euclaise/mathqa_programs huggingface dataset:
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 279 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 186 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 279 + l ) / 20 = l / 8 2232 + 8 l = 20 l l = 2232 / 12 = 186 m answer a"
Answer: a
Python program:
a = 20 - 8
b = 279 / a
c = b * 8
Problem: mary ' s income is 60 % more than tim ' s income and tim ' s income is 10 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 144 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.9 = 90 m = 90 * 1.6 = 144 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 144 * 100 / 100 = 144 ans : a"
Answer: a
Python program:
a = 100 - 10
b = 100 - 10
c = 60 / 100
d = b * c
e = a + d
Problem: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 75 th number in this set ?
Options: a ) 597 , b ) 608 , c ) 613 , d ) 616 , e ) 621
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 75 th number = 8 * ( 75 - 1 ) + 5 = 597 answer = a"
Answer: a
Python program:
a = 75 - 1
b = a * 8
c = b + 5
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 54 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 60
Rationale: "the total number of books is 75 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 54 books , thus the number of un - returned books is 75 - 54 = 21 books . 0.35 x = 21 x = 60 the answer is e ."
Answer: e
Python program:
a = 75 - 54
b = 65 / 100
c = 1 - b
d = a / c
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 86 . how much was lent at 5 % ?
Options: a ) 388 , b ) 2998 , c ) 277 , d ) 500 , e ) 400
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 86 5 x / 100 + 90 – 6 x / 100 = 86 x / 100 = 4 = > x = 400 . answer : e"
Answer: e
Python program:
a = 5 + 6 
b = a * 100
Problem: each of the positive integers a , b , and c is a 3 - digit integer . if each of the digits 1 through 9 appears in one of these 3 integers , what is the maximum possible value of the sum of a , b , and c ?
Options: a ) 2445 , b ) 2331 , c ) 2874 , d ) 2801 , e ) 2256
Rationale: according to the stem we should use the digits 1 through 9 to construct 3 three - digit integers , so that their sum is as big as possible . to maximize the sum , maximize the hundreds digits of a , b , and c , so make them 9 , 8 , and 7 . next , minimize tens digits . make them 6 , 5 , and 4 . use the remaining digits ( 3 , 2 , and 1 ) for units digits . so , a would be 963 , b would be 852 and c would be 741 . 741 + 852 + 963 = 2256 . answer : e .
Answer: e
Python program:
a = 2 + 3 
b = a * 3
c = b * 10
d = 9 * 3
e = d - 3
f = e * 100
g = c + f 
h = 3 + 3 
i = g + h 
j = i - 100
k = j - 100
Problem: the profits of qrs company rose 50 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 %
Rationale: "assume 100 in march , then 150 in april as 50 % increase , then 120 in may as 20 % decrease from april , and then 180 in june which is 150 % of 120 . so overall increase is from 100 to 180 is 80 % answer e"
Answer: e
Python program:
a = 50 / 100
b = 1 + a 
c = 50 / 100
d = 1 + c 
e = 20 / 100
f = 1 - e
g = d * f
h = b * g
i = h - 1
j = 100 * i
Problem: a certain bag contains 100 balls â € ” 20 white , 30 green , 10 yellow , 37 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 20 + 30 + 10 ) / 100 = 60 / 100 = 0.6 . answer is c"
Answer: c
Python program:
a = 37 + 3 
b = 100 - a
c = b / 100
Problem: what is the next number : 2 , 17 , 257 , __
Options: a ) 2977 , b ) 3837 , c ) 4097 , d ) 4847 , e ) 5387
Rationale: "4 ^ 0 + 1 = 2 4 ^ 2 + 1 = 17 4 ^ 4 + 1 = 257 4 ^ 6 + 1 = 4097 the answer is c ."
Answer: c
Python program:
a = 257 * 10
b = a - 100
c = b - 2
d = c - 2
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 15 % and its breadth is decreased by 10 % ?
Options: a ) 3.5 percent increase , b ) 9.5 percent increase , c ) 1.5 percent increase , d ) 3.9 percent increase , e ) 3.5 percent increase
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 15 % = 115 b decrease by 10 % = 90 115 * 90 = 10350 3.5 percent increase answer : e"
Answer: e
Python program:
a = 100 + 15 
b = 100 - 10
c = a * b
d = 100 * 100
e = c - d
f = 100 * 100
g = e / f
h = g * 100
Problem: in order to obtain an income of rs . 450 from 10 % stock at rs . 108 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 4860 , d ) 1987 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 108 . to obtain rs . 450 , investment = = rs . 4860 . answer : c"
Answer: c
Python program:
a = 108 / 10
b = a * 450
Problem: in a ratio which is equal to 4 : 6 , if the antecedent is 20 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 30 , d ) 51 , e ) 45
Rationale: "we have 4 / 6 = 20 / x 4 x = 20 * 6 x = 30 consequent = 30 answer is c"
Answer: c
Python program:
a = 20 / 2
b = 20 + a
Problem: the area of a rectangular plot is 20 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 20 × b ∴ l = 20 m and l – b = 10 ∴ b = 20 – 10 = 10 m answer a"
Answer: a
Python program:
a = 20 - 10
Problem: 78654 * 9999
Options: a ) 784598562 , b ) 765858254 , c ) 784569825 , d ) 786461346 , e ) none of these
Rationale: "explanation : 78654 * ( 10000 - 1 ) = 786540000 - 78654 = 786461346 option d"
Answer: d
Python program:
a = 78654 / 9999
b = a * 100
Problem: the weight of a glass of jar is 40 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 2 / 3
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 40 g weight of coffee beans = 60 g weight of jar and remaining beans = 60 g weight of remaining beans = 20 g fraction remaining = 20 / 60 = 1 / 3 answer is b ."
Answer: b
Python program:
a = 60 - 40
b = 100 - 40
c = a / b
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 75,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 60000 , c ) 50000 , d ) 70000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 175000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 175000 - x ) = x / 3 + x / 2 = 87500 = 5 x / 6 = 87500 = x = 87500 x 6 / 5 = 105000 savings in public provident fund = rs . ( 175000 - 105000 ) = rs . 70000 answer is d ."
Answer: d
Python program:
a = 100 * 10
b = a * 100
c = 100 * 10
d = c * 100
e = 2 * 100
f = e * 100
g = d - f
h = b + g 
i = 3 / 2
j = i + 1 
k = 1 / j
l = h * k
Problem: how many positive integers less than 120 are there such that they are multiples of 13 or multiples of 12 but not both ?
Options: a ) 13 , b ) 19 , c ) 15 , d ) 16 , e ) 17
Rationale: "for 13 : 13 . . . 117 = 13 * 9 = 117 for 12 : 12 . . . 120 = 12 * 10 = 120 but there is one integer 13 * 12 . so n = ( 9 ) + ( 10 ) = 19 b"
Answer: b
Python program:
a = 4 + 13 
b = a - 1
c = math.factorial(b)
d = math.factorial(13)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 9 € ( 4 € 5 ) =
Options: a ) 80 , b ) 720 , c ) 760 , d ) 840 , e ) 860
Rationale: "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 9 € 40 = 2 * 9 * 40 = 720 hence , answer is b"
Answer: b
Python program:
a = 2 * 9
b = 2 * 4
c = b * 5
d = a * c
Problem: jack and jill are marathon runners . jack can finish a marathon ( 43 km ) in 4.5 hours and jill can run a marathon in 4.3 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 43 / 45 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 43 / ( 9 / 2 ) = 86 / 9 average speed of jill = 43 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 86 / 9 ) / 10 = 86 / 90 = 43 / 45 answer b"
Answer: b
Python program:
a = 43 / 4
b = 43 / 4
c = a / b
Problem: two pipes a and b can fill a tank in 6 and 12 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "part filled by a in 1 min . = 1 / 6 part filled by b in 1 min . = 1 / 12 part filled by ( a + b ) in 1 min . = 1 / 6 + 1 / 12 = 1 / 4 . both the pipes can fill the tank in 4 minutes . answer : a"
Answer: a
Python program:
a = 6 * 100
b = 1 / 6
c = 1 / 12
d = b + c 
e = d * 2
f = 1 - e
g = f * 6
h = g * const_60
i = a + h
Problem: a car traveled 420 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 24 , e ) 27
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 420 miles will be covered in 420 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 420 / h = > 336 / c = 420 / ( c + 6 ) = > 336 c + 336 * 6 = 420 c = > c = 336 * 6 / 84 = 24 answer d ."
Answer: d
Python program:
a = 420 - 336
b = a / 6
c = 336 / b
Problem: 65 bags of nuts are to be divided among 13 students . each bag contains 15 nuts . how many nuts will each student receive ?
Options: a ) 75 , b ) 65 , c ) 43 , d ) 52 , e ) 78
Rationale: 65 ÷ 13 = 5 bags per student 5 x 15 = 75 nuts per student correct answer a
Answer: a
Python program:
a = 65 / 13
b = a * 15
Problem: if x = 1 - 4 t and y = 2 t - 2 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 / 5 , e ) 0
Rationale: we are given x = 1 – 4 t and y = 2 t – 2 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 4 t for x and 2 t – 2 for y in the equation x = y . this gives us : 1 – 4 t = 2 t – 2 3 = 6 t 1 / 2 = t the answer is b .
Answer: b
Python program:
a = 1 + 2 
b = 2 + 4 
c = a / b
Problem: the sum of two numbers is 528 and their h . c . f is 33 . the number of pairs of numbers satisfying the above conditions is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 6 , e ) 1
Rationale: "let the required numbers be 33 a and 33 b . then , 33 a + 33 b = 528 = > a + b = 16 . now , co - primes with sum 16 are ( 1 , 15 ) , ( 3 , 13 ) , ( 5 , 11 ) and ( 7 , 9 ) . required numbers are ( 33 * 1 , 33 * 15 ) , ( 33 * 3 , 33 * 13 ) , ( 33 * 5 , 33 * 11 ) , ( 33 * 7 , 33 * 9 ) . the number of such pairs is 4 . answer : a"
Answer: a
Python program:
a = 528 + 33 
b = 1 + 1 
c = a / b
d = 528 + 33 
e = 1 + 1 
f = d / e
g = f - 33
h = c * g
Problem: what is the last digit in ( 7 ^ 95 - 3 ^ 58 ) ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 9 , e ) 5.5
Rationale: explanation : unit digit in 795 = unit digit in [ ( 74 ) 23 x 73 ] = unit digit in [ ( unit digit in ( 2401 ) ) 23 x ( 343 ) ] = unit digit in ( 123 x 343 ) = unit digit in ( 343 ) = 3 unit digit in 358 = unit digit in [ ( 34 ) 14 x 32 ] = unit digit in [ unit digit in ( 81 ) 14 x 32 ] = unit digit in [ ( 1 ) 14 x 32 ] = unit digit in ( 1 x 9 ) = unit digit in ( 9 ) = 9 unit digit in ( 795 - 358 ) = unit digit in ( 343 - 9 ) = unit digit in ( 334 ) = 4 . so , answer c
Answer: c
Python program:
a = 4 * 4
b = a / 2
c = b / 2
Problem: how many cuboids of length 5 m , width 4 m and height 3 m can be farmed from a cuboid of 16 m length , 10 m width and 12 m height .
Options: a ) 32 , b ) 28 , c ) 36 , d ) 40 , e ) 50
Rationale: ( 16 ã — 10 ã — 12 ) / ( 5 ã — 4 ã — 3 ) = 32 answer is a .
Answer: a
Python program:
a = 16 * 10
b = a * 12
c = 5 * 4
d = c * 3
e = b / d
Problem: one night 10 percent of the female officers on a police force were on duty . if 200 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 200 number of female officers on duty on that night = 200 / 2 = 100 ( 10 / 100 ) * f = 100 = > f = 1000 answer e"
Answer: e
Python program:
a = 200 / 2
b = 10 / 100
c = a / b
Problem: a furniture dealer purchased a desk for $ 140 and then set the selling price equal to the purchase price plus a markup that was 30 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 80 , d ) $ 90 , e ) $ 100
Rationale: "purchase price = 140 selling price = x 140 + 0.3 * x = x 0.7 * x = 140 x = 200 profit = 200 - 140 = 60 answer : b"
Answer: b
Python program:
a = 30 / 100
b = 1 - a
c = 140 / b
d = c - 140
e = d * 100
f = e / 140
Problem: find 96 × × 97
Options: a ) 91 / 198 , b ) 91 / 12 , c ) 91 / 13 , d ) 91 / 10 , e ) 91 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 4 and - 3 compared with 100 . so answer : b"
Answer: b
Python program:
a = 96 / 97
Problem: of 3 numbers , the third is twice the first and the second is 4 times the first . if their average is 77 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 25 , c ) 20 , d ) 32 , e ) 33
Rationale: explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 2 x . so , x + 4 x + 2 x = 77 × 3 = 231 7 x = 231 x = 231 / 7 hence , smallest number x = 33 answer : e
Answer: e
Python program:
a = 77 * 3
b = 1 + 2 
c = b + 4 
d = a / c
Problem: the slant height of a cone is 21 cm and radius of the base is 10 cm , find the curved surface of the cone .
Options: a ) 330 , b ) 770 , c ) 660 , d ) 100 , e ) 600
Rationale: "π * 21 * 10 = 660 answer : c"
Answer: c
Python program:
a = math.pi * 10
b = a * 21
Problem: a store reported total sales of $ 400 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 25 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 400 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 400 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 400 – 320 ) / 320 ] x 100 = 25 % . the answer is c ."
Answer: c
Python program:
a = 400 - 320
b = a / 320
c = b * 100
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 20 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 3 : 5 , b ) 9 : 25 , c ) 5 : 2 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 10 / speed b since the times are same , 50 pi / speed a = 20 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 2 correct option : c"
Answer: c
Python program:
a = 50 / 2
b = circumface / (
Problem: in a company , 56 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 45 % , b ) 50 % , c ) 55 % , d ) 60 % , e ) 65 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 44 % of all employees are women , so non - union women are 44 % - 18 % = 26 % 40 % of all employees are non - union . the percent of non - union employees who are women is 26 % / 40 % = 65 % the answer is e ."
Answer: e
Python program:
a = 100 - 56
b = 70 / 100
c = 60 * b
d = 60 - c
e = a - d
f = 100 - 60
g = e / f
h = 100 * g
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 15 and the other one , that is cheaper , costs $ 10 . the factory holds a $ 140 worth stock of 13 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 11 , e ) 35
Rationale: "so the number of $ 10 modules must be 11 so that the leftover 2 modules are of $ 15 which will give a total value $ 140 . 11 * 10 + 2 * 15 = 110 + 30 = 140 answer : d"
Answer: d
Python program:
a = 140 - 15
b = a / 10
Problem: in a two digit number it is known that its unit ' s digit exceeds its 10 ' s digit by 4 and that the product of the given number and the sum of its digits is equal to 208 , what is the number ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: xy is 2 digit no . y - x = 4 ; ( 10 x + y ) * ( 2 x + 4 ) = 208 ; sub y = x + 4 ; we get 26 answer : c
Answer: c
Python program:
a = 10 + 1 
b = a * 4
c = 4 * 2
d = b + c 
e = d ** 2
f = 10 + 1 
g = f * 2
h = 4 * g
i = 4 * 4
j = 208 - i
k = h * j
l = e + k 
m = math.sqrt(l)
n = 10 + 1 
o = n * 4
p = 4 * 2
q = o + p 
r = m - q
s = 10 + 1 
t = s * 4
u = r / t
v = u + 4 
w = 10 + 1 
x = w * 4
y = 4 * 2
z = x + y 
A = z ** 2
B = 10 + 1 
C = B * 2
D = 4 * C
E = 4 * 4
F = 208 - E
G = D * F
H = A + G 
I = math.sqrt(H)
J = 10 + 1 
K = J * 4
L = 4 * 2
M = K + L 
N = I - M
O = 10 + 1 
P = O * 4
Q = N / P
R = Q * 10
S = v + R
Problem: if a fills a tank in 30 mins , and b fills the same tank in 20 mins , and c emptys it in 40 min , if a , b , c works together how much time will the tank take to fill ?
Options: a ) 15.14 mins , b ) 16.14 mins , c ) 17.14 mins , d ) 18.14 mins , e ) 19.14 mins
Rationale: 1 / 30 + 1 / 20 - 1 / 40 = 7 / 120 so total time = 120 / 7 = 17.14 mins answer : c
Answer: c
Python program:
a = 1 / 30
b = 1 / 20
c = a + b 
d = 1 / 40
e = c - d
f = 1 / e
Problem: an article is bought for rs . 560 and sold for rs . 340 , find the loss percent ?
Options: a ) 36 % , b ) 38 % , c ) 16 % , d ) 39 % , e ) 12 %
Rationale: 560 - - - - 220 100 - - - - ? = > 39 % answer : d
Answer: d
Python program:
a = 340 * 100
b = a / 560
c = 100 - b
Problem: jennifer had $ 180 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 4 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 24
Rationale: 1 / 5 x $ 180 = $ 36 for sandwich 1 / 6 x $ 180 = $ 30 for museum 1 / 2 x $ 180 = $ 90 for book $ 36 + $ 30 + $ 90 = $ 156 spent $ 180 - $ 156 = $ 24 left over correct answer e
Answer: e
Python program:
a = 1 / 5
b = 180 * a
c = 1 / 6
d = 180 * c
e = b + d 
f = 1 / 2
g = 180 * f
h = e + g 
i = 180 - h
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 12 miles per gallon , and from town b to town c , the car averaged 16 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 13.5 , c ) 14.4 , d ) 14.5 , e ) 15
Rationale: "ans is c given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 12 ) + ( x / 16 ) ) = 14.4 ( formula avg speed = total distance / total time )"
Answer: c
Python program:
a = 16 * 10
b = 16 * 10
c = b / 2
d = a + c 
e = 16 * 10
f = e / 12
g = 16 * 10
h = g / 2
i = h / 16
j = f + i 
k = d / j
Problem: the greater of two numbers is twice the less , and the sum of the numbers is 96 . what are the numbers ?
Options: a ) 64 , b ) 68 , c ) 70 , d ) 79 , e ) 80
Rationale: let x = the less number 2 x = the greater number the sum of the numbers is 96 x + 2 x = 96 3 x = 96 x = 32 2 x = 64 option a
Answer: a
Python program:
a = 2 + 1 
b = 96 / a
c = 2 * b
Problem: pipe p can fill a tank in 3 hours , pipe q in 9 hours and pipe r in 24 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 2.1 hours , c ) 3 hours , d ) 3.5 hours , e ) 4.5 hours
Rationale: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 3 + 1 / 9 + 1 / 24 ) = 35 / 72 all the three pipes together will fill the tank = 72 / 35 = 2.1 hours answer b"
Answer: b
Python program:
a = 1 / 24
b = 1 / 3
c = 1 / 9
d = b + c 
e = a + d 
f = 1/(e)
Problem: a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 8 km in stationary water ?
Options: a ) 2 hours , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 8 / 4 = 2 hrs answer : a"
Answer: a
Python program:
a = 1 / 10
b = a * const_60
c = 2 / 2
d = b + c 
e = d / 2
f = 8 / e
Problem: one woman and one man can build a wall together in five hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them nine hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 55 / 7 , b ) 1 , c ) 135 / 32 , d ) 222 / 37 , e ) 252 / 58
Rationale: solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 5 - - > ( 1 ) , w + 2 g = 1 / 5 - - > ( 2 ) and m + g = 1 / 9 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 27 , m = 2 / 27 and w = 17 / 135 . so , n = 1 / ( 32 / 135 ) = 135 / 32 option , c
Answer: c
Python program:
a = 4 + 1 
b = a + 4 
c = 1/(b)
d = 4 + 1 
e = 1/(d)
f = e * 2
g = c + f 
h = g / 2
i = 4 + 1 
j = 1/(i)
k = h - j
l = 3 / 2
m = k / l
n = 4 + 1 
o = 1/(n)
p = m + o 
q = 1/(p)