euclaise/mathqa_programs huggingface dataset:
Problem: what will be the ci on a sum of rs . 25000 after 3 years at the rate of 12 per year ?
Options: a ) rs . 10100 , b ) rs . 10110 , c ) rs . 10123.20 , d ) rs . 10135.50 , e ) rs . 10167.20
Rationale: amount = rs . 25000 x 1 + 12 3 100 = rs . 25000 x 28 x 28 x 28 25 25 25 = rs . 35123.20 c . i . = rs . ( 35123.20 - 25000 ) = rs . 10123.20 c
Answer: c
Python program:
a = 12 / 100
b = a + 1 
c = b ** 3
d = c * 25000
e = d - 25000
Problem: if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 10 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 30 km , c ) 18 km , d ) 16 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 10 ) / 15 5 x - 150 = > x = 30 km . answer : b"
Answer: b
Python program:
a = 15 - 10
b = 10 / a
c = 10 * b
Problem: a rectangular grass field is 85 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1450 , b ) 1971 , c ) 9676 , d ) 1679 , e ) 2691
Rationale: "area = ( l + b + 2 d ) 2 d = ( 85 + 55 + 2.5 * 2 ) 2 * 2.5 = > 725 725 * 2 = rs . 1450 answer : a"
Answer: a
Python program:
a = 2 * 5
b = 85 + a 
c = 2 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: the speed at which a man can row a boat in still water is 18 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 15.4 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 18 + 3 = 21 kmph = 21 * 5 / 18 = 35 / 9 m / s hence time taken to cover 60 m = 60 * 9 / 35 = 15.4 seconds . answer : b"
Answer: b
Python program:
a = 18 + 3 
b = a * const_0_2778
c = 60 / b
Problem: two trains are moving at 50 kmph and 70 kmph in opposite directions . their lengths are 170 m and 100 m respectively . the time they will take to pass each other completely is ?
Options: a ) 3 sec , b ) 8 sec , c ) 9 sec , d ) 5 sec , e ) 7 sec
Rationale: "70 + 50 = 120 * 5 / 18 = 100 / 3 mps d = 170 + 100 = 270 m t = 270 * 3 / 100 = 8 sec answer : b"
Answer: b
Python program:
a = 170 + 100 
b = 50 + 70 
c = b * const_0_2778
d = a / c
Problem: having scored 96 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 96 = 19 ( n + 4 ) = > n = 20 so , average score after 19 th innings = x + 4 = 24 . answer : e"
Answer: e
Python program:
a = 19 * 4
b = 96 - a
c = b + 4
Problem: what is the greatest possible length which can be used to measure exactly the lengths 8 m , 4 m 20 cm and 12 m 20 cm ?
Options: a ) 10 cm , b ) 30 cm , c ) 25 cm , d ) 20 cm , e ) 35 cm
Rationale: "required length = hcf of 800 cm , 420 cm , 1220 cm = 20 cm answer : option d"
Answer: d
Python program:
a = 12 * 4
Problem: what least number should be added to 1019 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 6
Rationale: 1019 ã · 25 = 40 with remainder = 19 19 + 6 = 25 . hence 6 should be added to 1019 so that the sum will be divisible by 25 answer : option e
Answer: e
Python program:
a = 25 - reminder
Problem: in a school having roll strength 286 , the ratio of boys and girls is 8 : 5 . if 22 more girls get admitted into the school , the ratio of boys and girls becomes
Options: a ) 12 : 7
b ) 10 : 7
c ) 8 : 7
d ) 4 : 3
e ) none
Rationale: solution : boys : girls = 8 : 5 ; ( let the boys = 8 x ; girl = 5 x ) total strength = 286 ; 8 x + 5 x = 286 ; 13 x = 286 ; or , x = 286 / 13 = 22 ; boys = 176 and girls = 110 ; 22 more girls get admitted then number of girls become , ( 5 x + 22 ) = 110 + 22 = 132 ; now , new ratio of boys and girls = 176 : 132 = 4 : 3 . answer : option d
Answer: d
Python program:
a = 8 + 5 
b = 286 / a
c = b * 8
d = 8 + 5 
e = 286 / d
f = e * 5
g = f + 22 
h = c / g
Problem: if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 5 ?
Options: a ) - 1 , b ) 0 , c ) 6 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 5 = x 2 ( x - 2 ) 2 + 5 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 5 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 5 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 5 = ( 2 - 1 ) 2 = 1 + 5 = 6 correct option : c"
Answer: c
Python program:
a = math.sqrt(2)
b = 1 + a 
c = b ** 2
d = math.sqrt(2)
e = 1 + d 
f = e - 2
g = f ** 2
h = c * g
i = h + 4
Problem: the ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17 : 325 . the value of n is
Options: a ) 15
b ) 25
c ) 35
d ) 30
e ) none of these
Rationale: sum of 1 st n natural no . s is n ( n + 1 ) / 2 , sum of sqaures of 1 st n natural no . s is n ( n + 1 ) ( 2 n + 1 ) / 6 , the ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers = n ( n + 1 ) ( 2 n + 1 ) * 2 * 2 / ( n * n * ( n + 1 ) * ( n + 1 ) ) = 2 ( 2 n + 1 ) / ( 3 n ( n + 1 ) ) now by hit and trial for the given options , if we put 25 then this will give 17 / 325 therefore the answer is 25 answer : b
Answer: b
Python program:
a = 325 + 100 
b = a / 17
Problem: harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1065 , d ) 1075 , e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 . b )"
Answer: b
Python program:
a = 8 * 70
b = 9 * 55
c = a + b
Problem: if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 9 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 8 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 9 x < = 2 x > = - 4 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 4 × - 6 = 24 minimum possible value of xy is - 4 × 8 = - 32 - 32 + 24 = - 8 answer : b"
Answer: b
Python program:
a = math.sqrt(9)
b = math.sqrt(64)
c = a + b
Problem: the difference between a two - digit number and the number obtained by interchanging the two digits is 63 . which is the smaller of the two numbers ?
Options: a ) 29 , b ) 70 , c ) 92 , d ) can not be determined , e ) none of these
Rationale: "explanation : let the ten ' s digit be x and units digit by y . then , ( 10 x + y ) - ( 10 y + x ) = 63 9 ( x - y ) = 63 x - y = 7 thus , none of the numbers can be determined . answer is d"
Answer: d
Python program:
a = 10 - 1
b = 63 / a
Problem: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 12 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 3120 , b ) 3330 , c ) 3540 , d ) 3750 , e ) 3960
Rationale: "the distance the sound traveled to the man is 12 * 330 = 3960 meters the answer is e ."
Answer: e
Python program:
a = 330 * 12
Problem: how many positive integers less than 5,000 are evenly divisible by neither 13 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 13 5000 / 13 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 13 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 13 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4349 answer e ."
Answer: e
Python program:
a = 4 + 13 
b = a - 1
c = math.factorial(b)
d = math.factorial(13)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 900 km , b ) 800 km , c ) 600 km , d ) 690 km , e ) 609 km
Rationale: explanation : d = 30 * 5 = 150 rs = 40 – 30 = 10 t = 150 / 10 = 15 d = 40 * 15 = 600 km answer : option c
Answer: c
Python program:
a = 3 + 2 
b = 30 * a
c = 40 - 30
d = b / c
e = d * 40
Problem: what is difference between biggest and smallest fraction among 2 / 5 , 3 / 4 , 4 / 5 and 5 / 6
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 2 / 5 = . 4 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 2 / 5 their difference is 5 / 6 - 2 / 5 = 13 / 30 option e"
Answer: e
Python program:
a = 4 / 5
b = 2 / 5
c = a - b
Problem: a 5 % stock yields 10 % . the market value of the stock is :
Options: a ) rs . 56 , b ) rs . 55 , c ) rs . 50 , d ) rs . 90 , e ) rs . 75
Rationale: "explanation : for an income of rs . 10 , investment = rs . 100 . for an income of rs 5 , investment = rs . 100 / 10 x 5 = rs 50 market value of rs . 100 stock = rs . 50 answer is c"
Answer: c
Python program:
a = 100 / 10
b = a * 5
Problem: a train 120 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: "speed of train relative to man : 120 / 6 * 18 / 5 km / hr = 72 km / hr let speed of train = x therefore x + 6 = 72 x = 72 - 6 x = 66 km / hr answer : c"
Answer: c
Python program:
a = 6 * const_0_2778
b = a * 6
c = 120 - b
d = c / 6
e = d / const_0_2778
Problem: every day daniel drives 64 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 45 % , e ) 55 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 64 miles at 4 miles / hour . d = ( r ) ( t ) 64 = ( 4 ) ( t ) 64 / 4 = 16 = t it takes 16 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 32 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 32 = ( 2 ) ( t ) 32 / 2 = 16 = t it takes 16 hours for the second part total time to drive home on monday = 4 + 16 = 20 hours we ' re asked by what percent 20 hours is greater than 16 hours . 20 / 16 = 1.25 , so it is 25 % greater . b"
Answer: b
Python program:
a = 32 / 2
b = 64 - 32
c = b * 2
d = a + c 
e = d - 64
f = e / 64
g = f * 100
Problem: what is the angle between the hands of a clock when time is 10 : 20 ?
Options: a ) 90 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 30 deg
Rationale: "angle between two hands = 20 h - 11 / 2 m = 20 * 10 - 20 * 11 / 2 = 200 - 110 = 90 deg answer : a"
Answer: a
Python program:
a = 3 * 2
b = 20 * a
c = b - 10
Problem: the diameter of a cylindrical tin is 14 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 230 , b ) 141 , c ) 66 , d ) 245 , e ) 21
Rationale: "r = 7 h = 5 π * 7 * 7 * 5 = 45 π cc answer : d"
Answer: d
Python program:
a = 14 / 2
b = volume_cylinder / (
Problem: if 40 men take 15 days to to complete a job , in how many days can 25 men finish that work ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: ans . 24 days
Answer: a
Python program:
a = 40 * 15
b = a / 25
Problem: it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 160 pages ?
Options: a ) 12 , b ) 18 , c ) 48 , d ) 20 , e ) 30
Rationale: if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 160 / 50 = 48 minutes to print 160 pages ( answer c )
Answer: c
Python program:
a = 4 * 2
b = a + 4 
c = 160 * b
d = c / 40
Problem: find the cost of fencing around a circular field of diameter 22 m at the rate of rs . 3 a meter ?
Options: a ) 288 , b ) 132 , c ) 772 , d ) 207.3 , e ) 261
Rationale: "2 * 22 / 7 * 11 = 69.1 69.1 * 3 = rs . 207.3 answer : d"
Answer: d
Python program:
a = 22 / 2
b = circumface * (
Problem: there are 6 people in the elevator . their average weight is 156 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 121 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 156 ) = 1057 - 936 = 121 . answer a
Answer: a
Python program:
a = 151 * 7
b = 6 * 156
c = a - b
Problem: each child has 2 pencils and 13 skittles . if there are 15 children , how many pencils are there in total ?
Options: a ) 30 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 15 = 30 . answer is a .
Answer: a
Python program:
a = 2 * 15
Problem: if a certain number x is divided by 62 , the reminder is 7 . what is the reminder when x + 11 is divided by 31 ?
Options: a ) 3 , b ) 5 , c ) 18 , d ) 6 , e ) 8
Rationale: x can be written as 62 k + 7 or x = 7 , 69,131 , etc . x + 11 = 62 k + 7 + 11 = 62 k + 18 or x + 11 = 18 , 80,142 etc . when divided by 31 , we will get the remainder 18 . c
Answer: c
Python program:
a = 7 + 11
Problem: if 7 ^ w is a factor of the product of the integers from 1 to 100 , inclusive , what is the largest value of w ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: so the question just means that we have to find all the multiples w of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e
Answer: e
Python program:
a = 100 / 7
b = 7 ** 2
c = 100 / b
d = a + c 
e = math.floor(d)
Problem: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 145 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 145 = 1450 3 * 100 + 5 * 150 = 1050 1450 – 1050 = 400 a"
Answer: a
Python program:
a = 3 + 5 
b = a + 2 
c = b * 145
d = 5 * 150
e = c - d
f = 3 * 100
g = e - f
Problem: if 2 pipes take an hour to fill a tank , then how long should 8 pipes take to fill the same tank ?
Options: a ) 20 min , b ) 10 min , c ) 15 min , d ) 25 min , e ) 30 min
Rationale: if 2 pipes take an hour to fill a tank , then 8 pipes will take 2 * 60 / 8 = 15 mins to dig a ditch of the same type . answer : c
Answer: c
Python program:
a = 2 * const_60
b = a / 8
Problem: there are 6 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 12
Rationale: method 2 : each person is one participant of 4 games . so there are in all 4 * 6 = 24 instances of one participant games . but each game has 2 participants so total number of games = 24 / 2 = 12 e
Answer: e
Python program:
a = 6 * 4
b = a / 2
Problem: a jar full of whisky contains 30 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 1 / 3 . hence , a is the correct answer ."
Answer: a
Python program:
a = 30 - 26
b = 30 - 19
c = a / b
Problem: worker a takes 4 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 40 / 14 , d ) 60 / 9 , e ) 80 / 9
Rationale: one day work of a = 1 / 4 one day work of b = 1 / 10 so one day work of a and b together = 1 / 4 + 1 / 10 = 14 / 40 so total days required = 40 / 14 answer : c
Answer: c
Python program:
a = 1 / 4
b = 1 / 10
c = a + b 
d = 1 / c
Problem: express a speed of 30 kmph in meters per second ?
Options: a ) 10 mps , b ) 8 mps , c ) 9 mps , d ) 7 mps , e ) 12 mps
Rationale: "30 * 5 / 18 = 8 mps answer : b"
Answer: b
Python program:
a = const_0_2778 * 30
Problem: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 100 more than the correct answer . find the number .
Options: a ) 192 , b ) 280 , c ) 384 , d ) 400 , e ) 500
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 100 25 * x / 48 = 100 x = 192 answer a"
Answer: a
Python program:
a = 100 * 16
b = a * 6
c = 5 * 16
d = 5 * 6
e = c - d
f = b / e
Problem: a boat running up stram takes 6 hours to cover a certain distance , while it takes 9 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 1 , c ) 4 : 5 , d ) 7 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 9 ( x - y ) 6 x + 6 y = 9 x - 9 y 15 y = 3 x 5 y = x x / y = 5 / 1 5 : 1 answer : option b"
Answer: b
Python program:
a = 9 - 6
Problem: the cost price of a radio is rs . 1900 and it was sold for rs . 1330 , find the loss % ?
Options: a ) 18 % , b ) 31 % , c ) 30 % , d ) 45 % , e ) 12 %
Rationale: "1900 - - - - 570 100 - - - - ? = > 30 % answer : c"
Answer: c
Python program:
a = 1900 - 1330
b = a / 1900
c = b * 100
Problem: someone on a skateboard is traveling 13 miles per hour . how many feet does she travel in 25 seconds ? ( 1 mile = 5280 feet )
Options: a ) 476.75 ft , b ) 450 ft , c ) 480 ft , d ) 490 ft , e ) 500 ft
Rationale: "per second = > 13 * 5280 ft / 60 * 60 = 19.07 ft 25 seconds = > 19.07 * 25 = 476.75 ft answer : a"
Answer: a
Python program:
a = 13 * 5280
b = a / 3600
c = 25 * b
Problem: there are 4 more women than there are men on a local co - ed softball team . if there are a total of 14 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 6 / 10 , e ) 5 / 9
Rationale: "w = m + 4 w + m = 14 m + 4 + m = 14 2 m = 10 m = 5 w = 9 ratio : 5 : 9 ans : e"
Answer: e
Python program:
a = 14 - 4
b = 1 + 1 
c = a / b
d = 14 - 4
e = 1 + 1 
f = d / e
g = f + 4 
h = c / g
Problem: 8900 ÷ 6 ÷ 4 = ?
Options: a ) 349 , b ) 541.75 , c ) 224.37 , d ) 370.833 , e ) none of these
Rationale: explanation : given exp . 8900 * 1 / 6 * 1 / 4 = 370.833 answer : d
Answer: d
Python program:
a = 8900 / 6
b = a / 4
Problem: the markup on a box of apples is 10 percent of the cost . the markup is what percent of the selling price ? ( markup = selling price - cost )
Options: a ) 9.09 % , b ) 10 % , c ) 12 1 / 2 % , d ) 15 % , e ) 16 2 / 3 %
Rationale: mp = 0.1 cp sp = cp + 0.1 cp = 1.1 cp hence mp = 0.1 / 1.1 sp = 1 / 1 sp . hence mp is 9.09 % of sp answer a
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = 10 / b
Problem: a train speeds past a pole in 15 seconds and a platform 100 m long in 40 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 100 m , e ) 145 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 40 = x / 15 x = 100 m . answer : d"
Answer: d
Python program:
a = 2 - 1
b = 100 * a
Problem: a train running at the speed of 30 km / hr crosses a pole in 12 seconds . what is the length of the train ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: "speed = ( 30 x ( 5 / 18 ) m / sec = ( 25 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 / 3 ) x 12 ) m = 100 m d"
Answer: d
Python program:
a = 30 * 1000
b = a / 3600
c = b * 12
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m is 2400 . their h . c . f is :
Options: a ) 40 , b ) 80 , c ) 120 , d ) 200 , e ) 220
Rationale: "let the numbers be 3 x , 4 x and 5 x . then , their l . c . m = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 * 40 ) , ( 4 * 40 ) and ( 5 * 40 ) . hence , required h . c . f = 40 . answer : a"
Answer: a
Python program:
a = 3 * 5
b = a * 100
c = 4 * 5
d = b + c
Problem: how many positive integers less than 9999 are such that the product of their digits is 210 .
Options: a ) 24 , b ) 58 , c ) 26 , d ) 34 , e ) 25
Rationale: "the prime factorization of 210 is 2 * 3 * 5 * 7 . so one way to make the right kind of number is to use those four digits , in any of the 4 ! = 24 orders you can put them in . notice though that we can also get 210 as a product by multiplying 5 , 6 and 7 . so we can make some 3 - digit numbers with the right product : 3 ! = 6 of them to be exact . but we can also get the right product using the digit 1 along with the digits 5 , 6 , and 7 . again we can arrange those digits in 4 ! = 24 orders . a"
Answer: a
Python program:
a = 4 + 210 
b = a - 1
c = math.factorial(b)
d = math.factorial(210)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: two stations p and q are 65 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 am , b ) 12 am , c ) 10.30 am , d ) 12.30 am , e ) 11 am
Rationale: assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 65 = > 20 x + 25 ( x - 1 ) = 65 = > 45 x = 90 = > x = 2 means , they meet after 2 hours after 7 am , ie , they meet at 9 am answer is a .
Answer: a
Python program:
a = 65 + 25 
b = 20 + 25 
c = a / b
d = c + 7
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase w in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase w = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Python program:
a = 385 - 320
b = a / 320
c = b * 100
Problem: a man saves 10 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 5 % , he is only able to save rs . 400 per month . what is his monthly salary ?
Options: a ) rs . 6500 , b ) rs . 7500 , c ) rs . 7200 , d ) rs . 7273 , e ) rs . 6300
Rationale: "income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 5 / 100 ) = rs . 94.5 present savings = 100 – 94.5 = rs . 5.50 if savings is rs . 5.50 , salary = rs . 100 if savings is rs . 400 , salary = 100 / 5.5 * 400 = 7273 answer : d"
Answer: d
Python program:
a = 400 * 100
b = 100 - 10
c = 100 - 10
d = 5 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g