euclaise/mathqa_programs huggingface dataset:
Problem: during a certain two - week period , 80 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 15 a , c ) 20 a , d ) 1 / 25 a , e ) 30 a
Rationale: "movies : 80 % comedies . 20 % remaining genre . now in this 20 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 4 x . total 5 x . 5 x = 20 ; x = 4 action movies : 4 % drama movies : 16 % we can say that out of 100 z , : comedies : 80 z action : 4 z drama : 16 z now action movies werea this means : a = 4 z . z = ( a / 4 ) comedies : 80 z = 80 * ( a / 4 ) 20 a c is the answer ."
Answer: c
Python program:
a = 4 + 1 
b = 80 / a
c = math.floor(b)
Problem: ( 100 x 60 ) + ( 138 x 400 ) = ? x 60
Options: a ) 880 , b ) 550 , c ) 1100 , d ) 1020 , e ) 600
Rationale: "explanation : ? = ( 100 x 60 ) + ( 138 x 400 ) / 60 = 6000 + 55200 / 60 = 1020 answer : option d"
Answer: d
Python program:
a = 4 + 1 
b = a ** 4
c = 100 * b
Problem: the speed of the boat in still water in 12 kmph . it can travel downstream through 42 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4.2 hours , d ) 5 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 42 / 3 = 14 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 14 / 2 = 10 km / hr so time taken in upstream = 42 / 10 = 4.2 hrs answer : c"
Answer: c
Python program:
a = 42 / 3
b = a - 12
c = 12 - b
d = 42 / c
Problem: tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bearsa number which is a multiple of 3 ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 ] p ( e ) = n ( e ) / n ( s ) = 6 / 20 = 3 / 10 c"
Answer: c
Python program:
a = 20 / 3
b = a / 20
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 4 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 8 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 4 ) = l cx = 4 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 4 l = 1 / 8 answer will be d"
Answer: d
Python program:
a = 1 / 4
b = 2 / 3
c = 1 - b
d = 2 / 3
e = c / d
f = a * e
Problem: harry started a 6 - mile hike with a full 7 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 5 miles of the hike ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 5 , e ) 4 / 5
Rationale: "a . no of cups leaked during the trip = 2 cups . no of cups harry drank = 4 cups . no of cups harry drank during the first 5 miles = 4 . drink / mile = 4 / 5 answer : e"
Answer: e
Python program:
a = 7 - 2
b = a - 1
c = b - 1
d = c / 5
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 60 kg . what is the correct weight ?
Options: a ) 58.6 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: actual total weight is ( 20 x 58.4 - 56 + 60 ) = 1172 kgs actual average weight is 1172 / 20 = 58.6 kgs a
Answer: a
Python program:
a = 58 * 4
b = 60 - 56
c = a + b 
d = c / 20
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 4,700 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 14.0 , b ) 13.0 , c ) 12.0 , d ) 11.0 , e ) 10.0
Rationale: "solution : h stopped 700 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . c"
Answer: c
Python program:
a = 500 / 100
b = a - 1
c = 800 / 1
d = b / c
e = 800 / 1
f = 500 / 700
g = e - f
h = d * g
i = 500 / 700
j = i + 1 
k = h / j
l = 500 / 100
m = l - 1
n = 800 / 700
o = m / n
p = k + o 
q = 6 + p
Problem: p and q are the only two applicants qualified for a short - term research project that pays 420 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 3 , b ) $ 5 , c ) $ 7 , d ) $ 9 , e ) $ 11
Rationale: let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 420 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 420 / 30 = $ 14 p ' s hourly wage is 420 / ( t - 10 ) = $ 21 which is $ 7 per hour more . the answer is c .
Answer: c
Python program:
a = 3 / 2
b = a - 1
c = 10 / b
d = 420 / c
e = 3 / 2
f = e - 1
g = 10 / f
h = g + 10 
i = 420 / h
j = d - i
Problem: log ( a ( a ( a ) ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 here base is a .
Options: a ) 0 , b ) 21 / 64 , c ) 1 , d ) 22 / 63 , e ) 23 / 65
Rationale: log ( a ( a ( a ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 1 + 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 16 ) ^ 1 / 4 = > log ( a ^ 1 + 5 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 64 ) = > 21 / 64 log ( a ) = > 21 / 64 answer : b
Answer: b
Python program:
a = 1 / 4
b = 1 + a 
c = b / 4
d = 1 + c 
e = d / 4
Problem: rahul is 30 years older than his daughter mary . in 20 years rahul will be twice as old as mary . what is mary current age .
Options: a ) 12 , b ) 14 , c ) 10 , d ) 16 , e ) 18
Rationale: now : mary = x , rahul = x + 30 in 20 years mary = x + 20 , rahul = x + 30 + 20 or 2 ( x + 20 ) x + 30 + 20 = 2 ( x + 20 ) x + 50 = 2 x + 40 50 - 40 = 2 x - x x = 10 mary is 10 years old answer : c
Answer: c
Python program:
a = 30 + 20 
b = 20 * 2
c = a - b
Problem: a rectangular field has to be fenced on three sides leaving a side of 2020 feet uncovered . if the area of the field is 680680 sq . feet , how many feet of fencing will be required ?
Options: a ) 95 , b ) 92 , c ) 88 , d ) 82 , e ) 80
Rationale: "explanation : area of the field = 680 sq . feet . length of the adjacent sides are 20 feet and 680 / 20 = 34 feet . required length of the fencing = 20 + 34 + 34 = 88 feet answer : option c"
Answer: c
Python program:
a = 680680 / 2020
b = rectangle_perimeter - (
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 13 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 320 , b ) 300 , c ) 310 , d ) 315 , e ) 330
Rationale: "( 3500 * 3 * 3 ) / 100 = > 315 answer : d"
Answer: d
Python program:
a = 3500 * 13
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11 - sided polygon ) ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 11
Rationale: "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 8 = 1 / 4 . the answer is c ."
Answer: c
Python program:
a = 11 - 3
b = 11 * a
c = b / 2
d = 11 / c
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 6 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 41 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.94 * 150 x = 141 x hence total profit = 41 % option e"
Answer: e
Python program:
a = 100 - 6
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100
Problem: the perimeter of a semi circle is 144 cm then the radius is ?
Options: a ) 22
b ) 28
c ) 99
d ) 77
e ) 16
Rationale: 36 / 7 r = 144 = > r = 28 answer : b
Answer: b
Python program:
a = 2 + math.pi 
b = 144 / a
Problem: find the area of the square , one of whose diagonals is 3.8 m long ?
Options: a ) 7.22 m ^ 2
b ) 3.86 m ^ 2
c ) 8.96 m ^ 2
d ) 2.68 m ^ 2
e ) 7.89 m ^ 2
Rationale: area of the square = 1 / 2 ( diagonal ) ^ 2 = ( 1 / 2 * 3.8 * 3.8 ) m ^ 2 = 7.22 m ^ 2 answer ( a )
Answer: a
Python program:
a = 1 / 2
b = 3 * 8
c = a * b
Problem: in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 1500 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 30,000 , b ) 15,450 , c ) 45,000 , d ) 60,000 , e ) 15,000
Rationale: "total # of votes cast = 100 x , out of these , let the # of votes won by the winner = w , and for the loser ( l ) = 100 x - w . given that w - ( 100 x - w ) = 10 % of total votes cast = 10 x thus , 2 w - 100 x = 10 x → → w = 55 x and l = 100 x - 55 x = 45 x . according to the new condition , if the loser had won 45 x + 1500 votes , then , ( 45 x + 1500 ) - ( 55 x - 1500 ) = 10 % of total votes cast = 10 x thus , 3000 = 20 x and 100 x = 15000 answer : e"
Answer: e
Python program:
a = 10 / 100
b = 1500 / a
Problem: in a certain game of dice , the player ’ s score is determined as a sum of three throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 216 , c ) 1 / 221 , d ) 1 / 84 , e ) 1 / 42
Rationale: "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and john will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : b ."
Answer: b
Python program:
a = 22 / 3
b = a - 1
c = b ** 2
d = 1 / c
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 8 , - 2 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "the midpoint of ( 2,8 ) and ( 8 , - 2 ) is ( 5,3 ) . the slope of a line through ( 0 , - 2 ) and ( 5,3 ) is ( 3 - ( - 2 ) ) / ( 5 - 0 ) = 5 / 5 = 1 the answer is d ."
Answer: d
Python program:
a = 8 - 2
b = a / 2
c = b + 2 
d = 2 + 8 
e = d / 2
f = c / e
Problem: the sale price sarees listed for rs . 340 after successive discount is 20 % and 15 % is ?
Options: a ) 298 , b ) 231 , c ) 342 , d ) 876 , e ) 291
Rationale: "340 * ( 80 / 100 ) * ( 85 / 100 ) = 231 answer : b"
Answer: b
Python program:
a = 340 * 20
b = a / 100
c = 340 - b
d = 340 * 20
e = d / 100
f = 340 - e
g = f * 15
h = g / 100
i = c - h
Problem: a train crosses a platform of 100 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 88 , c ) 77 , d ) 62 , e ) 350
Rationale: "length of the train be â € ˜ x â € ™ x + 100 / 15 = x + 250 / 20 4 x + 400 = 3 x + 750 x = 350 m answer : e"
Answer: e
Python program:
a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 100 * e
g = c - f
Problem: if 0.75 : x : : 5 : 9 , then x is equal to :
Options: a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 1.35 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 9 ) x = 6.75 / 5 = 1.35 answer : d"
Answer: d
Python program:
a = 0 * 75
b = a / 5
Problem: in the xy - plane , the point ( 3 , 1 ) is the center of a circle . the point ( 3 , - 2 ) lies inside the circle and the point ( - 2 , 1 ) lies outside the circle . if the radius r of the circle is an integer , then r =
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 3 , 1 ) and the point inside the circle ( 3 , - 2 ) is 3 units ( both points are on x = 3 line so the distance will simply be 1 - ( - 2 ) = 3 ) so the radius must be more than 3 units . the distance between the center ( 3,1 ) and the point outside the circle ( - 2,1 ) is 5 units ( both points are on y = 1 line so the distance will simply be 3 - ( - 2 ) = 5 ) so the radius must be less than 5 units , which implies 3 < r < 5 , thus as r is an integer then r = 4 . answer : c ."
Answer: c
Python program:
a = 2 + 2 
b = a + 1
Problem: s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits t are in s ( 99 ) ?
Options: a ) t = 350 , b ) t = 353 , c ) t = 354 , d ) t = 356 , e ) 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"
Answer: b
Python program:
a = const_60 + 4 
b = a + 4 
c = const_60 + 4 
d = c + 4 
e = d * 4
f = b + e 
g = 3 * 1
h = 3 * 2
i = h * 2
j = g + i 
k = f + j
Problem: you have been given a physical balance and 7 weights of 57 , 55 , 45 , 44 , 43 , 41 and 85 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 199 kgs .
Options: a ) 198 , b ) 195 , c ) 196 , d ) 197 , e ) 200
Rationale: "85 + 55 + 57 = 197 answer : d"
Answer: d
Python program:
a = 55 + 45 
b = a + 44 
c = b + 41
Problem: the average age of 7 men increases by 4 years when two women are included in place of two men of ages 26 and 30 years . find the average age of the women ?
Options: a ) 42 , b ) 40 , c ) 30 , d ) 18 , e ) 11
Rationale: "explanation : 26 + 30 + 7 * 4 = 84 / 2 = 42 answer : a"
Answer: a
Python program:
a = 26 + 30 
b = 7 * 4
c = a + b 
d = c / 2
Problem: 450.271 + 369.422 ÷ 0.03 - 108.612 x 2.001 = ?
Options: a ) 12980 , b ) 12532 , c ) 12610 , d ) 12430 , e ) 12560
Rationale: "explanation : ? = 450.271 + ( 369.422 ÷ 0.03 ) - ( 108.612 x 2.001 ) ≈ 450 + 369 / 0.03 - ( 109 x 2 ) ≈ 450 + 12300 - 218 ≈ 12532 answer : option b"
Answer: b
Python program:
a = 369 * 422
b = 108 / 612
c = a / b
d = 450 + 271
Problem: how many 3 - digit numerals begin with a digit that represents a prime number ?
Options: a ) 16 , b ) 80 , c ) 400 , d ) 180 , e ) 240
Rationale: prime digits 2 , 35 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : c
Answer: c
Python program:
a = 100 * 3
b = a + 100
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 150 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: "l + k = 150 and so k = 150 - l l + 10 = 1.5 k = 1.5 ( 150 - l ) 2.5 l = 215 l = 86 the answer is b ."
Answer: b
Python program:
a = 100 + 50 
b = a / 100
c = 150 * b
d = c - 10
e = 100 + 50 
f = e / 100
g = f + 1 
h = d / g
Problem: a group of workers had agreed on a very strange payment schedule . each of them would get $ 100 for every day that they had worked , but for every day they did not work will have to return $ 25 . after 30 days they realised they did not earn any money . how many days the workers did not work ?
Options: a ) 15 , b ) 24 , c ) 30 , d ) 20 , e ) 10
Rationale: the workers earn 4 times more than they have to return per day for not working . so the number of days they did not work is 4 times the number of days they worked . that means 24 days of not working in 30 days . correct answer b
Answer: b
Python program:
a = 25 * 30
b = 100 + 25 
c = a / b
d = 30 - c
Problem: a pump can fill a tank with a water in 2 hours . because of a leak , it took 2 x 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 5 hrs , b ) 7 hrs , c ) 12 hrs , d ) 14 hrs , e ) none
Rationale: "sol . work done by the leak in 1 hour = ( 1 / 2 - 3 / 7 ) = 1 / 14 . ∴ leak will empty the tank in 14 hrs . answer d"
Answer: d
Python program:
a = 1 / 2
b = 1 / 3
c = 2 + b 
d = 1 / c
e = a - d
f = 1 / e
Problem: if 2 x + y = 7 and x + 2 y = 5 , then ( 2 x + 2 y ) / 3 =
Options: a ) 3 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 2 * 3 + 2 * 1 ) / 3 = ( 6 + 3 ) / 3 = 9 / 3 = 3 a"
Answer: a
Python program:
a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l 
n = m / 2
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 25 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 6.6 miles , d ) 8 miles , e ) 10 miles
Rationale: answer : c ) 6.6 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 25 / ( 5 + 25 ) = 6.6 m / hr the distance between schoolhome should be half of that . ie . 6.6 miles answer c
Answer: c
Python program:
a = 1 / 5
b = 1 / 25
c = a + b 
d = 1 / c
e = d * const_1_6
Problem: what is the units digit of ( 12 ^ 3 ) ( 15 ^ 4 ) ( 31 ^ 7 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the units digit of 12 ^ 3 is the units digit of 2 ^ 3 which is 8 . the units digit of 15 ^ 4 is the units digit of 5 ^ 4 which is 5 . the units digit of 31 ^ 7 is the units digit of 1 ^ 7 which is 1 . the units digit of 8 * 5 * 1 is 0 . the answer is a ."
Answer: a
Python program:
a = math.factorial(12)
b = math.factorial(3)
c = a * b
d = math.factorial(12)
e = math.factorial(4)
f = d * e
g = c + f 
h = g / 12
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % ?
Options: a ) 37.5 % , b ) 37.6 % , c ) 38.5 % , d ) 17.5 % , e ) 37.2 %
Rationale: "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 88 gain % = 24 / 64 * 100 = 37.5 % . answer : a"
Answer: a
Python program:
a = 100 - 12
b = a / 64
c = b - 1
d = c * 100
Problem: the average of 25 results is 18 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 74 , b ) 75 , c ) 69 , d ) 78 , e ) 45
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 18 or , x = 78 . answer : option d"
Answer: d
Python program:
a = 25 * 18
b = 12 * 17
c = a - b
d = 12 * 14
e = c - d
Problem: an woman sitting in a train which is travelling at 20 kmph observes that a goods train travelling in a opposite direction , takes 15 seconds to pass him . if the goods train is 300 m long , find its speed .
Options: a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60
Rationale: relative speed = ( 300 / 15 ) m / s = ( 300 / 15 ) * ( 18 / 5 ) = 72 kmph speed of goods train = 72 - 20 = 52 kmph answer is a
Answer: a
Python program:
a = speed - (
Problem: a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is
Options: a ) 145 , b ) 185 , c ) 253 , d ) 370 , e ) none
Rationale: solution let the number be x . then 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digit is smaller than the units digit . hence , required number = 253 . answer c
Answer: c
Python program:
a = 10 / 2
b = a - 3
c = 100 * b
d = 10 / 2
e = d * 10
f = c + e 
g = f + 3
Problem: what least number must be subtracted from 7538 so that remaining no . is divisible by 14
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 7538 by 14 we get the remainder 6 , so 6 should be subtracted option c"
Answer: c
Python program:
a = 7538 / 14
b = math.floor(a)
c = b * 14
d = 7538 - c
Problem: in a survey of parents , exactly 5 / 6 of the mothers and 3 / 4 of the fathers held full - time jobs . if 60 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 12 % , b ) 15 % , c ) 18 % , d ) 20 % , e ) 25 %
Rationale: "fathers without full - time jobs are 1 / 4 * 2 / 5 = 2 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 6 * 3 / 5 = 1 / 10 of all the parents surveyed . the percent of parents without full - time jobs is 2 / 20 + 1 / 10 = 1 / 5 = 20 % the answer is d ."
Answer: d
Python program:
a = 100 - 60
b = 3 / 4
c = 100 - 60
d = b * c
e = a - d
f = 5 / 6
g = f * 60
h = 60 - g
i = e + h
Problem: on a scale of map , 0.4 cm represents 5.3 km . if the distance between the points on the map is 64 cm , the actual distance between these points is :
Options: a ) 9 km , b ) 72.5 km , c ) 190.75 km , d ) 848 km , e ) none of these
Rationale: explanation : let the actual distance be x km . then , more distance on the map , more is the actual distance ( direct proportion ) = > 0.4 : 64 : : 5.3 : x = > 0.4 x = 64 x 5.3 = > x = 64 x 5.3 / 0.4 = > x = 848 answer : d
Answer: d
Python program:
a = 5 / 3
b = a * 64