euclaise/mathqa_programs huggingface dataset:
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 3 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 216 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 3 ) or $ 216 . the best answer is therefore a . answer : a ."
Answer: a
Python program:
a = 2 / 3
b = 36 * a
c = 1 / 3
d = b / c
e = 2 * d
Problem: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 9 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 23 years , b ) 24 years , c ) 25 years , d ) 26 years , e ) 27 years
Rationale: "explanation let the average age of the whole team by x years . 11 x â € “ ( 26 + 38 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 52 2 x = 52 x = 26 . so , average age of the team is 26 years . answer d"
Answer: d
Python program:
a = 26 + 9 
b = 26 + a 
c = 9 * 9
d = b - c
e = d / 2
Problem: if ( 2 ^ 12 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 12 , b ) 8 , c ) 15 , d ) 16 , e ) 23
Rationale: "given 2 ^ 12 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 12 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans a on comparing the power of 2 = > m = 12"
Answer: a
Python program:
a = 10 / 5
b = a ** 4
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 125 resolutions ?
Options: a ) 794 m , b ) 704 m , c ) 454 m , d ) 186 m , e ) 176 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 125 resolutions . = 125 * 2 * 22 / 7 * 22.4 = 17600 cm = 176 m answer : e"
Answer: e
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 125
i = h / 100
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 160 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: "l + k = 160 and so k = 160 - l l + 10 = 1.5 k = 1.5 ( 160 - l ) 2.5 l = 230 l = 92 the answer is c ."
Answer: c
Python program:
a = 100 + 50 
b = a / 100
c = 160 * b
d = c - 10
e = 100 + 50 
f = e / 100
g = f + 1 
h = d / g
Problem: if 40 % of a certain number is 160 , then what is 60 % of that number ?
Options: a ) 270 , b ) 380 , c ) 260 , d ) 360 , e ) 240
Rationale: "explanation : 40 % = 40 * 4 = 160 60 % = 60 * 4 = 240 answer : option e"
Answer: e
Python program:
a = 40 / 100
b = 160 / a
c = 60 / 100
d = b * c
Problem: if 22 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 88 , d ) 80 , e ) 75
Rationale: "let x be the number of students in the school . 0.22 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.22 x / 0.25 = 0.88 x students went to the camping which is 88 % . the answer is c"
Answer: c
Python program:
a = 100 - 75
b = a / 100
c = 22 / b
Problem: if a : b : c = 3 : 4 : 7 , then the ratio ( a + b + c ) : c is equal to
Options: a ) 2 : 1 , b ) 14 : 3 , c ) 7 : 2 , d ) 1 : 2 , e ) none
Rationale: solution : ( a + b + c ) = 3 + 4 + 7 = 14 and c = 7 then , ( a + b + c ) : c = 2 : 1 . answer : option a
Answer: a
Python program:
a = 3 + 4 
b = a + 7 
c = b / 7
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.05 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: 1 st day fine - 0.05 2 nd day fine - 0.05 * 2 = 0.1 ( as doubling gives lower value ) 3 rd day fine - 0.1 * 2 = 0.2 ( as doubling gives lower value ) 4 th day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value we add 0.3 this time ) 5 th day fine - 0.4 + 0.3 = 0.7 ( as doubling gives higher value we add 0.3 this time ) answer : b .
Answer: b
Python program:
a = 0 * 5
b = a * 2
c = b * 2
d = c + 0
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 1000 , d ) $ 920 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d"
Answer: d
Python program:
a = 3 / 4
b = 1 - a
c = 230 / b
Problem: 45 x ? = 10 % of 900
Options: a ) 2 , b ) 4 , c ) 5 , d ) 500 , e ) none
Rationale: answer let 45 x a = ( 10 x 900 ) / 100 ∴ a = ( 10 x 9 ) / 45 = 2 correct option : a
Answer: a
Python program:
a = 10 / 100
b = a * 900
c = b / 45
Problem: a circle graph shows how the budget of a certain company was spent : 20 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?
Options: a ) 90 °
b ) 135 °
c ) 216 °
d ) 240 °
e ) 270 °
Rationale: the percent of the budget for salaries is 100 - ( 20 + 9 + 5 + 4 + 2 ) = 60 % 100 % of the circle is 360 degrees . then ( 60 % / 100 % ) * 360 = 216 degrees the answer is c .
Answer: c
Python program:
a = 20 + 9 
b = a + 5 
c = b + 4 
d = c + 2 
e = d * 360
f = e / 100
g = 360 - f
Problem: sales price is $ 44 , gross profit is 120 % of cost , what is the value of gross profit ?
Options: a ) 24 , b ) 33 , c ) 39 , d ) 40 , e ) 42
Rationale: cost + profit = sales cost + ( 120 / 100 ) cost = 44 cost = 20 profit = 44 - 20 = 24 answer ( a )
Answer: a
Python program:
a = 120 / 100
b = 1 + a 
c = 44 / b
d = 44 - c
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.67 %
Rationale: "x - wt of mix x added y - wt of mix y added 0.4 x + 0.25 y = 0.3 ( x + y ) 0.1 x = 0.05 y x / y = 5 / 10 = 1 / 2 y / x = 2 ( y + x ) / x = 3 = > x / ( y + x ) * 100 = 100 / 3 = 33.33 % answer : b"
Answer: b
Python program:
a = 25 + 1 
b = 30 - a
c = 40 / 100
d = 25 + 1 
e = d / 100
f = c - e
g = b / f
Problem: a circular road runs around a circular garden . if the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one - third of the outer circle , then the width of the road is :
Options: a ) 4 metres , b ) 5 metres , c ) 7 metres , d ) 6 metres , e ) 8 metres
Rationale: let radius of inner circle = r 1 radius of outer circle = r 2 also r 1 = 1 / 3 * r 2 3 * r 1 = r 2 circumference of inner circle = 2 * pi * r 1 circumference of outer circle = 2 * pi * r 2 = 6 * pi * r 1 ( since r 2 = 3 * r 1 ) 2 * pi * r 1 + 6 * pi * r 1 = 88 ( as per question ) r 1 = 3.5 m r 2 = 3 * 3.5 = 10.5 m width of road = 10.5 - 3.5 = 7 m ans . answer : c
Answer: c
Python program:
a = 88 / 4
b = a / 2
c = b - 4
Problem: in a multiple choice test comprising 5 questions , each with 4 choices , what is the probability of a student getting 3 or more questions correct ? each question has only one correct answer and the student is equally likely to choose any of the 4 choices .
Options: a ) 24 / 256 , b ) 53 / 512 , c ) 105 / 512 , d ) 459 / 512 , e ) 47 / 256
Rationale: probability for choosing correct answer is 1 / 4 and incorrect answer is 3 / 4 for 3 correct answers , c ( 5,3 ) * ( 1 / 4 ) ^ 3 * ( 3 / 4 ) ^ 2 = 90 / ( 4 ^ 5 ) for 4 correct answers , c ( 5,4 ) * ( 1 / 4 ) ^ 4 * ( 3 / 4 ) ^ 1 = 15 / ( 4 ^ 5 ) for 5 correct answers , c ( 5,5 ) * ( 1 / 4 ) ^ 5 * ( 3 / 4 ) ^ 0 = 1 / ( 4 ^ 5 ) so total probability = 106 / 1024 = 53 / 512 ans b
Answer: b
Python program:
a = 5 + 4 
b = a * 10
c = 3 * 5
d = b + c 
e = d + 1 
f = 2 ** 10
g = e / f
Problem: p and q together can do a work in 6 days . if p alone can do it in 15 days . in how many days can q alone do it ?
Options: a ) 5 , b ) 4 , c ) 10 , d ) 11 , e ) 12
Rationale: 1 / 6 - 1 / 15 = = > 1 / 10 = = > 10 answer c
Answer: c
Python program:
a = 1/(6)
b = 1/(15)
c = a - b
d = c * 100
Problem: in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 12 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?
Options: a ) 15 , b ) 45 , c ) 30 , d ) 45 , e ) 60
Rationale: this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 12 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 12 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 12 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 12 ) ( 1 ) 11 x = 7 x + 12 4 x = 12 x = 3 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 3 ) = 45 final answer : b
Answer: b
Python program:
a = 11 - 7
b = 12 / a
c = 15 * b
Problem: the ratio between the sale price and the cost price of an article is 9 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 23 , b ) 1 : 2 , c ) 4 : 5 , d ) 3 : 5 , e ) 25
Rationale: "c . p . = rs . 5 x and s . p . = rs . 9 x . then , gain = rs . 4 x required ratio = 4 x : 5 x = 4 : 5 c"
Answer: c
Python program:
a = 9 - 5
b = a / 5
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 300 , find the original price per kg ?
Options: a ) s . 7.7 , b ) s . 7.4 , c ) s . 7.5 , d ) s . 7.1 , e ) s . 7.9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 300 - - - 80 ? - - - 2 = > rs . 7.5 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 300
c = b / 10
d = 20 / 100
e = d * 300
f = c / e
g = f * 100
Problem: 8 is 6 % of a , and 6 is 8 % of b . c equals b / a . what is the value of c ?
Options: a ) 3 / 8 , b ) 8 / 15 , c ) 9 / 16 , d ) 12 / 25 , e ) 16 / 27
Rationale: "6 a / 100 = 8 a = 400 / 3 8 b / 100 = 6 b = 75 c = b / a = 75 * 3 / 400 = 9 / 16 the answer is c ."
Answer: c
Python program:
a = 6 / 8
b = a * 100
c = 8 / 6
d = c * 100
e = b / d
Problem: of the 65 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 ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: neither car nor garage = total - garage - ( swim - common ) = 65 - 50 - ( 40 - 35 ) = 65 - 55 = 10 answer a
Answer: a
Python program:
a = 50 - 35
b = 40 - 35
c = a + b 
d = c + 35 
e = 65 - d
Problem: exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 36 , c ) 39 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b ."
Answer: b
Python program:
a = 8 * 12
b = a * 3
c = b / 8
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 10 , and the difference between the total number of strawberries and the total number of blueberries would increase by 50 . each blue box contains how many blueberries ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "let x be the number of blueberries in each blue box . then there are x + 10 strawberries in each red box . x + ( x + 10 ) = 50 x = 20 the answer is c ."
Answer: c
Python program:
a = 50 - 10
b = a / 2
Problem: if x / y = 3 and ( 2 a - x ) / ( 3 b - y ) = 3 , then the value of a / b is ?
Options: a ) – 3 , b ) 9 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: x = 3 y 2 a - 3 y = 3 ( 3 b - y ) 2 a - 3 y = 9 b - 3 y 2 a = 9 b a / b = 9 / 2 answer : b
Answer: b
Python program:
a = 3 * 3
b = a / 2
Problem: if z is a multiple of 9702 , what is the remainder when z ^ 2 is divided by 4 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it depends on z .
Rationale: "2 is a factor of 9702 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ."
Answer: a
Python program:
a = 9702 / 3
b = a ** 2
c = b / 4
d = 4 - 2
e = 1000 * d
f = e * 100
g = 4 - 2
h = 1000 * g
i = h * 10
j = f + i 
k = 2 * 100
l = j + k 
m = 100 - 2
n = l + m 
o = c - n
p = o * 4
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) rs . 1200 , b ) rs . 890 , c ) rs . 600 , d ) rs . 1190 , e ) rs . 450
Rationale: "explanation : s . p . = 85 % of rs . 1400 = rs . ( 85 / 100 * 1400 ) = rs . 1190 answer : d"
Answer: d
Python program:
a = 100 - 15
b = a * 1400
c = b / 100
Problem: a and b can finish a work in 12 days while a alone can do the same work in 24 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 24 days
Rationale: "b = 1 / 12 – 1 / 24 = 1 / 24 = > 24 days answer : e"
Answer: e
Python program:
a = 1/(12)
b = 1/(24)
c = a - b
d = 1/(c)
Problem: when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 2 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 5 x + 3 , for some integer x ( n + 2 ) ^ 2 = ( 5 x + 5 ) ^ 2 = 5 y , for some integer y when we divide this by 5 , the remainder is 0 . the answer is a ."
Answer: a
Python program:
a = 5 + 3 
b = a - 2
c = b ** 2
d = 5 + 3 
e = d - 2
f = e ** 2
g = f / 5
h = math.floor(g)
i = h * 5
j = c - i
Problem: if an average hard drive had a capacity of 0.3 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 3072 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536
Rationale: "0.3 * 2 ^ 10 = 0.3 * 1024 = 307.2 the answer is a ."
Answer: a
Python program:
a = 0 * 3
b = a * 2
c = b * 2
d = c * 2
e = d * 2
f = e * 2
g = f * 2
h = g * 2
i = h * 2
j = i * 2
k = j + 0 
l = k * 10
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 250 resolutions ?
Options: a ) 277 m , b ) 704 m , c ) 352 m , d ) 288 m , e ) 378 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 250 resolutions . = 250 * 2 * 22 / 7 * 22.4 = 35200 cm = 352 m answer : c"
Answer: c
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 250
i = h / 100
Problem: if grapes are 93 % water and raisins are 16 % water , then how many kilograms did a quantity of raisins , which currently weighs 8 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108
Rationale: let x be the original weight . the weight of the grape pulp was 0.07 x . since the grape pulp is 84 % of the raisins , 0.07 x = 0.84 ( 8 ) . then x = 12 * 8 = 96 kg . the answer is b .
Answer: b
Python program:
a = 100 - 16
b = a / 100
c = b * 8
d = 100 - 93
e = d / 100
f = c / e
Problem: set a consists of all the prime numbers between 10 and 25 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 23 lowest number = 11 range = highest - lowest = 23 - 11 = 12 option a"
Answer: a
Python program:
a = 25 - 2
b = 10 + 4 
c = b + 1 
d = a - c
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 370 m long platform ?
Options: a ) 19 , b ) 27 , c ) 29 , d ) 47 , e ) 49
Rationale: let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 370 ) / 36 * 5 / 18 = 49 min . answer : e
Answer: e
Python program:
a = const_0_2778 * 36
b = a * 12
c = 370 + b 
d = const_0_2778 * 36
e = c / d
Problem: a train of 25 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 2.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = 25 * 60 + 2500 = 4000 m t = 4000 / 60 * 18 / 5 = 240 sec = 4 mins answer : a"
Answer: a
Python program:
a = 25 + 1 
b = a * 60
c = b / 1000
d = c + 2
Problem: the length of a rectangle is halved , while its breadth is tripled . what is the % change in area ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 65 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Python program:
a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
Problem: there were two candidates in an election . winner candidate received 60 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 864 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 288 60 % - - - - - - - - ? = > 864 answer : b"
Answer: b
Python program:
a = 100 - 60
b = 60 - a
c = b / 100
d = 288 / c
e = d * 60
f = e / 100
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer : option c"
Answer: c
Python program:
a = 23 * 14
Problem: a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of b .
Options: a ) 225 , b ) 500 , c ) 75 , d ) 800 , e ) none 0 of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a"
Answer: a
Python program:
a = 4 + 3 
b = a + 1 
c = 1 / b
d = c * 600
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions
Options: a ) 700 , b ) 704 , c ) 704 , d ) 706 , e ) 707
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : option b"
Answer: b
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 500
i = h / 100
Problem: a 220 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 280 , b ) 270 , c ) 260 , d ) 250 , e ) 240
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 220 ) / 9 = 500 / 9 = > x = 280 . answer : option a"
Answer: a
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 220
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 402 to 500 inclusive ?
Options: a ) 14,550 , b ) 18,550 , c ) 22,550 , d ) 26,550 , e ) 30,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 402 + 404 + . . . + 500 = 50 ( 400 ) + ( 2 + 4 + . . . + 100 ) = 20,000 + 2550 = 22,550 the answer is c ."
Answer: c
Python program:
a = 500 + 402 
b = a / 2
c = 500 - 402
d = c / 2
e = d + 1 
f = b * e
Problem: we run a business that rents out canoes and kayaks . a canoe rental costs $ 9 per day , and a kayak rental costs $ 12 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 432 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 10 , b ) 9 , c ) 8 , d ) 7 , e ) 6
Rationale: "let x be the number of canoes . then 3 x / 4 is the number of kayaks . 9 x + ( 3 x / 4 ) * 12 = 432 9 x + 9 x = 432 18 x = 432 x = 24 ( canoes ) 3 x / 4 = 18 ( kayaks ) there were 24 - 18 = 6 more canoes rented out . the answer is e ."
Answer: e
Python program:
a = 4 - 3
b = 4 * 9
c = 3 * 12
d = b + c 
e = 432 / d
f = a * e
Problem: ramu bought an old car for rs . 48000 . he spent rs . 14000 on repairs and sold it for rs . 72900 . what is his profit percent ?
Options: a ) 16 % , b ) 17.5 % , c ) 18.2 % , d ) 58.5 % , e ) 13 %
Rationale: "total cp = rs . 48000 + rs . 14000 = rs . 62000 and sp = rs . 72900 profit ( % ) = ( 72900 - 62000 ) / 62000 * 100 = 17.5 % answer : b"
Answer: b
Python program:
a = 48000 + 14000 
b = 72900 - a
c = 48000 + 14000 
d = b / c
e = d * 100
Problem: rs . 2600 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ?
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2600 - x ) * 6 * 1 ] / 100 = 140 x = 1600 answer : a"
Answer: a
Python program:
a = 6 * 2600
b = a / 100
c = 140 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f