euclaise/mathqa_programs huggingface dataset:
Problem: it takes avery 3 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "avery takes 3 hours tom takes 2 hours efficiency of avery is 1 / 3 units / hr efficiency of tom is 1 / 5 units / hr combined efficiency of tom and avery is 1 / 3 + 1 / 5 = 8 / 15 units / hr since they worked for 1 hour they completed 8 / 15 units of work and 7 / 15 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 7 / 15 / 1 / 5 hours = > 7 / 3 * 60 = 140 minutes . . . answer will be ( e )"
Answer: e
Python program:
a = 1 / 3
b = 1 / 5
c = a + b 
d = 1 - c
e = 1 / 5
f = d / e
g = f * const_60
Problem: a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 65 meters , what is the height of the building ( in meters ) ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 65 x = 26 the answer is c ."
Answer: c
Python program:
a = 18 / 45
b = 65 * a
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 75 respectively . the sum is :
Options: a ) 1360 , b ) 637.5 , c ) 1600 , d ) 1800 , e ) none
Rationale: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 75 / ( 85 - 75 ) = rs . 637.5 . answer b"
Answer: b
Python program:
a = 85 * 75
b = 85 - 75
c = a / b
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,700 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,700 , e ) 48,500
Rationale: median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.7 so , answer is d .
Answer: d
Python program:
a = 100 * 100
b = a * 4
Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many w ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: "5 choices for each of the 4 questions , thus total w of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."
Answer: c
Python program:
a = 5 ** 4
Problem: if 36 men can do a piece of work in 25 hours , in how many hours will 12 men do it ?
Options: a ) 22 , b ) 38 , c ) 60 , d ) 88 , e ) 75
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 12 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 12 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 12 } = 75 hence , 12 men can do it in 75 hours . answer : e ) 75"
Answer: e
Python program:
a = 36 * 25
b = a / 12
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 6 . the factory holds a $ 80 worth stock of 12 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 20 , b ) 25 , c ) 10 , d ) 30 , e ) 35
Rationale: "so the number of $ 6 modules must be 10 so that the leftover 2 modules are of $ 10 which will give a total value $ 80 . 10 * 6 + 2 * 10 = 60 + 20 = 80 answer : c"
Answer: c
Python program:
a = 80 - 10
b = a / 6
Problem: what is the value of ( 5 ) ^ - 5 ?
Options: a ) 1 / 3125 , b ) 1 / 3000 , c ) 1 / 658 , d ) 1 / 500 , e ) 1 / 75
Rationale: "5 ^ - 5 = 1 / ( 5 ) ^ 5 = 1 / 3125 answer : a"
Answer: a
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 5
d = c / 100
Problem: rahim bought 40 books for rs . 600 from one shop and 20 books for rs . 240 from another . what is the average price he paid per book ?
Options: a ) s . 14 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 10
Rationale: "average price per book = ( 600 + 240 ) / ( 40 + 20 ) = 840 / 60 = rs . 14 answer : a"
Answer: a
Python program:
a = 600 + 240 
b = 40 + 20 
c = a / b
Problem: the salary of a , b , c , d , e is rs . 9000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8200 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 9000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8200 correct option : b"
Answer: b
Python program:
a = 9000 + 5000 
b = a + 11000 
c = b + 7000 
d = c + 9000 
e = 4 + 1 
f = d / e
Problem: at a local appliance manufacturing facility , the workers received a 40 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 28 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 40 hours and earns 100 per hour . 10 * 100 = 1000 10 * 140 = 1400 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 140 = 7.14 so he can reduce his work by 2.86 hours . which is > 28 % . answer b"
Answer: b
Python program:
a = 40 - 1
Problem: a grocer has a sale of rs . 7435 , rs . 7920 , rs . 7855 , rs . 8230 and rs . 7560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?
Options: a ) 500 , b ) 2000 , c ) 5000 , d ) 6000 , e ) 7000
Rationale: "total sale for 5 months = rs . ( 7435 + 7920 + 7855 + 8230 + 7560 ) = rs . 39000 . required sale = rs . [ ( 7500 x 6 ) - 39000 ] = rs . ( 45000 - 39000 ) = rs . 6000 answer : option d"
Answer: d
Python program:
a = 5 + 1 
b = a * 7500
c = 7435 + 7920 
d = c + 7855 
e = d + 8230 
f = e + 7560 
g = b - f
Problem: david obtained 96 , 95 , 82 , 97 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 95 , c ) 93 , d ) 165 , e ) 11
Rationale: "explanation : average = ( 96 + 95 + 82 + 97 + 95 ) / 5 = 465 / 5 = 93 . answer : c"
Answer: c
Python program:
a = 96 + 95 
b = a + 82 
c = b + 97 
d = c + 95 
e = 2 + 3 
f = d / e
Problem: if x = 5 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.2 , c ) 0.01 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de 6 + 4 = 10 by inversing and squaring 0.01 answer : c"
Answer: c
Python program:
a = 2 / 2
b = a / 1000
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8100 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4500 , d ) 2981 , e ) 6100
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8100 = 32400 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 400 salary of may is rs . 6500 salary of january = rs . 6100 . answer : e"
Answer: e
Python program:
a = 8000 * 4
b = 8100 * 4
c = b - 6500
d = a - c
Problem: a invested some money in 10 % stock at 96 . if b wants to invest in an equally good 12 % stock , he must purchase a stock worth of :
Options: a ) rs . 80 , b ) rs . 115.20 , c ) rs . 120 , d ) rs . 125.40 , e ) none of these
Rationale: explanation : for an income of rs . 10 , investment = rs . 96 . for an income of rs . 12 , investment = ( 96 / 10 x 12 ) = 115.20 answer : b
Answer: b
Python program:
a = 96 / 10
b = a * 12
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 7 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 7 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "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 ( 7 * 3 * 1 ) / 3 = 21 / 3 = 7 c"
Answer: c
Python program:
a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l 
n = m / 7
Problem: a watch was sold at a loss of 8 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 1000 , b ) 2876 , c ) 1977 , d ) 1167 , e ) 2711
Rationale: "92 % 104 % - - - - - - - - 12 % - - - - 140 100 % - - - - ? = > rs . 1167 answer : d"
Answer: d
Python program:
a = 140 * 100
b = 100 + 4 
c = 100 - 8
d = b - c
e = a / d
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 4400 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 4400 x ( 2 / 11 ) ) = rs . 800 . answer is b
Answer: b
Python program:
a = 2 * 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 3 
f = 2 / e
g = 4400 * f
Problem: j is 25 % less than p and 20 % less than t . t is e % less than p . what is the value of e ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( e / 100 ) ] * p i . e . 100 - e = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . e = 6.25 answer : option d"
Answer: d
Python program:
a = 25 * 25
b = a / 100
Problem: walking at 5 / 6 th of its usual speed a cab is 12 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 32 m , d ) 50 m , e ) 60 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 12 m ut / 5 = 12 m ut = 60 m answer is e"
Answer: e
Python program:
a = 5 * 12
Problem: 6 points lie on the circumference of a ellipse . what is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 15 , e ) 20
Rationale: number of triangles can be formed out of 6 points = 6 c 3 = 20 number of quadrilaterals can be formed out of 6 points = 6 c 4 = 15 20 - 15 = 5 . answer = c
Answer: c
Python program:
a = math.factorial(6)
b = math.factorial(3)
c = math.factorial(3)
d = b * c
e = a / d
f = math.factorial(6)
g = math.factorial(4)
h = math.factorial(2)
i = g * h
j = f / i
k = e - j
Problem: the denominator of a fraction is 1 less than twice the numerator . if the numerator and denominator are both increased by 1 , the fraction becomes 3 / 5 . find the fraction ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 9 , e ) none of these
Rationale: let the numerator and denominator of the fraction be ' n ' and ' d ' respectively . d = 2 n - 1 ( n + 1 ) / ( d + 1 ) = 3 / 5 5 n + 5 = 3 d + 3 5 n + 5 = 3 ( 2 n - 1 ) + 3 = > n = 5 d = 2 n - 1 = > d = 9 hence the fraction is : 5 / 9 answer : d
Answer: d
Python program:
a = 3 * 2
b = a - 1
c = 5 * 2
d = c - 1
e = b / d
Problem: set s consists of integers { 13 , 57 } . if two numbers are chosen from set s at random , what is the probability that the product of 2 numbers is more than 15 ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) 2 / 3
Rationale: number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers product is more than 15 = ( 3,7 ) , ( 5,7 ) = 2 probability = 2 / 6 = 1 / 3 answer is b
Answer: b
Python program:
a = math.factorial(4)
b = a / 2
c = b / 2
d = 2 / c
Problem: a dealer offers a cash discount of 20 % and still makes a profit of 20 % when he further allows 10 articles to be sold at the cost price of 9 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 50 % , b ) 55 % , c ) 60 % , d ) 66 + ( 2 / 3 ) % , e ) 80 %
Rationale: "given cash discount - 20 % profit - 20 % items sold - 10 price sold at = list price of 9 assume list price = $ 10 total invoice = $ 90 - 20 % cash discount = $ 72 let cost price of 10 items be x so total cost = 10 * x given the shopkeeper had a profit of 20 % 10 * x * 120 / 100 = 72 or x = $ 6 which means his products were listed at $ 10 which is a 66 + ( 2 / 3 ) % markup over $ 6 answer d"
Answer: d
Python program:
a = 100 + 20 
b = a / 100
c = 10 - 9
d = c / 10
e = 1 - d
f = b / e
g = 100 - 20
h = g / 100
i = f / h
j = i - 1
k = j * 100
Problem: in a certain warehouse , 40 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 48 , d ) 102 , e ) 144
Rationale: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 40 % of the packages weigh less than 75 pounds so , 40 % oft = number of packages that weigh less than 75 pounds 40 % of 240 = 96 , so 96 packages weigh less than 75 pounds of those 96 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 96 - 48 = 48 = c"
Answer: c
Python program:
a = 100 - 80
b = 48 / a
c = b * 100
d = c * 40
e = d / 100
f = e - 48
Problem: if 0.5 % of a = 95 paise , then the value of a is ?
Options: a ) rs . 190 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 95 / 100 ∴ a = rs . ( 95 / 0.5 ) = rs . 190 correct option : a"
Answer: a
Python program:
a = 95 / 0
Problem: a company produces 60000 bottles of water everyday . if a case can hold 5 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 12000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 5 number of cases required to hold 60000 bottles = 60000 / 5 = 12000 cases . so the answer is a = 12000"
Answer: a
Python program:
a = 60000 / 5
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost e is what percent of the original cost ?
Options: a ) e = 200 , b ) e = 600 , c ) e = 800 , d ) e = 1600 , e ) 50
Rationale: "original cost e , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Python program:
a = 2 ** 4
b = a * 100
Problem: if 1 / 12 of the passengers on a ship are from north america , 1 / 4 are europeans , 1 / 9 are from africa , 1 / 6 are from asia and the remaining 42 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 96 , b ) 100 , c ) 104 , d ) 108 , e ) 112
Rationale: "1 / 12 + 1 / 4 + 1 / 9 + 1 / 6 = ( 3 + 9 + 4 + 6 ) / 36 = 11 / 18 let x be the number of passengers on the ship . 42 = ( 7 / 18 ) x x = 108 the answer is d ."
Answer: d
Python program:
a = 1 / 12
b = 1 / 4
c = a + b 
d = 1 / 9
e = c + d 
f = 1 / 6
g = e + f 
h = 1 - g
i = 42 / h
Problem: by selling an article at rs . 500 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 600 , b ) s . 480 , c ) s . 300 , d ) s . 450 , e ) s . 550
Rationale: "sp = 500 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 500 * [ 100 / 125 ] = 400 loss = 25 % = 25 % of 400 = rs . 100 sp = cp - loss = 400 - 100 = rs . 300 answer : c"
Answer: c
Python program:
a = 500 * 100
b = 25 + 100 
c = a / b
d = 500 * 100
e = 25 + 100 
f = d / e
g = f * 25
h = g / 100
i = c - h
Problem: a can do a work in 7 days b in 12 days and c in 5 days . if they work on it together then in how many days required to complete the work ?
Options: a ) 420 / 177 , b ) 420 / 179 , c ) 410 / 87 , d ) 90 / 14 , e ) 77 / 56
Rationale: "person ( a ) ( b ) ( c ) ( a + b + c ) time - ( 7 ) ( 12 ) ( 5 ) rate - ( 60 ) ( 35 ) ( 84 ) ( 179 ) work - ( 420 ) ( 420 ) ( 420 ) ( 420 ) therefore a + b + c requires ( 420 / 179 ) days to complete entire work = 420 / 179 answer is b"
Answer: b
Python program:
a = 7 * 12
b = a * 5
c = 7 + 12 
d = c + 5 
e = d * 7
f = b / e
Problem: find a sum for 1 st 5 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 ) = 28 note : 1 is not a prime number option b"
Answer: b
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b 
d = 2 + 3 
e = d + 2 
f = c + e 
g = 5 + 2 
h = f + g 
i = 5 + 2 
j = i + 2 
k = h + j 
l = 5 + 2 
m = l + 2 
n = m + 4 
o = k + n 
p = 5 + 2 
q = p + 2 
r = q + 4 
s = r + 2 
t = o + s 
u = 5 + 2 
v = u + 2 
w = v + 4 
x = w + 2 
y = x + 4 
z = t + y
Problem: a hiker walking at a constant rate of 5 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 25 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 25 = 25 / 12 km . the time it takes the hiker to complete this distance is ( 25 / 12 ) / 5 = 5 / 12 hours = 25 minutes the cyclist needs to wait 25 - 5 = 20 minutes the answer is c ."
Answer: c
Python program:
a = 5 / const_60
b = 25 * a
c = 5 / const_60
d = 5 * c
e = b - d
f = e / 5
g = f * const_60
Problem: each employee of company x is a member of precisely 1 of 3 shifts of employees . among the 60 members of the first shift , 20 percent participate in the pension program ; among the 50 members of the second shift , 40 percent participate in the pension program ; and among the 40 members of the third shift , 10 percent participate in the pension program . what percent of the workers at company x participate in the pension program ?
Options: a ) 20 % , b ) 24 % , c ) 36 % , d ) 37.5 % , e ) 70 %
Rationale: 60 members & 20 percent = 12 50 members & 40 percent = 20 40 members & 10 percent = 4 = > 36 / 150 ∗ 100 = 24 % answer b
Answer: b
Python program:
a = 20 / 100
b = a * 60
c = 40 / 100
d = c * 50
e = b + d 
f = 10 / 100
g = f * 40
h = e + g 
i = 60 + 50 
j = i + 40 
k = h / j
l = k * 100
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 60 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 51
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.4 = $ 14 - - > x = $ 35 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 35 + 21 = $ 51 . answer : e ."
Answer: e
Python program:
a = 40 / 100
b = 35 * a
c = b + 35
Problem: the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 5 : 4 . if the oil bill for february had been $ 30 more , the corresponding ratio would have been 3 : 2 . how much was the oil bill for january ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 100 , d ) $ 120 , e ) $ 140
Rationale: "5 : 4 = 15 : 12 and 3 : 2 = 18 : 12 . an increase in $ 30 increases the ratio by 3 : 12 . therefore an increase in $ 10 increases the ratio by 1 : 12 . therefore , january ' s bill was 12 ( $ 10 ) = $ 120 . the answer is d ."
Answer: d
Python program:
a = 3 / 2
b = 5 / 4
c = a - b
d = 30 / c
Problem: a driver goes on a trip of 50 kilometers , the first 25 kilometers at 66 kilometers per hour and the remaining distance at 33 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 38 , b ) 40 , c ) 44 , d ) 45 , e ) 48
Rationale: the time for the first part of the trip was 25 / 66 hours . the time for the second part of the trip was 25 / 33 hours . the total time fro the trip was 25 / 66 + 25 / 33 = 75 / 66 = 25 / 22 hours . the average speed for the trip was 50 / ( 25 / 22 ) = 44 kph the answer is c .
Answer: c
Python program:
a = 25 / 66
b = 50 - 25
c = b / 33
d = a + c 
e = 50 / d
Problem: a hollow spherical metallic ball has an external diameter 6 cm and is 1 / 2 cm thick . the volume of metal used in the metal is :
Options: a ) 47 1 / 5 cm 3
b ) 47 3 / 5 cm 3
c ) 47 7 / 5 cm 3
d ) 47 9 / 5 cm 3
e ) none of these
Rationale: explanation : please note we are talking about ` ` hollow ' ' ball . do not ignore this word in this type of question in a hurry to solve this question . if we are given with external radius and thickness , we can get the internal radius by subtracting them . then the volume of metal can be obtained by its formula as , external radius = 3 cm , internal radius = ( 3 - 0.5 ) cm = 2.5 cm volume of sphere = 4 / 3 π r 3 = 4 / 3 ∗ 22 / 7 ∗ [ 3 ( 2 ) − 2.52 ] cm 3 = 4 / 3 ∗ 22 / 7 ∗ 91 / 8 cm 3 = 143 / 3 cm 3 = 47 2 / 3 cm 3 option b
Answer: b
Python program:
a = 6 / 2
b = volume_sphere - (
Problem: if a book is sold at 6 % profit instead of 6 % loss , it would have brought rs 15 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 60 , d ) 70 , e ) 125
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.06 x - 0.94 x = 15 = > 0.12 x = 15 = 15 / 0.12 = rs 125 answer : e"
Answer: e
Python program:
a = 6 / 2
b = 100 * a
c = b / 6
Problem: at what rate percent per annum will a sum of money double in 10 years ?
Options: a ) 10 % , b ) 15 % , c ) 18 % , d ) 20 % , e ) 25 %
Rationale: "let principle = p s . i . = p t = 10 yrs rate = 100 * p / p * 10 = 10 % answer is a"
Answer: a
Python program:
a = 100 / 10
Problem: the average of 9 observations was 5 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 45 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 5 = 45 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 45 = 45 option a"
Answer: a
Python program:
a = 10 * 5
b = 5 * 5
c = a + b 
d = 5 * 9
e = c - d
Problem: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 600 shares of the company ' s stock ?
Options: a ) $ 92 , b ) $ 312 , c ) $ 104 , d ) $ 120 , e ) $ 240
Rationale: eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 600 - - > $ 312 answer is b
Answer: b
Python program:
a = 0 / 8
b = 1 - 1
c = b * 10
d = c * 0
e = a + d 
f = e * 600