divide(n1,n2)|divide(#0,#1)|add(#2,const_1)|divide(n0,#3)
general
allenai/math_qa
how many positive integers less than 8,000 are there in which the sum of the digits equals 5 ?
"basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . b"
a ) 57 , b ) 56 , c ) 55 , d ) 54 , e ) 53
b
divide(factorial(subtract(add(const_4, 5), const_1)), multiply(factorial(5), factorial(subtract(const_4, const_1))))
add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)|
general
allenai/math_qa
sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ?
"6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 350 - - > x = 1.676 . 1.25 x = ~ 2.09 . answer : c ."
a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.09 , d ) $ 2.50 , e ) $ 3.25
c
multiply(divide(add(multiply(multiply(32, divide(75, const_100)), multiply(add(const_4, 1), const_2)), 350), add(multiply(subtract(multiply(add(const_4, 1), const_2), 4), 32), multiply(multiply(divide(add(const_100, 25), const_100), 4), 32))), divide(add(const_100, 25), const_100))
add(n5,const_4)|add(n1,const_100)|divide(n2,const_100)|divide(#1,const_100)|multiply(n3,#2)|multiply(#0,const_2)|multiply(#4,#5)|multiply(n4,#3)|subtract(#5,n4)|add(n0,#6)|multiply(n3,#8)|multiply(n3,#7)|add(#10,#11)|divide(#9,#12)|multiply(#13,#3)|
gain
allenai/math_qa
a and b can do a piece of work in 12 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
"c 30 days c = 1 / 3 – 1 / 12 = 1 / 4 = > 4 days"
a ) 40 days , b ) 2 days , c ) 4 days , d ) 8 days , e ) 40 days
c
inverse(subtract(3, divide(3, 12)))
divide(n1,n0)|subtract(n1,#0)|inverse(#1)|
physics
allenai/math_qa
a batsman scored 120 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets ?
"explanation : number of runs made by running , = > 120 βˆ’ ( 5 Γ— 4 + 5 Γ— 6 ) . = > 120 βˆ’ ( 50 ) . = > 70 . hence , the required percentage is : - = > 70 / 120 * 100 = > 58.33 % answer : b"
a ) 45 , b ) 58.33 % , c ) 600 / 11 , d ) 55 , e ) 35
b
multiply(divide(subtract(120, add(multiply(5, 5), multiply(5, 5))), 120), const_100)
multiply(n1,n2)|multiply(n1,n2)|add(#0,#1)|subtract(n0,#2)|divide(#3,n0)|multiply(#4,const_100)|
general
allenai/math_qa
five machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 10 days ?
rate of one machine = 1 job / ( 20 * 5 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 5 * 20 ) * 10 * x = 1 job x = 10 10 - 5 = 5 answer : d
a ) 4 , b ) 6 , c ) 8 , d ) 5 , e ) 10
d
subtract(divide(multiply(20, add(const_4, const_1)), 10), add(const_4, const_1))
add(const_1,const_4)|multiply(n0,#0)|divide(#1,n1)|subtract(#2,#0)
physics
allenai/math_qa
what should be the least number to be added to the 51234 number to make it divisible by 9 ?
"the least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits . sum of digits = 15 . nearest multiple of 9 greater than sum of digits = 18 . hence 3 has to be added . answer : c"
a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2
c
subtract(9, reminder(51234, 9))
reminder(n0,n1)|subtract(n1,#0)|
general
allenai/math_qa
two airplanes take off from one airfield at noon . one flies due east at 204 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
b in two hours : the plane flying east will be 408 miles away from airport . the other plane will be 566 miles away from airport . 566 / 408 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 408 miles apart . b
a ) 166 , b ) 408 , c ) 400 , d ) 483 , e ) 566
b
sqrt(subtract(power(multiply(283, const_2), const_2), power(multiply(204, 2), const_2)))
multiply(n1,const_2)|multiply(n0,n2)|power(#0,const_2)|power(#1,const_2)|subtract(#2,#3)|sqrt(#4)
physics
allenai/math_qa
a string of 25 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.06 , what is the probability that the string of light bulbs will fail during the time period t ?
"the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 25 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.06 = 0.94 the probability that none of the 25 light bulbs fails is 0.94 ^ 25 . hence , the probability that at least one light bulb fails is 1 - 0.94 ^ 25 . answer : d . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 25 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.06 = 6 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
a ) 0.06 , b ) ( 0.06 ) ^ 25 , c ) 1 - ( 0.06 ) ^ 25 , d ) 1 - ( 0.94 ) ^ 25 , e ) ( 0.94 ) ^ 25
d
subtract(const_1, power(subtract(const_1, 0.06), 25))
subtract(const_1,n1)|power(#0,n0)|subtract(const_1,#1)|
probability
allenai/math_qa
a can give b 60 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?
"a runs 1000 m while b runs 940 m and c runs 880 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 880 ) / 940 = 936.17 m . b can give c = 1000 - 936.17 = 63.83 m . answer : a"
a ) 63.83 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 101.12
a
subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 120)), subtract(multiply(const_100, const_10), 60)))
multiply(const_10,const_100)|subtract(#0,n1)|subtract(#0,n0)|multiply(#0,#1)|divide(#3,#2)|subtract(#0,#4)|
physics
allenai/math_qa
if 638521 is to be divisible by 5 , what is the least whole number that should be added to ?
"a number is divisible by 5 if the last digit is either 0 or 5 . here , 638521 = 1 ( last digit is neither 0 or 5 ) . the next multiple of 5 i . e to make the last digit 0 or 5 add 4 4 must be added to 638521 to make it divisible by 5 d"
a ) 8 , b ) 7 , c ) 5 , d ) 4 , e ) 3
d
add(floor(5), const_1)
floor(n1)|add(#0,const_1)|
general
allenai/math_qa
if x is an integer and 6.1 Γ— 10 ^ x is less than 620 what is the greatest possible value for x ?
if x = 2 6.1 Γ— 10 ^ 2 = 610 < 620 so , x = 2 answer : a
a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
a
floor(divide(log(divide(620, 6.1)), log(10)))
divide(n2,n0)|log(n1)|log(#0)|divide(#2,#1)|floor(#3)
general
allenai/math_qa
the price of lunch for 20 people was $ 300 including a 20 % gratuity for service . what was the average price per person , excluding the gratuity ?
"clearly b is the answer i used poe here lets consider option ( b ) 20 * 12.5 = 250 now 250 ( 120 / 100 ) = 300 = > possible answer imo b"
a ) 11.73 , b ) 12.5 , c ) 13.8 , d ) 14 , e ) 15.87
b
divide(divide(multiply(300, subtract(const_100, 20)), const_100), 20)
subtract(const_100,n2)|multiply(n1,#0)|divide(#1,const_100)|divide(#2,n0)|
general
allenai/math_qa
find the smallest number which should be multiplied with 1152 to make it a perfect square .
1152 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 required smallest number = 2 2 is the smallest number which should be multiplied with 1152 to make it a perfect square . answer : a
['a ) 2', 'b ) 1', 'c ) 3', 'd ) 5', 'e ) 6']
a
divide(divide(divide(divide(divide(1152, const_3), const_3), const_4), const_4), const_4)
divide(n0,const_3)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_4)|divide(#3,const_4)
geometry
allenai/math_qa
what least value should be replaced by * in 223431 * so the number become divisible by 5
explanation : trick : number is divisible by 5 , if last digit is 0 or 5 so that least number is 0 . answer : option a
a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7
a
subtract(5, subtract(5, 5))
subtract(n1,n1)|subtract(n1,#0)
general
allenai/math_qa
how is 4 % expressed as a decimal fraction ?
"4 / 100 = 0.04 answer : b"
a ) 0.4 , b ) 0.04 , c ) 0.004 , d ) 0.0004 , e ) 4
b
divide(4, const_100)
divide(n0,const_100)|
gain
allenai/math_qa
how many zeros does 1000 ! end with ?
"according to above 1000 ! has 1000 / 5 + 1000 / 25 + 1000 / 125 + 1000 / 625 = 200 + 40 + 8 + 1 = 249 trailing zeros . answer : c"
a ) 20 o , b ) 24 o , c ) 249 , d ) 30 o , e ) 325
c
add(add(divide(1000, add(const_4, const_1)), divide(subtract(1000, add(const_4, const_1)), power(add(const_4, const_1), const_2))), divide(subtract(1000, add(const_4, const_1)), power(add(const_4, const_1), const_3)))
add(const_1,const_4)|divide(n0,#0)|power(#0,const_2)|power(#0,const_3)|subtract(n0,#0)|divide(#4,#2)|divide(#4,#3)|add(#1,#5)|add(#7,#6)|
other
allenai/math_qa
5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope . the letter is said to be put in correct position if for example letter 1 goes into envelope 1 . now what is the probability that all letters be put into wrong envelopes ?
this q is based on derangement , a permutation in which all elements are in the wrong position . number of derangements = n ! ( 12 ! βˆ’ 13 ! + 14 ! + . . . + ( ( βˆ’ 1 ) n ) n ! ) n ! ( 12 ! βˆ’ 13 ! + 14 ! + . . . + ( ( βˆ’ 1 ) n ) n ! ) . . of course it can be derived but thats not required . . since there are 5 letters and 5 envelopes : - derangements = 5 ! ( 12 ! βˆ’ 13 ! + 14 ! βˆ’ 15 ! ) derangements = 5 ! ( 12 ! βˆ’ 13 ! + 14 ! βˆ’ 15 ! ) = > 120 ( 1 / 2 βˆ’ 1 / 6 + 1 / 24 βˆ’ 1 / 120 ) = 60 βˆ’ 20 + 5 βˆ’ 1 = 44.120 ( 1 / 2 βˆ’ 1 / 6 + 1 / 24 βˆ’ 1 / 120 ) = 60 βˆ’ 20 + 5 βˆ’ 1 = 44 . total possible ways = 5 ! = 120 . therefore required prob , p = 44 / 120 = 11 / 30 . ans d
a ) 1 / 3 , b ) 2 / 3 , c ) 11 / 120 , d ) 11 / 30 , e ) 76 / 120
d
subtract(add(subtract(inverse(factorial(const_2)), inverse(factorial(const_3))), inverse(factorial(const_4))), inverse(factorial(5)))
factorial(const_4)|factorial(const_2)|factorial(const_3)|factorial(n0)|inverse(#0)|inverse(#1)|inverse(#2)|inverse(#3)|subtract(#5,#6)|add(#4,#8)|subtract(#9,#7)
probability
allenai/math_qa
machine p and machine q are each used to manufacture 110 sprockets . it takes machine p 10 hours longer to produce 110 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 10 / x = 110 / 1.1 x + 10 1.1 ( 110 ) = 110 + 11 x 11 x = 11 x = 1 the answer is e
a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 1
e
divide(subtract(110, divide(110, add(divide(10, const_100), const_1))), 10)
divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)|divide(#3,n1)
gain
allenai/math_qa
a cyclist covers a distance of 500 m in 4 min 30 sec . what is the speed in km / hr of the cyclist ?
distance = 500 m time = 4 min 10 sec = 250 sec speed = ( 500 / 250 ) m / s = 2 m / s speed in km / hr = 2 * 18 / 5 = 3.2 km / hr correct option is c
a ) 2 , b ) 2.5 , c ) 3.2 , d ) 4.6 , e ) 2.8
c
multiply(divide(500, add(multiply(4, const_60), 30)), const_3_6)
multiply(n1,const_60)|add(n2,#0)|divide(n0,#1)|multiply(#2,const_3_6)
physics
allenai/math_qa
when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ?
"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c"
a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12
c
divide(6, subtract(6.12, floor(6.12)))
floor(n1)|subtract(n1,#0)|divide(n0,#1)|
general
allenai/math_qa
what is x if x + 2 y = 10 and y = 3 ?
"substitute y by 3 in x + 2 y = 10 x + 2 ( 3 ) = 10 x + 6 = 10 if we substitute x by 4 in x + 6 = 10 , we have 4 + 6 = 10 . hence x = 4 correct answer d"
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
d
subtract(10, multiply(2, 3))
multiply(n0,n2)|subtract(n1,#0)|
general
allenai/math_qa
a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.5 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
"volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.5 = 300 answer : b"
a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 2,400
b
multiply(0.5, divide(1.08, divide(divide(divide(multiply(multiply(15, 12), 10), const_100), const_100), const_100)))
multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|divide(n3,#4)|multiply(n4,#5)|
general
allenai/math_qa
if xy = 1 , x / y = 36 , for positive numbers x and y , y = ?
"very easy question . 2 variables and 2 easy equations . xy = 1 - - - > x = 1 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 1 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 1 / 36 - - - > y = 1 / 6 or - 1 / 6 the question states that x and y are positive integers . therefore , y = 1 / 6 is the answer . answer e ."
a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6
e
sqrt(divide(1, 36))
divide(n0,n1)|sqrt(#0)|
general
allenai/math_qa
the population of a town increased from 1 , 45,000 to 2 , 30,500 in a decade . the average percent increase of population per year is :
"explanation : increase in 10 years = ( 230500 - 145000 ) = 85500 . increase % = ( 85500 / 145000 x 100 ) % = 58 % . required average = ( 58 / 10 ) % = 5.8 % . answer : option b"
a ) 4.37 % , b ) 5.8 % , c ) 6.8 % , d ) 8.75 % , e ) none
b
add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(2, 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
if 5 x = 7 y and xy β‰  0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?
"5 x = 7 y = > x / y = 7 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 7 / 5 ) * ( 6 / 5 ) = 42 / 25 ans : b"
a ) 25 / 6 , b ) 42 / 25 , c ) 6 / 5 , d ) 5 / 6 , e ) 25 / 36
b
multiply(divide(divide(1, const_3.0), divide(1, 5)), divide(7, 5))
divide(n3,const_3.0)|divide(n3,n0)|divide(n1,n0)|divide(#0,#1)|multiply(#3,#2)|
general
allenai/math_qa
in order to obtain an income of rs . 500 from 30 % stock at rs . 90 , one must make an investment of
"explanation : market value = rs . 90 required income = rs . 500 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 30 ( ie , 30 % of the face value 100 ) , investment = rs . 90 to obtain rs . 15000 , investment = 90 / 30 Γ£ β€” 500 = rs . 1500 answer : option e"
a ) rs . 1550 , b ) rs . 1430 , c ) rs . 1450 , d ) rs . 1400 , e ) rs . 1500
e
multiply(divide(90, 30), 500)
divide(n2,n1)|multiply(n0,#0)|
gain
allenai/math_qa
if m and n are positive integers and m = 15 n - 1 , what is the remainder when m is divided by 5 ?
this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that m and n are positive integers and m = 15 n - 1 . we ' re asked for the remainder when m is divided by 5 . if . . . . n = 1 m = 14 14 / 5 = 2 remainder 4 final answer : e
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
e
subtract(subtract(multiply(15, const_2), 1), multiply(5, 5))
multiply(n0,const_2)|multiply(n2,n2)|subtract(#0,n1)|subtract(#2,#1)
general
allenai/math_qa
if the average ( arithmetic mean ) of a and b is 150 , and the average of b and c is 90 , what is the value of a βˆ’ c ?
"a + b = 300 b + c = 180 a - c = 120 . imo option c ."
a ) βˆ’ 220 , b ) βˆ’ 100 , c ) 120 , d ) 135 , e ) it can not be determined from the information given
c
subtract(multiply(90, const_2), multiply(150, const_2))
multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)|
general
allenai/math_qa
the radius of a cylinder is 10 m , height 14 m . the volume of the cylinder is :
"cylinder volume = Ο€ r ( power 2 ) h = 22 / 7 Γ— 10 Γ— 10 Γ— 14 = 4400 m ( power 3 ) answer is e ."
a ) 2200 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4400
e
multiply(circumface(10), 14)
circumface(n0)|multiply(n1,#0)|
geometry
allenai/math_qa
the ratio of 2 numbers is 3 : 4 and their h . c . f . is 4 . their l . c . m . is ?
"let the numbers be 3 x and 4 x their h . c . f . = 4 so the numbers are 3 * 4 , 4 * 4 = 12,16 l . c . m . = 48 answer is c"
a ) 20 , b ) 24 , c ) 48 , d ) 36 , e ) 60
c
sqrt(divide(4, add(power(4, 3), add(power(2, 3), power(3, const_2)))))
power(n0,n1)|power(n1,n1)|power(n2,const_2)|add(#0,#1)|add(#3,#2)|divide(n3,#4)|sqrt(#5)|
other
allenai/math_qa
the β€œ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 Γ— 2 Γ— 3 Γ— 5 . ) what is the greatest possible length of integer z if z < 2500 ?
"to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 11 = 2048 < 2500 , then the greatest possible length of integer z is 11 . the answer is c ."
a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
c
log(power(2, const_10))
power(n3,const_10)|log(#0)|
general
allenai/math_qa
what will be the difference between simple and compound interest at 12 % per annum on a sum of rs . 1000 after 4 years ?
"s . i . = ( 1000 * 12 * 4 ) / 100 = rs . 480 c . i . = [ 1000 * ( 1 + 12 / 100 ) 4 - 1000 ] = rs . 573.5 difference = ( 573.5 - 480 ) = rs . 93.5 answer : c"
a ) 94.19 , b ) 94.12 , c ) 93.5 , d ) 64.1 , e ) 64.11
c
subtract(subtract(multiply(1000, power(add(divide(12, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(12, const_100)), 4))
divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|multiply(n2,#2)|power(#1,n2)|multiply(n1,#4)|subtract(#5,n1)|subtract(#6,#3)|
gain
allenai/math_qa
cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 3 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
"ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 3 ) / ( 10 - 5 ) = 2 / 5 so they should be mixed in the ratio 2 : 5 answer - a"
a ) 2 : 5 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
a
divide(subtract(5, 3), subtract(10, 5))
subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|
general
allenai/math_qa
if t = 5 / 9 * ( k - 32 ) , and if t = 75 , then what is the value of k ?
k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 75 ) / 5 + 32 = 167 the answer is d .
a ) 158 , b ) 161 , c ) 164 , d ) 167 , e ) 170
d
add(divide(multiply(75, 9), 5), 32)
multiply(n1,n3)|divide(#0,n0)|add(n2,#1)
general
allenai/math_qa
in a recent election , james received 15 percent of the 10000 votes cast . to win the election , a candidate needed to receive more than 51 percent of the vote . how many additional votes would james have needed to win the election ?
"james = ( 15 / 100 ) * 10000 = 1500 votes to win = ( 51 / 100 ) * total votes + 1 = ( 51 / 100 ) * 10000 + 1 = 5101 remaining voted needed to win election = 5101 - 1500 = 3601 answer : option e"
a ) 1004 , b ) 1000 , c ) 3600 , d ) 1201 , e ) 3601
e
subtract(add(const_1000, const_1000), multiply(add(const_1000, const_1000), 15))
add(const_1000,const_1000)|multiply(n0,#0)|subtract(#0,#1)|
general
allenai/math_qa
if 60 honey bees make 60 grams of honey in 60 days , then 1 honey bee will make 1 gram of honey in how many days ?
"explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 60 : : 60 : x honey 60 : 1 = > 1 x 60 x x = 60 x 1 x 60 = > x = 60 . answer : e"
a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 60
e
divide(1, divide(1, 60))
divide(n3,n0)|divide(n3,#0)|
physics
allenai/math_qa
if an integer n is to be chosen at random from the integers 1 to 92 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
"n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 46 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 46 + 12 ) / 92 = 58 / 96 = 29 / 46 ans is d"
a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 29 / 46 , e ) 3 / 4
d
divide(add(divide(92, 2), divide(92, 8)), 92)
divide(n1,n3)|divide(n1,n4)|add(#0,#1)|divide(#2,n1)|
general
allenai/math_qa
a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 50 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
"1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 50 % of 100 = 50 pounds of decaffeinated coffee 3 . wt have 130 pounds of decaffeinated out of 500 pounds , that means 130 / 500 * 100 % = 26 % . the correct answer is a ."
a ) 26 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
a
multiply(divide(add(multiply(divide(20, 100), 400), multiply(100, divide(50, 100))), add(400, 100)), 100)
add(n0,n2)|divide(n1,n2)|divide(n3,n2)|multiply(n0,#1)|multiply(n2,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,n2)|
gain
allenai/math_qa
a man invests some money partly in 12 % stock at 132 and partly in 10 % stock at 80 . to obtain equal dividends from both , he must invest the money in the ratio :
"solution for an income of rs . 1 in 12 % stock at 132 , investment = rs . ( 132 / 12 ) = rs . 11 . for an income of rs . 1 in 10 % stock at 80 , investment = rs . ( 80 / 10 ) = rs . 8 . ∴ ratio of investments = 11 : 8 = 11 : 8 answer c"
a ) 3 : 4 , b ) 3 : 5 , c ) 11 : 8 , d ) 16 : 15 , e ) none
c
divide(multiply(132, const_2), multiply(80, const_3))
multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)|
other
allenai/math_qa
if the personal income tax rate is lowered from 42 % to 28 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 34500 ?
"saving = ( 42 - 28 ) % of 34500 = 4830 . answer : c"
a ) $ 3500 , b ) $ 5000 , c ) $ 4830 , d ) $ 7000 , e ) $ 10000
c
multiply(divide(34500, const_100), subtract(42, 28))
divide(n2,const_100)|subtract(n0,n1)|multiply(#0,#1)|
gain
allenai/math_qa
in the rectangle below , the line mn cuts the rectangle into two regions . find x the length of segment nb so that the area of the quadrilateral mnbc is 40 % of the total area of the rectangle .
solution we first note that mc = 20 - 5 = 15 the quadrilateral mnbc is a trapezoid and its area a is given by a = ( 1 / 2 ) Γ— 10 Γ— ( x + mc ) = 5 ( x + 15 ) 40 % of the area of the rectangle is equal to 40 % Γ— ( 20 Γ— 10 ) = ( 40 / 100 ) Γ— 200 = 80 since the area of mnbc is equal to 40 % the area of the rectangle , we can write 5 ( x + 15 ) = 80 5 x + 75 = 80 5 x = 5 x = 1 meter answer is a
a ) 1 meter , b ) 2 meter , c ) 3 meter , d ) 4 meter , e ) 5 meter
a
subtract(subtract(divide(40, const_12), const_0_33), const_2)
divide(n0,const_12)|subtract(#0,const_0_33)|subtract(#1,const_2)
geometry
allenai/math_qa
a can go round a circular path 8 times in 40 minutes . if the diameter of the circle is increased to 10 times the original diameter , then the time required by a to go round the new path once , travelling at the same speed as before is
solution let original diameter be d metres . then , its circumference = ( Ο€ d ) metres . time taken to cover ( 8 Ο€ d ) m = 40 min . new diameter = ( 10 d ) m . then , its circumference = ( Ο€ x 10 d ) m . time taken to go round it once β€Ή = β€Ί [ 40 / 8 Ο€ d x 10 Ο€ d ] m β€Ή = β€Ί 50 min . answer c
a ) 20 min , b ) 35 min , c ) 50 min , d ) 70 min , e ) none
c
divide(multiply(40, 10), 8)
multiply(n1,n2)|divide(#0,n0)
physics
allenai/math_qa
a man walks at a rate of 10 mph . after every ten miles , he rests for 6 minutes . how much time does he take to walk 60 miles ?
"to cover 60 miles the man needs ( time ) = ( distance ) / ( rate ) = 60 / 10 = 6 hours = 360 minutes . he will also rest 5 times ( after 10 , 20 , 30,40 and 50 miles ) , so total resting time = 5 * 6 = 30 minutes . total time = 360 + 30 = 390 minutes . answer : e ."
a ) 300 , b ) 318 , c ) 322 , d ) 324 , e ) 390
e
add(multiply(6, const_4), multiply(divide(60, 10), const_60))
divide(n2,n0)|multiply(n1,const_4)|multiply(#0,const_60)|add(#1,#2)|
physics
allenai/math_qa
find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm .
let abcd is a rhombus with diagonals ac and bd which intersect each other at o . ac = 24 β‡’ ao = 12 let bo = x and ab = 13 cm ( given ) by pythagorean theorem c 2 = a 2 + b 2 13 2 = 12 2 + x 2 169 = 144 + x 2 x 2 = 169 – 144 x 2 = 25 x = 5 cm bo = 5 cm diagonal bd = 2 x 5 = 10 cm . area = Β½ x [ product of diagonals ] = Β½ x 24 x 10 area = 120 sq . cm answer is b
['a ) 150 sq . cm', 'b ) 120 sq . cm', 'c ) 130 sq . cm', 'd ) 125 sq . cm', 'e ) 110 sq . cm']
b
rhombus_area(24, multiply(sqrt(subtract(power(13, const_2), power(divide(24, const_2), const_2))), const_2))
divide(n1,const_2)|power(n0,const_2)|power(#0,const_2)|subtract(#1,#2)|sqrt(#3)|multiply(#4,const_2)|rhombus_area(n1,#5)
geometry
allenai/math_qa
how many cubes of 10 cm edge can be put in a cubical box of 1 m edge
"explanation : number of cubes = ( 100 x 100 x 100 ) / ( 10 x 10 x 10 ) = 1000 answer : c"
a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
c
divide(volume_cube(1), volume_cube(divide(10, const_100)))
divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)|
physics
allenai/math_qa
the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 100 metres ?
"speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 100 m = 100 / 5 = 20 seconds . answer : b"
a ) 16 seconds , b ) 20 seconds , c ) 14 seconds , d ) 12 seconds , e ) 15 seconds
b
divide(100, multiply(add(15, 3), const_0_2778))
add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)|
physics
allenai/math_qa
convert 700 miles into meters ?
"1 mile = 1609.34 meters 700 mile = 700 * 1609.34 = 1126538 meters answer is b"
a ) 784596 , b ) 1126538 , c ) 804670 , d ) 784596 , e ) 864520
b
divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 700), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))
add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)|
physics
allenai/math_qa
a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 150 = 390 m . time taken = 390 / 10 = 39 sec . answer : c"
a ) 28 sec , b ) 16 sec , c ) 39 sec , d ) 18 sec , e ) 17 sec
c
divide(add(240, 150), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))
add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5)|
general
allenai/math_qa
if jenee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ?
perhaps it is also easy to just translate the % into fractions : 6 % : 6 / 100 = 3 / 50 7 % : 7 / 100 8 % : 8 / 100 = 4 / 50 = 2 / 25 9 % : 9 / 100 only 3 / 50 exists in the answer choices , so ans d
a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 3 / 50 , e ) 1 / 20
d
divide(const_3, multiply(5, 10))
multiply(n0,n1)|divide(const_3,#0)
general
allenai/math_qa
on a wedding catering service , an experienced chef can prepare a service for a wedding in 6 hours while an novice chef would finish the preparations in 7 hours . if the catering service employs the same number of novice and experienced chefs , then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes ?
experienced chefs work = 1 wedding / 6 hours novice chefs work = 1 wedding / 7 hours since we do n ' t know the number of experienced or novice chefs but know that there is an equal number each , let the number of chefs for each group equalx 1 hr and 36 mins = 8 / 5 an hour x / 6 + x / 7 = 1 wedding / ( 8 / 5 ) x / 6 + x / 7 = 5 / 8 x = 2 so there are 2 novice chefs and 2 experienced chefs . in total there are 4 . the answer is c .
a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
c
floor(divide(const_2, multiply(add(divide(const_1, 6), divide(const_1, 7)), add(1, divide(36, const_60)))))
divide(const_1,n0)|divide(const_1,n1)|divide(n3,const_60)|add(#0,#1)|add(n2,#2)|multiply(#3,#4)|divide(const_2,#5)|floor(#6)
physics
allenai/math_qa
if ( 1 – 1.25 ) n = 2 , then n =
"( 1 – 1.25 ) n = 2 simplify to get : - 0.25 n = 2 rewrite as ( - 1 / 4 ) n = 2 multiply both sides by - 4 to get : n = - 8 answer : c"
a ) βˆ’ 400 , b ) βˆ’ 140 , c ) βˆ’ 8 , d ) 4 , e ) 400
c
negate(multiply(2, const_4))
multiply(n2,const_4)|negate(#0)|
general
allenai/math_qa
a dessert recipe calls for 50 % melted chocolate and 50 % raspberry puree to make a particular sauce . a chef accidentally makes 15 cups of the sauce with 40 % melted chocolate and 60 % raspberry puree instead . how many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50 % of each ?
we have 15 cups of sauce with 4040 choc and 6060 rasb cups of choc = 0.4 βˆ— 15 = 6 cups of rasb = 0.6 βˆ— 15 = 9 now let say we removed x cup of original mix and replaced with x cups of choc . therefore final number of cups of choc = 6 βˆ’ 0.4 x + x now this number of cup should be 50 % of total = 15 / 2 = 7.5 therefore 6 βˆ’ 0.4 x + x = 7.5 on solving x = 2.5 answer : b
a ) 1.5 , b ) 2.5 , c ) 3 , d ) 4.5 , e ) 5
b
divide(divide(subtract(add(50, 50), 50), subtract(50, 40)), const_2)
add(n0,n0)|subtract(n0,n3)|subtract(#0,n0)|divide(#2,#1)|divide(#3,const_2)
gain
allenai/math_qa
the tax on a commodity is diminished by 10 % and its consumption increases by 10 % . find the effects on revenue ?
"since tax consumption = revenue . therefore , net % change in revenue = ( x + y + xy / 100 ) % = [ - 10 + 10 + ( - 10 x 10 ) / 100 ] % or - 1 % . therefore , revenue decreased by 1 % . answer : a"
a ) 1 % decrease , b ) 2 % increase , c ) 3 % decrease , d ) 4 % decrease , e ) none of these
a
subtract(const_100, multiply(multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(10, const_100))), const_100))
divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)|
general
allenai/math_qa
solution for 3.15 + . 014 + . 458
"3.15 + . 014 + . 458 = 0 0 = 0 - 3.15 - 0.014 - 0.458 0 = - 3.622 answer : a"
a ) 3.622 , b ) 3.911 , c ) 4.938 , d ) 2.986 , e ) 2.999
a
add(add(3.15, divide(014, const_1000)), divide(458, const_1000))
divide(n1,const_1000)|divide(n2,const_1000)|add(n0,#0)|add(#2,#1)|
general
allenai/math_qa
a retailer bought a machine at a wholesale price of $ 126 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
my solution : wholesale price = 126 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 126 + 1 / 5 ( 126 ) x = 168 ; answer : e
a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 168
e
divide(multiply(add(126, divide(multiply(126, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10))
multiply(n0,n2)|multiply(const_3,const_3)|divide(#0,const_100)|multiply(n1,#1)|add(n0,#2)|multiply(#4,const_100)|divide(#5,#3)
gain
allenai/math_qa
what least number must be added to 1078 , so that the sum is completely divisible by 23 ?
"47 * 23 = 1081 1081 - 1078 = 3 answer : a"
a ) 3 , b ) 2 , c ) 4 , d ) 5 , e ) 6
a
subtract(multiply(add(multiply(const_4, const_10), const_2), 23), 1078)
multiply(const_10,const_4)|add(#0,const_2)|multiply(n1,#1)|subtract(#2,n0)|
general
allenai/math_qa
a man is 24 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
"let present age of the son = x years then present age the man = ( x + 24 ) years given that in 2 years man ' s age will be twice the age of his son x = 22 answer b"
a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 30 years
b
divide(subtract(24, 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
find the least number that must be subtracted from 1387 so that the remaining number is divisible by 15 .
on dividing 1387 by 15 we get the remainder 7 , so 7 should be subtracted . the answer is c .
a ) 1 , b ) 5 , c ) 7 , d ) 9 , e ) 13
c
subtract(1387, multiply(subtract(const_100, multiply(const_2, const_4)), 15))
multiply(const_2,const_4)|subtract(const_100,#0)|multiply(n1,#1)|subtract(n0,#2)
general
allenai/math_qa
in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 60 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
"percent of students who are 25 years old or older is 0.6 * 48 + 0.2 * 52 = ~ 39 , so percent of people who are less than 25 years old is 100 - 39 = 61 . answer : b ."
a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
b
subtract(const_1, multiply(divide(60, const_100), divide(subtract(const_100, 20), const_100)))
divide(n2,const_100)|subtract(const_100,n3)|divide(#1,const_100)|multiply(#0,#2)|subtract(const_1,#3)|
general
allenai/math_qa
if the sum of two numbers is 16 and the sum of their squares is 200 , then the product of the numbers is
"according to the given conditions x + y = 16 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 16 ^ 2 = 200 + 2 xy so xy = 56 / 2 = 28 answer : e"
a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 28
e
divide(subtract(power(16, const_2), 200), const_2)
power(n0,const_2)|subtract(#0,n1)|divide(#1,const_2)|
general
allenai/math_qa
when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.2 centimeter . the actual diameter of the tissue , in centimeters , is
"it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.2 then x = 0.2 / 1000 = 0.0002 . the answer is e"
a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
e
divide(0.2, 1,000)
divide(n1,n0)|
geometry
allenai/math_qa
a can finish a piece of work in 12 days . b can do it in 20 days . they work together for 9 days and then a goes away . in how many days will b finish the work ?
"9 / 12 + ( 9 + x ) / 20 = 1 = > x = 5 days answer : c"
a ) 6 days , b ) 4 days , c ) 5 days , d ) 3 days , e ) 7 days
c
divide(subtract(const_1, add(multiply(divide(const_1, 12), const_2), multiply(divide(const_1, 20), const_2))), divide(const_1, 20))
divide(const_1,n0)|divide(const_1,n1)|multiply(#0,const_2)|multiply(#1,const_2)|add(#2,#3)|subtract(const_1,#4)|divide(#5,#1)|
physics
allenai/math_qa
if n is an integer and 101 n ^ 2 is less than or equal to 3600 , what is the greatest possible value of n ?
"101 * n ^ 2 < = 3600 n ^ 2 < = 3600 / 101 which will be less than 81 since 3600 / 100 = 36 which is the square of 9 next closest value of n where n ^ 2 < = 36 is 5 ans b"
a ) 7 , b ) 5 , c ) 9 , d ) 10 , e ) 11
b
floor(sqrt(divide(3600, 101)))
divide(n2,n0)|sqrt(#0)|floor(#1)|
general
allenai/math_qa
in how many seconds will a train 180 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
"speed = 36 * 5 / 18 = 10 m / s time = 180 / 10 = 18 seconds the answer is c ."
a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
c
divide(180, multiply(const_0_2778, 36))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
allenai/math_qa
find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 16 per cubic meter ?
"22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 16 = 1584 answer : e"
a ) 2998 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 1584
e
multiply(volume_cylinder(divide(3, const_2), 14), 16)
divide(n1,const_2)|volume_cylinder(#0,n0)|multiply(n2,#1)|
physics
allenai/math_qa
a bowl of fruit contains 14 apples and 25 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
"number of apples = 14 number of oranges = 25 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 25 - x ) = 39 - x 14 / ( 39 - x ) = 7 / 10 = > 20 = 39 - x = > x = 19 answer e"
a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 19
e
divide(subtract(multiply(add(14, 25), divide(70, const_100)), 14), divide(70, const_100))
add(n0,n1)|divide(n2,const_100)|multiply(#0,#1)|subtract(#2,n0)|divide(#3,#1)|
gain
allenai/math_qa
the average ( arithmetic mean ) of 10 , 30 , and 50 is 8 more than the average of 20 , 40 , and x . what is x ?
"the average of 10 , 30 , and 50 is 30 . the average of 20 , 40 and x is 22 . then 20 + 40 + x = 66 . x = 6 . the answer is c ."
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
c
subtract(add(add(10, 30), 50), add(add(multiply(8, const_3), 20), 40))
add(n0,n1)|multiply(n3,const_3)|add(n2,#0)|add(n4,#1)|add(n5,#3)|subtract(#2,#4)|
general
allenai/math_qa
if k is an integer and 0.0010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?
"0.0010101 * 10 ^ k > 100 we need to move the decimal point to the right 5 places to get 101.01 this is equivalent to multiplying by 10 ^ 5 . the answer is d ."
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
d
divide(log(divide(100, 0.0010101)), log(10))
divide(n2,n0)|log(n1)|log(#0)|divide(#2,#1)|
general
allenai/math_qa
calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days ,
"the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c"
a ) 6 days , b ) 3 days , c ) 4 days , d ) 2 days , e ) 5 days
c
divide(multiply(multiply(5, 4), 35), multiply(25, 7))
multiply(n2,n4)|multiply(n0,n3)|multiply(n1,#0)|divide(#2,#1)|
physics
allenai/math_qa
if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly once in 3 consecutive flips ?
total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 th thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : b
a ) 0.125 , b ) 0.375 , c ) 0.325 , d ) 0.5 , e ) 0.666
b
multiply(power(divide(const_1, const_2), const_3), 3)
divide(const_1,const_2)|power(#0,const_3)|multiply(n0,#1)
probability
allenai/math_qa
if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 61 , how much does one shirt cost ?
3 j + 2 s = 69 2 j + 3 s = 61 - - - - - - - - - - - - - - - - 5 j + 5 s = 130 - - - - ( divide by 5 ) - - - > j + s = 26 3 j + 2 s = j + 2 ( j + s ) = j + 52 = 69 - - - > j = 17 3 * 17 + 2 s = 69 51 + 2 s = 69 2 s = 18 s = 9 answer : a
a ) $ 9 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80
a
divide(subtract(multiply(61, 3), multiply(69, 2)), subtract(multiply(3, 3), multiply(2, 2)))
multiply(n0,n5)|multiply(n1,n2)|multiply(n0,n0)|multiply(n1,n1)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)
general
allenai/math_qa
how many integers between 1 and 10 ^ 20 are such that the sum of their digits is 2 ?
"the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 19 and there are 20 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 19 thus , the total number of integers is 1 + 2 + . . . + 19 + 20 = 20 * 21 / 2 = 210 the answer is b ."
a ) 190 , b ) 210 , c ) 211 , d ) 230 , e ) 231
b
subtract(10, 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
if 20 % of a number = 400 , then 120 % of that number will be ?
"let the number x . then , 20 % of x = 400 x = ( 400 * 100 ) / 20 = 2000 120 % of x = ( 120 / 100 * 2000 ) = 2400 . answer : d"
a ) 20 , b ) 120 , c ) 360 , d ) 2400 , e ) 2820
d
divide(multiply(120, 400), 20)
multiply(n1,n2)|divide(#0,n0)|
gain
allenai/math_qa
the ratio between the presents of the a and b is 6 : 7 . if b is 4 years older than a , what will be the ratio of the ages of a and b after 4 years ?
let a and b ages will be 6 x and 7 x 7 x - 6 x = 4 x = 4 required ratio = 6 x + 4 : 7 x + 4 = 28 : 32 = 7 : 8 answer is c
a ) 1 : 2 , b ) 9 : 11 , c ) 7 : 8 , d ) 6 : 7 , e ) 3 : 4
c
divide(add(subtract(multiply(7, 4), 4), 4), add(multiply(7, 4), 4))
multiply(n1,n2)|add(n2,#0)|subtract(#0,n2)|add(n2,#2)|divide(#3,#1)
other
allenai/math_qa
what is the value of 3 x ^ 2 βˆ’ 1.8 x + 0.6 for x = 0.6 ?
"3 x ^ 2 - 1.8 x + 0.6 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.6 = 0 + 0.6 = 0.6 answer : b"
a ) βˆ’ 0.3 , b ) 0.6 , c ) 0.3 , d ) 1.08 , e ) 2.46
b
subtract(multiply(divide(divide(subtract(power(3, 2), power(1.8, 0.6)), const_1000), const_1000), 3), divide(divide(subtract(power(3, 2), power(1.8, 0.6)), const_1000), const_1000))
power(n0,n1)|power(n2,n3)|subtract(#0,#1)|divide(#2,const_1000)|divide(#3,const_1000)|multiply(n0,#4)|subtract(#5,#4)|
general
allenai/math_qa
find the least number must be added to 228712 so that remaining no . is divisible by 9 ?
on dividing 228712 by 9 we get the remainder 4 , so 5 should be subtracted a
a ) 5 , b ) 3 , c ) 1 , d ) 6 , e ) 2
a
subtract(9, reminder(228712, 9))
reminder(n0,n1)|subtract(n1,#0)
general
allenai/math_qa
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 38.7 % . 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£ β€” ( 100 + 38.7 ) / ( 100 Γ’ Λ† ’ 5 ) = 146 hence , required % profit = 146 Γ’ € β€œ 100 = 46 % answer b"
a ) 28.5 , b ) 46 , c ) 30 , d ) data inadequate , e ) none of these
b
subtract(divide(multiply(add(const_100, 38.7), 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
john makes $ 60 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
"increase = ( 15 / 60 ) * 100 = ( 1 / 4 ) * 100 = 25 % . b"
a ) 16.12 % , b ) 25 % , c ) 16.56 % , d ) 17.66 % , e ) 18.1 %
b
multiply(divide(subtract(75, 60), 60), const_100)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|
gain
allenai/math_qa
if x is real , find the maximum value of the expression - 2 x ^ 2 + 5 x + 7 .
this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 5 x + 7 = ( - 2 x + 7 ) ( x + 1 ) the roots are 7 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 1.25 the maximum value is - 2 ( 1.25 ) ^ 2 + 5 ( 1.25 ) + 7 = 10.125 the answer is c .
a ) 6.125 , b ) 8.125 , c ) 10.125 , d ) 12.125 , e ) 14.125
c
subtract(add(multiply(5, divide(multiply(2, 2), 5)), 7), multiply(2, power(divide(multiply(2, 2), 5), 2)))
multiply(n0,n0)|divide(#0,n2)|multiply(n2,#1)|power(#1,n0)|add(n3,#2)|multiply(n0,#3)|subtract(#4,#5)
general
allenai/math_qa
a train leaves delhi at 9 a . m . at a speed of 35 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
"d = 35 * 5 = 175 rs = 40 – 35 = 5 t = 175 / 5 = 35 d = 40 * 35 = 1400 km answer : e"
a ) 229 , b ) 288 , c ) 600 , d ) 888 , e ) 1400
e
multiply(divide(multiply(35, add(const_3, 2)), subtract(40, 35)), 40)
add(n2,const_3)|subtract(n3,n1)|multiply(n1,#0)|divide(#2,#1)|multiply(n3,#3)|
physics
allenai/math_qa
at what price must an article costing rs . 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ?
"cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.54 answer : a"
a ) 64.54 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
a
divide(multiply(add(47.50, divide(multiply(47.50, 25), const_100)), const_100), subtract(const_100, 8))
multiply(n0,n2)|subtract(const_100,n1)|divide(#0,const_100)|add(n0,#2)|multiply(#3,const_100)|divide(#4,#1)|
gain
allenai/math_qa
a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference ?
"total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 2 = 8 feet answer : b"
a ) 10 feet , b ) 8 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
b
multiply(divide(16, 4), 2)
divide(n1,n0)|multiply(n2,#0)|
geometry
allenai/math_qa
of the 90 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
"neither car nor garage = total - garage - ( swim - common ) = 90 - 50 - ( 40 - 35 ) = 90 - 55 = 35 answer e"
a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35
e
subtract(90, add(add(subtract(50, 35), subtract(40, 35)), 35))
subtract(n1,n3)|subtract(n2,n3)|add(#0,#1)|add(n3,#2)|subtract(n0,#3)|
other
allenai/math_qa
i bought two books ; for rs . 460 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
"x * ( 85 / 100 ) = ( 460 - x ) 119 / 100 x = 280 answer : d"
a ) 337.33 , b ) 280.33 , c ) 299.33 , d ) 268.33 , e ) 289.33
d
divide(multiply(460, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19)))
add(n2,const_100)|subtract(const_100,n1)|add(#0,#1)|multiply(n0,#0)|divide(#3,#2)|
gain
allenai/math_qa