euclaise/mathqa_programs huggingface dataset:
Problem: a train running at the speed of 120 km / hr crosses a pole in 12 seconds . what is the length of the train ?
Options: a ) 200 m , b ) 250 m , c ) 300 m , d ) 350 m , e ) 400 m
Rationale: "speed = ( 120 * 5 / 18 ) m / sec = ( 100 / 3 ) m / sec length of the train = ( speed x time ) = ( 100 / 3 * 12 ) m = 400 m . answer : e"
Answer: e
Python program:
a = 120 * 1000
b = a / 3600
c = b * 12
Problem: the function f ( y ) represents the number of ways that prime numbers can be uniquely summed to form a certain number y such that y = a + b + c + d … where those summed variables are each prime and a ≤ b ≤ c ≤ d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: it is so better to start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d
Answer: d
Python program:
a = 2 + 2 
b = a + 3
Problem: a person can swim in still water at 20 km / h . if the speed of water 12 km / h , how many hours will the man take to swim back against the current for 40 km ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 20 s = 12 us = 20 - 12 = 8 d = 40 t = 40 / 8 = 5 answer : c"
Answer: c
Python program:
a = 20 - 12
b = 40 / a
Problem: a person was asked to state his age in years . his reply was , ` ` take my age 3 years hence , multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 27 , d ) 26 , e ) 19
Rationale: "explanation : let the present age of person be x years . then , 3 ( x + 3 ) - 3 ( x - 3 ) = x < = > ( 3 x + 9 ) - ( 3 x - 9 ) = x < = > x = 18 . . answer : a ) 18"
Answer: a
Python program:
a = 3 * 3
b = 3 * 3
c = a + b
Problem: the average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 48 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 63 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 48 + 10 x 1.5 48 + 15 = 63 kg ans : ' b '"
Answer: b
Python program:
a = 1 / 1
b = 1 + a 
c = 10 * b
d = 48 + c
Problem: a man rows his boat 105 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 7 kmph , c ) 12 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 105 / ( 2 1 / 2 ) = 42 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 42 - 18 ) / 2 = 12 kmph answer : c"
Answer: c
Python program:
a = 105 / 2
b = 45 / 2
c = a - b
d = c / 2
Problem: a can do a job in 20 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 16 days , c ) 24 days , d ) 11 days , e ) 19 days
Rationale: "c 1 / 20 + 1 / 30 = 1 / 12 12 * 2 = 24 days"
Answer: c
Python program:
a = 1 / 20
b = 1 / 30
c = a + b
Problem: if the average of 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 and x is 750 , what is the value of x ?
Options: a ) 750 , b ) 752 , c ) 754 , d ) 755 , e ) 756
Rationale: "sum of the deviations of the numbers in the set from the mean is always zero 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 mean is 750 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 750 + 5 = 755 d"
Answer: d
Python program:
a = 750 * 10
b = 744 + 745 
c = b + 747 
d = c + 748 
e = d + 749 
f = e + 752 
g = f + 752 
h = g + 753 
i = h + 755 
j = a - i
Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 2 : 50 : 100 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 50 , b ) 200 , c ) 400 , d ) 625 , e ) 800
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 2 : 50 : 100 initial soap : alcohol = 2 / 50 = 2 : 50 after doubled soap : alcohol = 2 * 2 / 50 = 4 : 50 initial soap : water = 2 / 100 = 2 : 100 after halved soap : water : 1 / 2 * 2 / 100 = 1 / 100 = 1 : 100 = 4 : 400 after soap : alcohol : water - - > 4 : 50 : 400 given alcohol 100 cumeter . ratio is 8 : 100 : 800 ( 4 : 50 : 400 ) for 100 cu meter of alcohol - - - 800 cu m water is required answer : e"
Answer: e
Python program:
a = volume_rectangular_prism / (
b = a / 3
c = b / 2
d = c / 2
e = d / 2
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "possible values of n = 12 , 24 , 36 and 48 . but it is 12 that can divide all the possible values of n . if we consider 48 , it will not divide 12 , 24 and 36 . hence , 12 is the value that must divide n . answer : b"
Answer: b
Python program:
a = 72 / 2
b = math.sqrt(a)
c = b * 2
Problem: little john had $ 20.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?
Options: a ) $ 17.05 , b ) $ 17.55 , c ) $ 17.15 , d ) $ 17.35 , e ) $ 17.25
Rationale: "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 20.10 - 3.05 = $ 17.05 answer : a"
Answer: a
Python program:
a = 1 + 0 
b = 1 + 5 
c = 20 - 10
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1625
Rationale: "since pumping in additional 300 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 300 = 0.8 * { total } - - > { total } = 1,625 . answer : e ."
Answer: e
Python program:
a = 300 * 100
b = a / 30
c = b + 300 
d = 80 / 100
e = c / d
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 еў is ?
Options: a ) 35 m 2 , b ) 36 m 2 , c ) 37 m 2 , d ) 38 m 2 , e ) 40 m 2
Rationale: "30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c"
Answer: c
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 30 / g
i = f * h
Problem: there are two positive numbers in the ratio 3 : 11 . if the larger number exceeds the smaller by 32 , then what is the smaller number ?
Options: a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 17
Rationale: "let the two positive numbers be 3 x and 11 x respectively . 11 x - 3 x = 32 8 x = 32 = > x = 4 thus , the smaller number = 3 x = 12 . answer : c"
Answer: c
Python program:
a = 32 * 3
b = a / 4
Problem: if the volume and surface area of a sphere are numerically the same , then its radius is : ?
Options: a ) 2
b ) 4
c ) 1
d ) 5
e ) 3
Rationale: 4 / 3 π r ( power 3 ) = 4 π r ( power 2 ) r = 3 answer is e .
Answer: e
Python program:
a = 4 / 3
b = a * math.pi
c = 4 * math.pi
d = b / c
e = 1 / d
Problem: there are 200 female managers in a certain company . find the total number t of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 300 , b ) t = 400 , c ) t = 500 , d ) 600 , e ) none of these
Rationale: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."
Answer: c
Python program:
a = 2 / 5
b = 200 / a
Problem: 60 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 81
Rationale: "explanation : 60 + 5 * 12 / ( 180 / 3 ) = 60 + 5 * 12 / ( 60 ) = 60 + ( 5 * 12 ) / 60 = 60 + 1 = 61 . answer : d"
Answer: d
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 60 + c
Problem: to a sugar solution of 3 liters containing 40 % sugar , one liter of water is added . the percentage of sugar in the new solution is ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 15 % , e ) 50 %
Rationale: quantity of sugar = 40 * 3 / 100 = 1.2 kg new percentage = 1.2 / 4 * 100 = 30 % answer is b
Answer: b
Python program:
a = 40 / 100
b = a * 3
c = 3 + 1 
d = b / c
e = d * 100
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 20 % on the cost price . he then sold the articles by offering a discount of 5 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 24 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 120 . sp = rs . 120 - 5 % of 120 = rs . 120 - 6 = rs . 124 . gain = rs . 124 â € “ rs . 100 = rs . 24 therefore , gain / profit percent = 24 % . answer : option a"
Answer: a
Python program:
a = 100 + 20 
b = 100 + 20 
c = 5 / 100
d = b * c
e = a - d
f = e - 100
Problem: by selling 11 pencils for a rupee a man loses 30 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 11 , e ) 9
Rationale: "70 % - - - 12 130 % - - - ? 70 / 130 * 11 = 6 answer : d"
Answer: d
Python program:
a = 100 + 30 
b = 100 - 30
c = 1 / b
d = a * c
e = 1 / d
f = e * 11
Problem: a can do a job in 18 days and b can do it in 30 days . a and b working together will finish thrice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 33 3 / 4 days , d ) 12 ½ days , e ) none of these
Rationale: "explanation : 1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 45 / 4 = 45 / 4 * 3 = 33 3 / 4 days answer : c"
Answer: c
Python program:
a = 1 / 18
b = 1 / 30
c = a + b
Problem: the length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size . if the area of the new rectangle is equal to 1800 square meters , what is the area of the original rectangle ?
Options: a ) 300 square meters
b ) 400 square meters
c ) 500 square meters
d ) 600 square meters
e ) 700 square meters
Rationale: if l and w be the original length and width of the rectangle and its area is given by l ? w after increase the length becomes 2 l and the width becomes 3 w . the area is then given by ( 2 l ) ? ( 3 w ) and is known . hence ( 2 l ) ? ( 3 w ) = 1800 solve the above equation to find l ? w 6 l ? w = 1800 l ? w = 1800 / 6 = 300 square meters , area of original rectangle correct answer a
Answer: a
Python program:
a = 2 * 3
b = 1800 / a
Problem: there are 200 female managers in a certain company . find the total number y of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 300 , b ) y = 400 , c ) y = 500 , d ) y = 600 , e ) none of these
Rationale: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."
Answer: c
Python program:
a = 2 / 5
b = 200 / a
Problem: a and b r 2 men who enter into business and they invest rs 1000 , rs 2000 respectively . how will they divide the income of rs 5000
Options: a ) 33361667 , b ) 33391667 , c ) 33331666 , d ) 33331668 , e ) 33331669
Rationale: they invested in the ratio 1 : 2 a ' s share = 1 / 3 * 5000 = 1666 b ' s share = 2 / 3 * 5000 = 3333 answer : c
Answer: c
Python program:
a = 1000 + 2000 
b = a + 5000 
c = b * 2
d = c * 4
e = d * 2000
f = 2 + 1 
g = e / f
h = 2000 * 5000
i = g - h
Problem: if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 3 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 3 = 2 ^ 4 / 2 ^ 3 = 2 the answer is a .
Answer: a
Python program:
a = 2 ** 4
b = 2 ** 2
c = a / b
d = 2 ** c
e = 2 ** 3
f = d / e
Problem: a survey was taken among 100 brainiacs . of those surveyed , twice as many brainiacs likerebus teasers as math teasers . if 18 brainiacs like both rebus teasers and math teasers and 4 like neither kind of teaser , how many brainiacs like math teasers but not rebus teasers ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: let x brainiacs like only rebus teasers and y brainiacs like only math teasers . now , x + y = 100 - 18 - 4 = 78 . also given that , x + 18 = 2 ( y + 18 ) x = 2 y + 18 . 78 - y = 2 y + 18 3 y = 60 y = 20 so 20 brainiacs like math teasers but not rebus teasers answer : d
Answer: d
Python program:
a = 100 - 4
b = a + 18 
c = 1 + 2 
d = b / c
e = d - 18
Problem: in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 80 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 3,200 , d ) 4,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 80 ) * 100 = 2.5 % so , x * 2.5 % = 80 x = 3200 ans c ."
Answer: c
Python program:
a = 2 / 80
b = 80 / a
Problem: x is a positive integer of t less than 500 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: took me more than 2 mins to solve . that ' s how i did it . x is between 1 - 499 included . smallest number that can be written as 7 n + 1 ( 7 * 0 + 1 ) is 1 largest number that can be written as 7 n + 1 is ( 7 * 71 + 1 ) is 498 so there are total 72 numbers that can be written as 7 n + 1 because x can also be written as 3 m + 2 , we have to see how many numbers that can be written as 7 n + 1 also can be written as 3 m + 2 7 * 0 + 1 can not be written in the form 3 m + 2 7 * 1 + 1 can be written in the form 3 m + 2 7 * 2 + 1 can not be written in the form 3 m + 2 7 * 3 + 1 can not be written in the form 3 m + 2 7 * 4 + 1 can be written in the form 3 m + 2 here we see a sequence that one out of every 4 numbers can be written as 3 m + 1 72 / 4 = 24 numbers can be written as 3 m + 1 d is the answer
Answer: d
Python program:
a = 2 + 3 
b = 500 - a
c = b / 3
d = c / 7
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1400 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 28875 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1400 × 20.625 ) = 28875 . answer d"
Answer: d
Python program:
a = 5 * 5
b = 1400 * a
Problem: in a rectangular box measuring 12 inches by 14 inches by 16 inches if small rectangular boxes measuring 3 inches by 7 inches by 2 inches are arranged in it , what is the max number of boxes that fit into it ?
Options: a ) 23 , b ) 32 , c ) 44 , d ) 15 , e ) 64
Rationale: the 3 inch side should be aligned to the 12 inch side ( 4 layer ) 7 inch side should be aligned to the 14 inch side . ( 2 layer ) and 2 inch side should be aligned to the 16 inch side . ( 8 layer ) maximum number of rectangles = 4 * 2 * 8 = 64 answer is e
Answer: e
Python program:
a = 12 / 3
b = 14 / 7
c = a * b
d = 16 / 2
e = c * d
Problem: ashis ' s height is 25 % more than babji , by how much percent babji ' s height is less than ashis .
Options: a ) 30 % , b ) 25 % , c ) 75 % , d ) 20 % , e ) none of these
Rationale: explanation : solution : babji is less than ashis by ( 25 / ( 100 + 25 ) * 100 ) % = 20 % answer : d
Answer: d
Python program:
a = 100 + 25 
b = 25 / a
c = b * 100
Problem: what is the difference between the place value and the face value of 7 in the numeral 297832 ?
Options: a ) none of these , b ) 5993 , c ) 994 , d ) 5994 , e ) 995
Rationale: explanation : place value of 6 = 7000 face value of 6 = 7 difference = 6000 - 7 = 5993 answer : b
Answer: b
Python program:
a = 297832 / 7
b = a / 7
Problem: in a graduating class , 40 percent of the students are male . in this class , 40 percent of the male students and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.9 , b ) 0.72 , c ) 0.45 , d ) 0.35 , e ) 0.28
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.6 * 0.4 x + 0.8 * 0.6 x = 0.72 x the answer is b ."
Answer: b
Python program:
a = 40 / 100
b = 40 / 100
c = a * b
d = 20 / 100
e = 40 / 100
f = 1 - e
g = d * f
h = c + g 
i = 1 - h
Problem: what is the least number to be subtracted from 696 to make it a perfect square ?
Options: a ) 1 , b ) 16 , c ) 20 , d ) 71 , e ) 60
Rationale: "the numbers less than 696 and are squares of certain numbers are 676 , 625 . the least number that should be subtracted from 696 to make it perfect square = 696 - 676 = 20 . answer : c"
Answer: c
Python program:
a = 3 * 2
b = 10 + a 
c = 100 * b
d = c - 696
Problem: if the remainder is 12 when the integer n is divided by 22 , what is the remainder when 2 n is divided by 11 ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: "n = 22 k + 12 2 n = 2 ( 22 k + 12 ) = 4 * 11 k + 24 = 4 * 11 k + 2 * 11 + 2 = 11 j + 2 . the answer is b ."
Answer: b
Python program:
a = 12 * 2
b = a - 22
Problem: the average marks of a class of 30 students is 40 and that of another class of 50 students is 80 . find the average marks of all the students ?
Options: a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 65
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 80 = 4000 sum of the marks for the class of 80 students = 1200 + 4000 = 5200 average marks of all the students = 5200 / 80 = 65 answer : e"
Answer: e
Python program:
a = 30 * 40
b = 50 * 80
c = a + b 
d = 30 + 50 
e = c / d
Problem: a jar contains a mixture of a & b in the ratio 4 : 1 . when 10 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 20 , e ) 25
Rationale: 10 litres of mixture that is replaced will contain 8 litres of a and 2 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 8 ] / [ k - 2 + 10 ] = 2 / 3 solve for k which is k = 4 so initial volume of liquid a = 4 k = 16 litres answer : c
Answer: c
Python program:
a = 4 + 1 
b = 4 / a
c = 4 + 1 
d = 4 / c
e = 10 * d
f = 4 + 1 
g = 4 / f
h = 2 + 3 
i = 2 / h
j = g - i
k = e / j
l = b * k
Problem: at an m & m factory , two types of m & ms are produced , red and blue . the m & ms are transported individually on a conveyor belt . anna is watching the conveyor belt , and has determined that 4 out of every 5 red m & ms are followed by a blue one , while one out of every 6 blue m & ms is followed by a red one . what proportion of the m & ms are red ?
Options: a ) 1 / 29 , b ) 2 / 29 , c ) 3 / 29 , d ) 4 / 29 , e ) 5 / 29
Rationale: suppose that the fraction of red m & ms is fr and the fraction of blue m & ms is fb . then the probability that anna sees a red one emerge next is fr . this probabil - ity can also be expressed using conditional probabilities as fr = p ( blue ) p ( red after blue ) + p ( red ) p ( red after red ) , or fr = fb ( 1 = 6 ) + fr ( 1 = 5 ) . likewise , we find fb = fr ( 4 = 5 ) + fb ( 5 = 6 ) . solving the system of equations gives fb = 24 29 and fr = 5 / 29 correct answer e
Answer: e
Python program:
a = 4 * 5
b = 4 + 5 
c = a + b 
d = 5 / c
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 50 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.5 * 300 / 450 = 150 / 450 = 1 / 3 the sum of the probabilities is 2 / 3 the answer is b ."
Answer: b
Python program:
a = 50 * 50
b = 40 / a
c = 1 - b
d = c * 150
e = d / 450
f = 50 * 50
g = 50 / f
h = g * 300
i = 50 * 50
j = 40 / i
k = j * 150
l = h + k 
m = l / 450
n = e + m
Problem: ravi and kavi start a business by investing â ‚ ¹ 5000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .
Options: a ) 2 : 72 , b ) 5 : 72 , c ) 7 : 72 , d ) 1 : 72 , e ) 3 : 72
Rationale: "ratio of profit = ratio of investments = 5000 : 72000 = 5 : 72 answer : b"
Answer: b
Python program:
a = 5000 / 72000
Problem: if a ( a + 2 ) = 99 and b ( b + 2 ) = 99 , where a ≠ b , then a + b =
Options: a ) - 2 , b ) - 5 , c ) - 8 , d ) - 10 , e ) - 12
Rationale: "i . e . if a = 9 then b = - 11 or if a = - 11 then b = 9 but in each case a + b = - 11 + 9 = - 2 answer : a"
Answer: a
Python program:
a = 99 / 10
b = 99 / 10
c = 99 / b
d = a + c
Problem: three numbers are in the ratio 5 : 4 : 6 and their average is 750 . the largest number is :
Options: a ) 30 , b ) 98 , c ) 900 , d ) 21 , e ) 22
Rationale: "explanation : let the numbers be 5 x , 4 x and 6 x , then , ( 5 x + 4 x + 6 x ) / 3 = 750 = > 15 x = 750 * 3 = > x = 150 largest number 6 x = 6 * 150 = 900 answer : c"
Answer: c
Python program:
a = 5 * 6
b = a * 100
c = 4 * 6
d = b + c
Problem: by selling 18 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 12 , c ) 6 , d ) 4 , e ) 9
Rationale: "80 % - - - 18 120 % - - - ? 80 / 120 * 18 = 12 answer : b"
Answer: b
Python program:
a = 100 + 20 
b = 100 - 20
c = 1 / b
d = a * c
e = 1 / d
f = e * 18
Problem: find the average of all numbers between 3 and 69 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 ) / 13 = 455 / 13 = 35 answer : option e"
Answer: e
Python program:
a = 5 * 3
b = 5 * 2
c = 5 + b 
d = a + c 
e = 5 * 4
f = d + e 
g = 4 + 1 
h = g * 5
i = f + h 
j = i / 5
Problem: if x is a sum of all even integers on the interval 13 . . . 63 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 13 , c ) 26 , d ) 25 , e ) 1014
Rationale: x = 14 + 16 + . . . + 62 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 62 ) / 2 * 25 = 38 * 25 . gcd of 25 and 39 * 25 is 25 . answer : d .
Answer: d
Python program:
a = 13 - 10
b = a + 2 
c = 13 - 10
d = c + 2 
e = b * d
Problem: joe invested a certain sum of money in a simple interest bond whose value grew to $ 260 at the end of 3 years and to $ 360 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 6 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %
Rationale: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 260 - $ 60 = 200 . the interest rate is $ 20 / $ 200 = 10 % the answer is c ."
Answer: c
Python program:
a = 360 - 260
b = a / 5
c = 360 - 260
d = c / 5
e = d * 3
f = 260 - e
g = b / f
h = g * 100