euclaise/mathqa_programs huggingface dataset:
Problem: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 12 % if no discount was offered ?
Options: a ) 17608 , b ) 17920 , c ) 17604 , d ) 17600 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 16000 * 112 / 100 = rs . 17920 . answer : b"
Answer: b
Python program:
a = 100 + 12 
b = 12500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: if x / ( 12 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 48 , e ) 99
Rationale: x / ( 12 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 12 * lowest value of p = 2 * 12 * 2 = 48 answer d
Answer: d
Python program:
a = 12 * 2
b = a * 2
Problem: there are 8 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 28 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 8 c 2 = 8 * 7 / 2 = 28 so option c is correct"
Answer: c
Python program:
a = 8 - 1
b = 8 * a
c = b / 2
Problem: a driver just filled the car ' s gas tank with 45 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1.3 , b ) 1.7 , c ) 2.1 , d ) 2.5 , e ) 2.9
Rationale: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 45 ) + x = 0.1 ( 45 + x ) 0.9 x = 4.5 - 2.25 = 2.25 x = 2.5 liters the answer is d ."
Answer: d
Python program:
a = 45 * 5
b = 100 - 10
c = a / b
Problem: think of a number , divide it by 5 and add 23 to it . the result is 42 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 95
Rationale: "explanation : 42 - 23 = 19 19 x 5 = 95 answer : e"
Answer: e
Python program:
a = 42 - 23
b = a * 5
Problem: ms . lopez deposits $ 100 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
Options: a ) $ 118.00 , b ) $ 120.00 , c ) $ 121.00 , d ) $ 122.00 , e ) $ 140.00
Rationale: "et me explain the concept for those who are not familiar with compounded semi annually / quarterly etc . . it basically means , here , that the interest will be paid twice , after 6 months and at the end of year . . so twice . . but interest is 20 % , which will get distributed semiannually that is 10 % . . . so the q literally means . . after 6 months . . 100 * 10 / 100 + 100 = 110 . . at the end of year 110 * 10 / 100 + 110 = 121 . . or we put it in compound interest formula . . where ci = 10 % , t is 2 and p = 100 . . so amount = 100 ( 1 + 10 / 100 ) ^ 2 = 100 * 1.1 * 1.1 = 121 . . answer : c"
Answer: c
Python program:
a = 20 / 100
b = a / 2
c = 1 + b 
d = c ** 2
e = 100 * d
Problem: here ' s an easy question of averages , but let ' s try to see innovative ways of solving this . a class has 12 boys and x girls . average score of boys and girls is 84 and 92 respectively . the average of the whole class is 86 , what is the value of x ?
Options: a ) a ) 6 , b ) b ) 4 , c ) c ) 8 , d ) d ) 10 , e ) e ) 12
Rationale: 12 ( 84 ) + 92 x / 12 + x = 86 1008 + 92 x / 12 + x = 86 1008 + 92 x = 86 ( 12 + x ) 1008 + 92 x = 1032 + 86 x x ' s one side , numbers one side we get , 92 x - 86 x = 1032 - 1008 6 x = 24 hence , x = 4 answer b
Answer: b
Python program:
a = 86 * 12
b = 84 * 12
c = a - b
d = 92 - 86
e = c / d
Problem: the present population of a town is 1000 . population increase rate is 20 % p . a . find the population of town after 2 years ?
Options: a ) 1440 , b ) 1220 , c ) 1400 , d ) 1500 , e ) 1620
Rationale: "p = 1000 r = 20 % required population of town = p * ( 1 + r / 100 ) ^ t = 1000 * ( 1 + 20 / 100 ) ^ 2 = 1000 * ( 6 / 5 ) ^ 2 = 1440 ( approximately ) answer is a"
Answer: a
Python program:
a = 1000 * 20
b = a / 100
c = 1000 + b
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 4 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 8774 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 4 = 8774 answer : d"
Answer: d
Python program:
a = 100 + 4 
b = a / 100
c = 100 + 4 
d = c / 100
e = b * d
f = 7500 * e
Problem: kim can do a work in 3 days while david can do the same work in 2 days . both of them finish the work together and get rs . 150 . what is the share of kim ?
Options: a ) 77 , b ) 60 , c ) 99 , d ) 26 , e ) 21
Rationale: kim ' s wages : david ' s wages = kim ' s 1 day work : david ' s 1 day work = 1 / 3 : 1 / 2 = 2 : 3 kim ' s share = 2 / 5 * 150 = rs . 60 answer : b
Answer: b
Python program:
a = 2 + 3 
b = 2 / a
c = 150 * b
Problem: at what price must an article costing rs . 51.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 60.5 , b ) 69.5 , c ) 67.5 , d ) 67.7 , e ) 22.5
Rationale: "cp = 51.50 sp = 51.50 * ( 125 / 100 ) = 64.375 mp * ( 95 / 100 ) = 64.375 mp = 67.7 answer : d"
Answer: d
Python program:
a = 51 * 50
b = a / 100
c = 51 + 50 
d = c * 100
e = 100 - 5
f = d / e
Problem: 4,7 , 11,18 , 29,47 , . . . ? . . , 123,199
Options: a ) 84 , b ) 102 , c ) 76 , d ) 70 , e ) none of the above
Rationale: "the addition of difference between each no . is equal to latter no . so , difference between 47 and 76 is 29 which is previous no . of 47 answer c"
Answer: c
Python program:
a = negate - (
Problem: there are two cars . one is 60 miles north of the other . simultaneously , the car to the north is driven westward at 15 miles per hour and the other car is driven eastward at 25 miles per hour . how many miles apart are the cars after 2 hours ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: "here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 60 and a height of 80 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 60 lines up with the ' 3 ' and the 80 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 20 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 60 / 80 / 100 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : c"
Answer: c
Python program:
a = 25 * 2
b = 15 * 2
c = a + b 
d = c ** 2
e = 25 * 2
f = e ** 2
g = d + f 
h = math.sqrt(g)
Problem: the diluted wine contains only 8 liters of wine and the rest is water . a new mixture whose concentration is 30 % , is to be formed by replacing wine . how many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : wine water 8 l 32 l 1 : 4 20 % 80 % ( original ratio ) 30 % 70 % ( required ratio ) in ths case , the percentage of water being reduced when the mixture is being replaced with wine . so the ratio of left quantity to the initial quantity is 7 : 8 therefore , \ frac { 7 } { 8 } = \ left [ 1 - \ frac { k } { 40 } \ right ] \ rightarrow \ frac { 7 } { 8 } = \ left [ \ frac { 40 - k } { 40 } \ right ] \ rightarrow k = 5 l answer : b ) 5
Answer: b
Python program:
a = 8 + 32 
b = 3 + 4 
c = b / 8
d = 1 - c
e = a * d
Problem: the length of the side of a square is represented by x + 2 . the length of the side of an equilateral triangle is 2 x . if the square and the equilateral triangle have equal perimeter , then the value of x is ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 8 , e ) 6
Rationale: since the side of the square is x + 2 , its perimeter = 4 ( x + 2 ) = 4 x + 8 since the side of the equilateral triangle is 2 x , its perimeter = 3 * 2 x = 6 x also , the perimeters of both are equal . ( i . e . ) 4 x + 8 = 6 x ( i . e . ) 2 x = 8 è x = 4 . answer : c
Answer: c
Python program:
a = 2 * 4
b = 2 * 3
c = b - 4
d = a / c
Problem: the cost price of 8 articles is equal to the selling price of 5 articles . what is the profit percent ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "5 * sp = 8 * cp sp = 1.6 * cp the profit percent is 60 % . the answer is d ."
Answer: d
Python program:
a = 8 * 4
b = 4 + 1 
c = a / b
Problem: a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 20 , e ) 28
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 2 = 2 ( x + 2 ) x + 32 = 2 x + 4 = > x = 28 . answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 30 - b
d = 2 - 1
e = c / d
Problem: in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 2 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 7 ) = 5 / 2 answer : b"
Answer: b
Python program:
a = 8 - 75
b = 8 - 75
c = a / b
d = 8 - 75
e = 8 - 75
f = d / e
g = 1 - f
h = c / g
Problem: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 20 , what is the greatest possible value of q minus r ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 20 . the greatest multiple of 9 which is less than 20 is 18 . the answer is d ."
Answer: d
Python program:
a = 10 - 1
b = reminder * (
Problem: a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 24 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 6 - 1 / x = 1 / 8 , solving 1 / x = 1 / 24 so in 24 hours full cistern will be empty . answer : a"
Answer: a
Python program:
a = 1 / 6
b = 6 + 2 
c = 1 / b
d = a - c
e = 1/(d)
Problem: a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is - 8 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 , d ) 4 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = - 8 i . e x ^ 2 + 4 x + 8 = 0 is the quadratic equation which needs to be solved . no solution imo e"
Answer: e
Python program:
a = 8 ** 2
b = a / 4
Problem: if the sum of two positive integers is 20 and the difference of their squares is 40 , what is the product of the two integers ?
Options: a ) 108 , b ) 99 , c ) 128 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 20 - - 1 x ^ 2 - y ^ 2 = 40 = > ( x + y ) ( x - y ) = 40 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 11 y = 9 product = 11 * 9 = 99 answer b"
Answer: b
Python program:
a = 40 / 20
b = 20 - a
c = 40 / 20
d = b / c
e = 40 / 20
f = 20 - e
g = 40 / 20
h = f / g
i = 40 / 20
j = h + i 
k = d * j
Problem: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 20 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 4 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 20 women ’ s 1 day ’ s work = 1 / 192 × 20 = 5 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 10 men + 20 women + 10 children ) ’ s 1 day ’ s work = 5 / 48 + 5 / 48 + 1 / 24 = 1 / 4 the required no . of days = 4 days answer : option d"
Answer: d
Python program:
a = 24 * 10
b = 1/(a)
c = 10 * b
d = 12 * 8
e = 1/(d)
f = e * 10
g = 48 * 4
h = 1/(g)
i = h * 4
j = f + i 
k = c + j 
l = 1/(k)
Problem: what is the remainder when 3 ^ 86 is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 0 , e ) 3
Rationale: "3 ^ 0 = 1 3 ^ 1 = 3 3 ^ 2 = 9 3 ^ 3 = 27 3 ^ 4 = . . . 1 3 ^ 5 = . . . . 3 3 ^ 6 = . . . . . . 9 and so on . 86 / 4 = 21 ( with a remainder 2 ) so the last number is a 9 . so when 3 ^ 86 is divided by 5 the remainder is 4 , ans = c"
Answer: c
Python program:
a = 5 / 2
b = 3 * 3
c = a - b
Problem: if the ratio of two number is 2 : 5 and lcm of the number is 160 then what is the number .
Options: a ) 15 , b ) 20 , c ) 16 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 2 x * 5 x = 160 * x x = 16 answer : c"
Answer: c
Python program:
a = 2 * 5
b = 160 / a
Problem: the moon revolves around the earth at a speed of approximately 1.03 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,708 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.03 * 3600 = 3708 kilometers per hour . option d is correct"
Answer: d
Python program:
a = 1 * 3
Problem: the average marks obtained by 100 candidates in an examination is 50 . find how many candidates have passed in the examination , if the average marks of candidates who passed is 70 and that of failed candidates is 20 .
Options: a ) 33 , b ) 77 , c ) 60 , d ) 29 , e ) 11
Rationale: explanation : let the number of students who passed the examination be x number of students failed = ( 100 - x ) total marks of students who have passed = 70 x total marks of 100 students = 100 * 50 = 5000 total marks of students who have failed = 20 ( 100 – x ) 20 ( 100 – x ) + 70 x = 5000 2000 – 20 x + 70 x = 5000 50 x = 3000 x = 60 answer : c
Answer: c
Python program:
a = 100 * 50
b = 20 * 100
c = a - b
d = 70 - 20
e = c / d
Problem: set v consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set v , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: v = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 016 , - 59 } y > 21 so l = median of v = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c
Answer: c
Python program:
a = 19 - 3
b = 26 / 2
c = 26 / 2
d = b / c
e = d * 16
f = a / e
g = f * 2
h = g - 3
i = 19 - 3
j = 26 / 2
k = 26 / 2
l = j / k
m = l * 16
n = i / m
o = n * 2
p = o - 3
q = h + p
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 11.0 million and $ 14.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 16 2 / 3 % , c ) 25 % , d ) 4 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 11 = 4.6 million $ profit in 1983 = 18.8 - 14 = 4.8 million $ percentage increase in profit = ( 4.8 - 4.6 ) / 4.6 * 100 % = 4 1 / 3 % answer d"
Answer: d
Python program:
a = 14 - 0
b = a * 100
c = 18 - 8
d = b / c
e = 100 - d
Problem: how many integers between 1 and 1,800 are divisible by 20 , 30,40 ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "lcm of the given numbers = 120 therefore , number of integers = 1800 / 120 = 15 option b is answer"
Answer: b
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 1 - 800
Problem: a sum of rs . 2704 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1672 , b ) 1664 , c ) 1677 , d ) 1698 , e ) 1679
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2704 - x ) * 3 * 5 ) / 100 24 x / 100 = 40560 / 100 - 15 x / 100 39 x = 40560 = > x = 1040 second sum = 2704 â € “ 1040 = 1664 answer : b"
Answer: b
Python program:
a = 3 * 5
b = a * 2704
c = 3 * 5
d = 8 * 3
e = c + d 
f = b / e
g = 2704 - f
Problem: 150 is increased by 40 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 180 , d ) 190 , e ) 220
Rationale: "final number = initial number + 40 % ( original number ) = 150 + 40 % ( 150 ) = 150 + 60 = 210 . answer b"
Answer: b
Python program:
a = 40 / 100
b = 150 * a
c = 150 + b
Problem: a person ' s salary is getting reduced by 20 % . what percentage should be added to get back his original salary ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 85 % , e ) 95 %
Rationale: salary he get after reduced 20 % = 100 - 20 % = 80 % so , percentage should be added to get back his salary = ( 20 / 80 ) * 100 = 25 % answer : a
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 1 / b
d = c - 1
e = d * 100
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 18 white marbles . how many red marbles could be in bag a ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 18 = 6 k + 4 p = > k = 1 , p = 3 total red ' s in bag a will be 2 k = 2 a"
Answer: a
Python program:
a = 3 * 2
b = a + 4 
c = 18 / b
Problem: the price of lunch for 10 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.8 , d ) 14 , e ) 18
Rationale: clearly e is the answer i used poe here lets consider option ( e ) 10 * 18 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo e
Answer: e
Python program:
a = 100 - 15
b = 207 * a
c = b / 100
d = c / 10
Problem: in an office , totally there are 1800 employees and 60 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 756 , b ) 750 , c ) 600 , d ) 760 , e ) none of these
Rationale: "number of male employees = 1800 * 60 / 100 = 1080 required number of male employees who are less than 50 years old = 1080 * ( 100 - 30 ) % = 1080 * 70 / 100 = 756 . answer : a"
Answer: a
Python program:
a = 1800 * 60
b = a / 100
c = 100 - 30
d = c / 100
e = b * d
Problem: if 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 2300 , b ) 600 , c ) 250 , d ) 300 , e ) none of these
Rationale: "1 st line - 0 points 2 nd line - new 1 point 3 td line - new 2 points + old 1 point 4 th line - new 3 points + old 2 + 1 points 5 th line - new 4 points + old 3 + 2 + 1 points n - th line - ( n - 1 ) points + ( n - 2 ) . . . . 3 + 2 + 1 therefore , s = 1 + 2 + 3 . . . ( n - 1 ) s = ( n - 1 ) n / 2 = 24 * 25 / 2 = 300 ans ; d"
Answer: d
Python program:
a = math.factorial(25)
b = 25 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: in a renowned city , the average birth rate is 5 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 85,400 , b ) 86,400 , c ) 87,400 , d ) 88,400 , e ) 89,400
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 5 - 3 = 2 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 2 = 86,400 . hence b ."
Answer: b
Python program:
a = 5 - 3
b = a * 3600
c = b * 12
Problem: population is 21000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 27951 , c ) 36621 , d ) 26621 , e ) 26821
Rationale: "population after 1 st year = 21000 * 10 / 100 = 2100 = = = > 21000 + 2100 = 23100 population after 2 nd year = 23100 * 10 / 100 = 2310 = = = > 23100 + 2310 = 25410 population after 3 rd year = 254100 * 10 / 100 = 2541 = = = > 25410 + 2541 = 27951 answer : b"
Answer: b
Python program:
a = 3 * 10
b = a / 100
c = 1 + b 
d = 21000 * c
Problem: a , b , c hired a car for rs . 720 and used it for 9 , 10 and 13 hours respectively . hire charges paid by b are :
Options: a ) rs 220 , b ) rs . 225 , c ) rs . 230 , d ) rs . 235 , e ) rs . 255
Rationale: "a : b : c = 9 : 10 : 13 . hire charges paid by b = rs . 720 * 10 / 32 = rs . 225 . answer : b"
Answer: b
Python program:
a = 9 + 10 
b = a + 13 
c = 10 / b
d = 720 * c
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 12 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 67.5 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 88 / 100 ) = 59.375 mp = 67.5 c"
Answer: c
Python program:
a = 100 + 25 
b = 47 * 50
c = b / 100
d = 100 - 12
e = c / d
f = e * 100
Problem: the average of 45 results is 13 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 695
Rationale: "23 th result = sum of 45 results - sum of 44 results 13 * 45 - 15 * 22 + 20 * 22 = 585 - 330 + 440 = 695 answer is e"
Answer: e
Python program:
a = 45 * 13
b = 22 * 20
c = a - b
d = 22 * 15
e = c - d
Problem: if log 1087.5 = 5.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 70 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 5.9421 + 1 ) = 10 ( 6.9421 ) = 69.421 x = antilog ( 69.421 ) therefore , number of digits in x = 70 . answer : b"
Answer: b
Python program:
a = 4 * 5
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d