euclaise/mathqa_programs huggingface dataset:
Problem: a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 20 inches . find b .
Options: a ) 8 , b ) 16 , c ) 4 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 20 ( 2 ^ 2 * 5 ) , sob = 2 ^ 2 or 2 ^ 2 * 5 ( 4 or 20 ) . combining 2 premises shows the answer is c ( 4 ) ."
Answer: c
Python program:
a = 20 / 4
b = a ** 2
c = 12 ** 2
d = b - c
e = math.sqrt(d)
Problem: anita has 360 apples . there are 60 students are studying in her class . she would like to give each student the same amount of apples , how much should she give to each student ?
Options: a ) 12 , b ) 6 , c ) 9 , d ) 15 , e ) 7
Rationale: 360 / 60 = 6 the answer is b .
Answer: b
Python program:
a = 360 / 60
Problem: a number is increased by 60 % and then decreased by 60 % . find the net increase or decrease per cent .
Options: a ) 19 % , b ) 18 % , c ) 27 % , d ) 33 % , e ) 36 %
Rationale: "let the number be 100 . increase in the number = 60 % = 60 % of 100 = ( 60 / 100 ã — 100 ) = 60 therefore , increased number = 100 + 60 = 160 this number is decreased by 60 % therefore , decrease in number = 60 % of 160 = ( 60 / 100 ã — 160 ) = 9600 / 100 = 96 therefore , new number = 160 - 96 = 64 thus , net decreases = 100 - 64 = 36 hence , net percentage decrease = ( 36 / 100 ã — 100 ) % = ( 3600 / 100 ) % = 36 % answer : e"
Answer: e
Python program:
a = 60 + 100 
b = 100 - 60
c = a * b
d = c / 100
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 36 â ° is ?
Options: a ) 52.6 , b ) 45.3 , c ) 52.8 , d ) 52.1 , e ) 52.2
Rationale: "36 / 360 * 22 / 7 * 12 * 12 = 45.3 m 2 answer : b"
Answer: b
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 36 / g
i = f * h
Problem: 6 persons standing in queue with different age group , after two years their average age will be 43 and seventh person joined with them . hence the current average age has become 45 . find the age of seventh person ?
Options: a ) 65 , b ) 67 , c ) 68 , d ) 69 , e ) 50
Rationale: explanation : let the sum of current ages of 6 persons = x given average age of 6 person after 2 years = 43 = > x + 6 ( 2 ) / 6 = 43 = > x + 12 = 258 = x = 246 let the seventh ' s person age will be y given current average age of 7 persons = 45 [ sum of current 6 person ' s age ( x ) + seventh person ' s age ( y ) ] / 7 = 45 = > 246 + y = 45 ( 7 ) = > y = 315 - 246 = > y = 69 hence seventh person ' s age = 69 hence ( d ) is the correct answer . answer : d
Answer: d
Python program:
a = 6 + 1 
b = 45 * a
c = 43 - 2
d = c * 6
e = b - d
Problem: one fourth of a solution that was 15 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 16 % , e ) 8.5 %
Rationale: "instead of using complex calculations and remembering formulae , why dont u directly get to weighted average . 3 parts of 15 % + 1 part of x ( unknown ) % = 4 parts of 16 % = > x % = 64 % - 45 % = 16 % ans d it is ."
Answer: d
Python program:
a = 16 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 15 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 1600 ?
Options: a ) 3000 , b ) 4200 , c ) 2025 , d ) 1205 , e ) 3251
Rationale: "1800 * 9 / 8 * 9 / 8 = 2025 answer : c"
Answer: c
Python program:
a = 1 / 8
b = a * 1600
c = 1600 + b 
d = 1 / 8
e = 1 / 8
f = e * 1600
g = 1600 + f 
h = d * g
i = c + h
Problem: how many unique positive odd integers less than 110 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 6 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 110 are odd multiples of 5 so we have 5 , 15,25 , 35,45 , . . and 105 = 11 ans c"
Answer: c
Python program:
a = 110 / 5
b = a / 2
Problem: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 72 , how many more green disks than blue disks are in the bag ?
Options: a ) 20 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 72 - - > x = 4 . g - b = 8 x - 3 x = 5 x = 20 . the answer is a ."
Answer: a
Python program:
a = 3 + 7 
b = a + 8 
c = 72 / b
d = 8 - 3
e = c * d
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 40.5 meters . how many times did the ball bounce ?
Options: a ) 3 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "division of total distance travelled will be 16 + 16 + 8 + 0.5 ans : a"
Answer: a
Python program:
a = 16 / 2
b = a / 2
Problem: what is the probability of getting atmost one head when two unbiased coin are tossed ?
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 1 / 2 , e ) 2 / 6
Rationale: "here s = { hh , ht , th , tt } let ee = event of getting one head e = { tt , ht , th } p ( e ) = n ( e ) / n ( s ) = 3 / 4 option a"
Answer: a
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: if 5 x + 3 = 10 x – 22 , what is the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: solve for x : 5 x + 3 = 10 x - 22 25 = 5 x 5 = x correct answer e ) 5
Answer: e
Python program:
a = 3 + 22 
b = 10 - 5
c = a / b
Problem: a jogger running at 9 km / hr along side a railway track is 270 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 39 sec , d ) 87 sec , e ) 45 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 270 + 120 = 390 m . time taken = 390 / 10 = 39 sec . answer : c"
Answer: c
Python program:
a = 270 + 120 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: the speed of a boat in still water in 26 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 20 minutes is :
Options: a ) 10.4 km , b ) 10.66 km , c ) 11.4 km , d ) 11.22 km , e ) 12 km
Rationale: "explanation : speed downstream = ( 26 + 6 ) = 32 kmph time = 20 minutes = 20 / 60 hour = 1 / 3 hour distance travelled = time × speed = ( 1 / 3 ) × 32 = 10.66 km answer : option b"
Answer: b
Python program:
a = 26 + 6 
b = 20 / const_60
c = a * b
Problem: find the average of all the numbers between 6 and 39 which are divisible by 5 ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 23
Rationale: "average = ( 10 + 15 + 20 + 25 + 30 + 35 ) 6 = 135 / 6 = 23 answer is e"
Answer: e
Python program:
a = 6 + 4 
b = 39 - 4
c = a + b 
d = c / 2
Problem: add : + 47 and - 27
Options: a ) - 30 , b ) + 30 , c ) 0 , d ) 27 , e ) 47
Rationale: the absolute values of + 47 and - 27 are 47 and 27 respectively ; and their difference = 47 – 27 = 30 . ( + 47 ) + ( - 27 ) = + 30 answer : b
Answer: b
Python program:
a = 27 + 3
Problem: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet . what is its area , in square feet ?
Options: a ) 76,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 400 , you can deduce the following a = 240 b = 320 240 x 320 = 76,800 a is the answer ."
Answer: a
Python program:
a = 2 + 3 
b = 400 / a
c = b * 3
d = 2 + 3 
e = 400 / d
f = e * 4
g = c * f
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 40 vehicles were involved in accidents . if 2 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 800 , b ) 900 , c ) 100 , d ) 1000 , e ) 950
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 40 accidents as 2 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 2,000 million rather than 2 billion . creating a proportion we have : 100 / 40 = 2,000 / x cross multiplying gives us : 100 x = 2,000 * 40 x = 20 * 40 = 800 answer : a"
Answer: a
Python program:
a = 2 * 10
b = 40 * a
Problem: find the value of ( √ 1.21 ) / ( √ 0.64 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 3.089 , e ) 185 / 63
Rationale: "( √ 1.21 ) / ( √ 0.64 ) + ( √ 1.44 ) / ( √ 0.49 ) 11 / 8 + 12 / 7 = > 3.089 answer is d"
Answer: d
Python program:
a = math.sqrt(1)
b = math.sqrt(0)
c = a / b
d = math.sqrt(1)
e = math.sqrt(0)
f = d / e
g = c + f
Problem: a and b together can do a piece of work in 5 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
Rationale: "b = 1 / 5 – 1 / 20 = 0.15 days answer : e"
Answer: e
Python program:
a = 1/(5)
b = 1/(20)
c = a - b
d = 1/(c)
Problem: a boat moves upstream at the rate of 1 km in 25 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 2 kmph , c ) 3 kmph , d ) 1.3 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 25 * 60 ) = 2.4 kmph rate dowm stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 2.4 ) = 1.3 kmph answer : d"
Answer: d
Python program:
a = 1 / 12
b = a * const_60
c = 1 / 25
d = c * const_60
e = b - d
f = e / 2
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 50 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 960 , d ) $ 870 , e ) $ 660
Rationale: "c $ 960 let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 150 % of $ 640 = 150 / 100 * 640 = $ 960 ."
Answer: c
Python program:
a = 832 + 448 
b = a / 2
c = b * 50
d = c / 100
e = 832 + 448 
f = e / 2
g = d + f
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 56 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 58
Rationale: "amount earned by james = 40 * x + 16 * 2 x = 72 x therefore , amount earned by harry = 72 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 72 x ] ] so x * ( 1.5 y - 45 + 30 ) = 72 x or x * ( 1.5 y - 15 ) = 72 x so 1.5 y - 15 = 72 so 1.5 y = 87 so y = 58 answer is e"
Answer: e
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: simplify : 100 x 100 - 50 x 50
Options: a ) 7612 , b ) 7614 , c ) 7500 , d ) 7615 , e ) none of them
Rationale: "( 100 ) ^ 2 - ( 50 ) ^ 2 = ( 100 + 50 ) ( 100 - 50 ) = 150 x 50 = 7500 . answer is c ."
Answer: c
Python program:
a = 100 * 100
b = 50 * 50
c = a + b
Problem: a worker ' s daily wage is increased by 40 % and the new wage is $ 28 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 18 , b ) $ 20 , c ) $ 22 , d ) $ 24 , e ) $ 25
Rationale: "let x be the daily wage before the increase . 1.4 x = $ 28 x = $ 20 the answer is b ."
Answer: b
Python program:
a = 40 / 100
b = 1 + a 
c = 28 / b
Problem: two pipes can fill a tank in 15 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 15 + 1 / 15 - 1 / 45 = 1 / 9 so , the tank becomes full in 9 minutes . answer : d"
Answer: d
Python program:
a = 1 / 15
b = 1 / 15
c = a + b 
d = 1 / 45
e = c - d
Problem: set r is composed of 9 numbers , labeled r 1 through r 9 . set s is also composed of 9 numbers , labeled s 1 through s 9 . set s is defined as follows : s 1 = 1 + r 1 ; s 2 = 2 + r 2 ; and so on , including s 9 = 9 + r 9 . how much larger is the sum of set s ' s mean and range than the sum of set r ' s mean and range ?
Options: a ) 8 , b ) can not be determined , c ) 4 , d ) 6 , e ) 9
Rationale: yes , the correct answer is b
Answer: b
Python program:
a = 9 - 1
b = a - 4
Problem: the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 60 * 5 = 300 lowest is 45 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 45 = 180 . on the fifth day it is 300 - 180 = 120 range is therefore 120 - 45 = 75 answer e"
Answer: e
Python program:
a = 2 + 3 
b = 60 * a
c = 45 * 4
d = b - c
e = d - 45
Problem: at a certain organisation , the number of male members went up by 12 % in the year 2001 from year 2000 , and the number of females members went down by 5 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 7
Rationale: "men increase by 12 % = = > 1.12 m = males in 2001 women decrease by 5 % = = > 0.95 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.12 m + 0.95 f = 1.012 * ( m + f ) 1.12 m + 0.95 f = 1.012 m + 1.012 f 1.12 m - 1.012 m = 1.012 f - 0.95 f 0.108 m = 0.062 f m / f = ( 0.062 ) / ( 0.108 ) = 62 / 108 = 4 / 7 answer = ( e )"
Answer: e
Python program:
a = 1 / 2
b = 1 + a 
c = b * 1000
d = 5 / 100
e = 1 - d
f = e * 1000
g = c - f
h = 12 / 100
i = 1 + h 
j = i * 1000
k = 1 / 2
l = 1 + k 
m = l * 1000
n = j - m
o = g / n
Problem: if the average of 9 digits is 18 and the average of 4 of them is 8 , calculate the average of the remaining 5 numbers ?
Options: a ) 21 , b ) 26 , c ) 27 , d ) 22 , e ) 29
Rationale: explanation : total of the 9 digits - 9 * 18 = 162 total of the 4 digits - 4 * 8 = 32 total of the remaining 5 digits - 162 - 32 = 130 average of the remaining 3 numbers = 130 / 5 = 26 answer : b
Answer: b
Python program:
a = 9 * 18
b = 4 * 8
c = a - b
d = c / 5
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 3 ) ^ ( 45 ) is :
Options: a ) 2 , b ) 8 , c ) 6 , d ) 9 , e ) 0
Rationale: "any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . 2 nd part 3 ^ 45 has a units digit of 3 therefore , the second term has a units digit of 3 . of course 5 + 3 = 8 , so something with a units digit of 5 plus something with a units digit of 3 answer = b"
Answer: b
Python program:
a = reminder * (
b = reminder + (
Problem: in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 20 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 75 , b ) 25 , 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 dogs to the number of cats is 15 : 7 . we ' re then told that 20 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 20 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 20 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 20 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 20 ) ( 1 ) 11 x = 7 x + 20 4 x = 20 x = 5 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 5 ) = 75 final answer : a
Answer: a
Python program:
a = 7 * 20
b = 11 - 7
c = a / b
d = c / 7
e = d * 15
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 60 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 59 , b ) 57 , c ) 59.5 , d ) 58 , e ) 55.5
Rationale: "d 75 * t = 1 km = > t = 1 / 60 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 60 + 2 / 3600 ) = 1 = > v = 58 km / h"
Answer: d
Python program:
a = 1 / 60
b = 3600 * a
c = b + 2 
d = c / 3600
e = 1 / d
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 17 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 17 a – d = 3 a + d = 17 2 d = 14 d = 7 anser e"
Answer: e
Python program:
a = 3 * 16
b = 17 - 16
c = b + 3 
d = a - c
e = d - 16
Problem: mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24624 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 2052 , d ) 4845.6 , e ) none of these
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 24624 ⁄ 12 = 2052 answer c"
Answer: c
Python program:
a = 100 - 60
b = a * 50
c = b / 100
d = c / 100
e = 24624 / d
f = 3 * 4
g = e / f
h = 100 - 60
i = h * 50
j = i / 100
k = j / 100
l = g * k
Problem: a train 210 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 18 sec , e ) 12 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 210 * 2 / 35 = 18 sec answer : d"
Answer: d
Python program:
a = 63 * 1000
b = 210 / a
c = b * 3600
Problem: drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 2 / 5 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 4 / 5 , b ) 8 / 15 , c ) 11 / 15 , d ) 9 / 20 , e ) 13 / 20
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 2 / 5 ) y = ( 13 / 20 ) y the answer is e ."
Answer: e
Python program:
a = 2 / 5
b = a * 12
c = 12 / 2
d = 1 / 2
e = c * d
f = b + e 
g = f / 12
Problem: joe drives 180 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 50 , c ) 50 , d ) 54 , e ) 56
Rationale: "t 1 = 180 / 60 = 3 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 6 hours avg speed = total distance / t = 300 / 6 = 50 mph = b"
Answer: b
Python program:
a = 180 + 120 
b = 180 / 60
c = 120 / 40
d = b + c 
e = a / d
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 140 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 140 male associates implies 70 female associates which means the remaining 20 females must be managers b . 20"
Answer: b
Python program:
a = 40 * 1
Problem: a train travels 250 km in 2 hours and 350 km in 4 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 70 kmph , d ) 100 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 250 + 350 = 600 km thus , total speed = 6 hrs or , average speed = 600 / 6 or , 100 kmph . answer : d"
Answer: d
Python program:
a = 250 + 350 
b = 2 + 4 
c = a / b
Problem: the difference of the areas of two squares drawn on two line segments in 32 sq . cm . find the length of the greater line segment if one is longer than the other by 2 cm
Options: a ) 9 cm
b ) 8 cm
c ) 7 cm
d ) 6 cm
e ) 5 cm
Rationale: explanation : let the lengths of the line segments be x and x + 2 cm then , ( x + 2 ) 2 − x 2 = 32 x 2 + 4 x + 4 − x 2 = 324 x = 28 x = 7 cm option c
Answer: c
Python program:
a = 2 * 2
b = 32 - a
c = b / 4
Problem: if the cost price of 24 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 50 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 24 articles = rs . 24 . selling price of 16 articles = rs . 24 therefore , selling price of 24 articles is : - = > 24 / 16 ã — 24 = > 36 . therefore , profit = selling price - cost price . = > 36 â ˆ ’ 24 = 12 . hence , the percentage of profit = profit x 100 / c . p . = > 12 / 24 ã — 100 . = > 50 % profit . answer : b"
Answer: b
Python program:
a = 100 * 16
b = a / 24
c = 100 - b
d = 100 * 16
e = d / 24
f = c / e
g = 100 * f
Problem: x and y can do a piece of work in 20 days and 12 days respectively . x started the work alone and then after 4 days y joined him till the completion of the work . how long did the work last ?
Options: a ) 6 days , b ) 10 days , c ) 15 days , d ) 16 days , e ) 20 days
Rationale: work done by x in 4 days = ( 1 / 20 ) * 4 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 . ( x + y ) ' s 1 day ' s work = 1 / 20 + 1 / 12 = 8 / 60 = 2 / 15 . now , 2 / 15 work is done by x and y in 1 day . so , 4 / 5 work will be done by x and y in ( 15 / 2 x 4 / 5 ) = 6 days . hence , total time taken = ( 6 + 4 ) days = 10 days . option b
Answer: b
Python program:
a = 4 / 20
b = 1 - a
c = 20 * b
d = 12 * c
e = 20 + 12 
f = d / e
g = 4 + f
Problem: a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 144 ft , b ) 88 ft , c ) 22 ft , d ) 112 ft , e ) 146 t
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 10 x breadth = 680 breadth = 68 feet area to be fenced = 2 b + l = 2 ( 68 ) + 20 = 146 feet answer : e ) 146 ft"
Answer: e
Python program:
a = 680 / 10
b = a * 2
c = b + 10