euclaise/mathqa_programs huggingface dataset:
Problem: the c . p of 20 pens is equal to the s . p of 12 pens . find his gain % or loss % ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "20 cp = 12 sp 20 - - - 8 cpgain 100 - - - ? = > 40 % answer : d"
Answer: d
Python program:
a = 20 - 12
b = a / 20
c = b * 100
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 15 % solution ?
Options: a ) a ) 5.8 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 15 / 100 200 + 20 x = 300 + 3 x 17 x = 100 x = 5.8 answer is a
Answer: a
Python program:
a = 15 - 10
b = 15 / 100
c = 1 - b
d = a / c
Problem: how many multiples of 4 are there between 16 and 112 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 4 up to 4 * 28 . 28 - 4 + 1 = 25 . the answer is e ."
Answer: e
Python program:
a = 112 - 16
b = a / 4
c = b + 1
Problem: jill has 35 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 60 , c ) 9 , d ) 12 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 35 1 3 / 4 w = 35 w = 20 the total number of jars = 3 w = 60 answer : b
Answer: b
Python program:
a = 1 / 2
b = const_0_25 + a 
c = 1 + b 
d = 35 / c
e = d * 3
Problem: a cycle is bought for rs . 850 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 27 , c ) 99 , d ) 88 , e ) 11
Rationale: 850 - - - - 180 100 - - - - ? = > 27 % answer : b
Answer: b
Python program:
a = 1080 - 850
b = a / 850
c = b * 100
Problem: the number of singles that a baseball player hit increased 5 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 2 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 4 : 3 , b ) 9 : 11 , c ) 3 : 1 , d ) 2 : 1 , e ) 11 : 3
Rationale: "soln : - 1.05 s + 0.98 d = 1.02 [ s + d ] 0.03 s = 0.04 d s / d = 4 / 3 answer : a"
Answer: a
Python program:
a = 100 - 2
b = 100 + 5 
c = a / b
Problem: a person is traveling at 25 km / hr and reached his destiny in 5 hr find the distance ?
Options: a ) 100 km , b ) 95 km , c ) 135 km , d ) 80 km , e ) 125 km
Rationale: speed = 25 km / hr time = 5 hr distance = 25 * 5 = 125 km answer is e
Answer: e
Python program:
a = 25 * 5
Problem: in a theater , the first row has 14 seats and each row has 3 more seats than previous row . if the last row has 50 seats , what is the total number of seats in the theater ?
Options: a ) 404 , b ) 408 , c ) 412 , d ) 416 , e ) 420
Rationale: the number of seats in the theater is 14 + ( 14 + 3 ) + . . . + ( 14 + 36 ) = 13 ( 14 ) + 3 ( 1 + 2 + . . . + 12 ) = 13 ( 14 ) + 3 ( 12 ) ( 13 ) / 2 = 13 ( 14 + 18 ) = 13 ( 32 ) = 416 the answer is d .
Answer: d
Python program:
a = 14 + 50 
b = a / 2
c = 50 - 14
d = c + 3 
e = d / 3
f = b * e
Problem: a train 200 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 85 kmph , b ) 115 kmph , c ) 105 kmph , d ) 95 kmph , e ) 125 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 200 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 3600 x = 115 kmph answer is b"
Answer: b
Python program:
a = 200 / 6
b = a / const_0_2778
c = b - 5
Problem: 8 ^ 100 is divisible by 17 then find the remainder ?
Options: a ) 8 , b ) 10 , c ) 16 , d ) 17 , e ) 18
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Python program:
a = 17 - 8
Problem: a student scored an average of 80 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 21 , b ) 27 , c ) 26 , d ) 80 , e ) 28
Rationale: "given m + p + c = 80 * 3 = 240 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 240 = 80 . answer : d"
Answer: d
Python program:
a = 90 * 2
b = 70 * 2
c = a + b 
d = 80 * 3
e = c - d
Problem: in an election , candidate douglas won 54 percent of the total vote in counties x and y . he won 62 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 25 % , b ) 28 % , c ) 32 % , d ) 38 % , e ) 40 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 62 % voted means 62 * 200 = 124 votes combined for xy has 300 voters and voted 54 % so total votes = 162 balance votes = 162 - 124 = 38 as y has 100 voters so 38 votes means 38 % of votes required ans d"
Answer: d
Python program:
a = 54 / 100
b = 62 / 100
c = 2 / 3
d = b * c
e = a - d
f = 1 / 3
g = e / f
h = g * 100
Problem: the radius of a wheel is 14.6 cm . what is the distance covered by the wheel in making 100 resolutions ?
Options: a ) 754 m , b ) 704 m , c ) 90.524 m , d ) 706 m , e ) 91.688 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 100 resolutions . = 100 * 2 * 22 / 7 * 14.6 = 9168.8 cm = 91.688 m answer : e"
Answer: e
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 14
g = f * 2
h = g * 100
i = h / 100
Problem: harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 2 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 2 m = 30 books total = 40 books m ' = 40 = 5 / 6 * 60 ratio : 5 / 6 ans : e
Answer: e
Python program:
a = 1 / 3
b = 1 / 2
c = a * b
d = 1 - c
Problem: what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 448 * 348 ) ^ 2
Options: a ) 86 , b ) 76 , c ) 56 , d ) 36 , e ) 16
Rationale: "( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 348 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,8 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 48 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 48 ) ) ^ 2 = ( 44 * 88 ) ^ 2 = 72 ^ 2 = 84 hence answer is a"
Answer: a
Python program:
a = 100 / 4
b = 2 * 3
c = 1 - 2
d = b * c
e = 1 - 2
f = d * e
g = 1 - 2
h = f * g
i = a + h 
j = i * 4
Problem: the number of sailors on a ship is 82 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 47 : 25 , d ) 22 : 25 , e ) 91 : 50
Rationale: "sailor = 1.82 * officer sailor / officer = 1.82 / 1 = 182 / 100 = 91 / 50 answer will be e"
Answer: e
Python program:
a = 82 + 100 
b = a / 100
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 50 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: the question is finding y such that ( 50 - y ) ! is a multiple of 50 . that means we need to have 2 * 5 ^ 2 in ( 50 - y ) ! 10 ! is the smallest factorial number with 2 * 5 ^ 2 as a factor . 50 - y = 10 y = 40 the answer is c .
Answer: c
Python program:
a = 50 / 2
b = 1 + 4 
c = a / b
d = 2 * c
e = 50 - d
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 9 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 18 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 9 ? 9 ^ 9 = ( 3 ^ 2 ) ^ 9 = 3 ^ 18 d . 18"
Answer: d
Python program:
a = 9 - 9
b = a * 9
Problem: the speed of a railway engine is 84 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
Options: a ) 19 , b ) 18 , c ) 16 , d ) 17 , e ) 14
Rationale: "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 84 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 84 - k * sqrt ( 9 ) = 84 - 3 k k = 20 now , we need to know : what value of n makes s go to zero ? 0 = 84 - 20 * sqrt ( n ) 20 * sqrt ( n ) = 84 sqrt ( n ) = 4.2 n = 4.2 ^ 2 > 17 with 18 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 17 is the maximum number of cars the engine can pull and still move . d"
Answer: d
Python program:
a = 84 - 24
b = math.sqrt(9)
c = a / b
d = 84 / c
e = d ** 2
Problem: a train covers a distance of 90 km in 20 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 675 , b ) 680 , c ) 685 , d ) 690 , e ) 695
Rationale: "speed = ( 90 / 20 * 60 ) km / hr = ( 270 * 5 / 18 ) m / sec = 75 m / sec . length of the train = 75 * 9 = 675 m . answer : option a"
Answer: a
Python program:
a = 90 / 20
b = a - 9
c = 90 / b
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 3 men and 2 women will do that task .
Options: a ) 4 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 13 / 16 , e ) 4 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 3 m + 2 w = 8 w answer is 8 / 14 = 4 / 7 answer : a"
Answer: a
Python program:
a = 8 - 2
b = 6 - 3
c = a / b
d = c * 3
e = d + 2 
f = 8 - 2
g = 6 - 3
h = f / g
i = 6 * h
j = i + 2 
k = e / j
Problem: a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 20 . if he got 360 marks in two subjects together how many marks did he got in english ?
Options: a ) 120,60 , b ) 240,120 , c ) 280,90 , d ) 220,140 , e ) none of them
Rationale: "let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 20 2 x - 3 y = 120 â € ¦ â € ¦ > ( 1 ) x + y = 360 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 240 and y = 120 answer is b ."
Answer: b
Python program:
a = 360 - 20
b = 1 / 2
c = 1 + b 
d = a / c
e = d + 20
Problem: in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is ?
Options: a ) 11 , b ) 82 , c ) 10 , d ) 28 , e ) 23
Rationale: "explanation : total employees = \ inline \ frac { ( 25 - 10 ) \ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c"
Answer: c
Python program:
a = 20 - 10
Problem: in the fifth grade at parkway elementary school there are 500 students . 350 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 . , d ) 91 . , e ) 115 .
Rationale: "total students = 500 boys = 350 , girls = 150 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 150 - 35 = 115 . correct option : e"
Answer: e
Python program:
a = 500 - 350
b = 250 * 86
c = b / 100
d = 250 - c
e = a - d
Problem: for what value of x between − 8 and 8 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 8 , b ) − 2 , c ) 0 , d ) 2 , e ) 8
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 8 will give the greatest value . . ans a"
Answer: a
Python program:
a = negate ** (
b = a + 2 
c = b - 16
Problem: what positive number , when squared , is equal to the cube of the positive square root of 16 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 16 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 64 = > x = 8 answer c"
Answer: c
Python program:
a = 1 / 2
b = 16 ** a
c = b ** 3
d = math.sqrt(c)
Problem: the difference of two numbers is 1515 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310
Rationale: "let the smaller number be x . then larger number = ( x + 1515 ) . x + 1515 = 6 x + 15 5 x = 1500 x = 300 smaller number = 300 . d )"
Answer: d
Python program:
a = 1515 + 15 
b = 6 - 1
c = a / b
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 115 mangoes .
Options: a ) 360 , b ) 383 , c ) 400 , d ) 406 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 115 mangoes = 115 * 3.33 = 383 . answer b"
Answer: b
Python program:
a = 1 / 10
b = 1 - a
c = 360 / b
d = c - 360
e = d / 12
f = e * 115
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability r that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability r = 1 / 24 . answer c ."
Answer: c
Python program:
a = 20 + 4 
b = 1 / a
Problem: a and b can do a work in 4 days , b and c in 5 days , c and a in 7 days . if a , b and c work together , they will complete the work in ?
Options: a ) 3 days , b ) 5 days , c ) 7 days , d ) 1 days , e ) 2 dasy
Rationale: "a + b 1 day work = 1 / 4 b + c 1 day work = 1 / 5 c + a 1 day work = 1 / 7 adding we get 2 ( a + b + c ) = 1 / 4 + 1 / 5 + 1 / 7 = 83 / 140 a + b + c 1 day work = 83 / 280 a , b , c can finish the work in 280 / 83 days = 3 days approximately answer is a"
Answer: a
Python program:
a = 1/(4)
b = 1/(5)
c = a + b 
d = 1/(7)
e = c + d 
f = e / 2
g = 1 / f
Problem: there are 9 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 62 , b ) 70 , c ) 72 , d ) 71 , e ) 76
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 9 and for second = 8 so total methods = 9 * 8 = 72 answer : c"
Answer: c
Python program:
a = math.comb(9, 2)
b = math.comb(9, 2)
c = a + b
Problem: how many cubes of 3 cm edge can be cut out of a cube of 18 cm edge
Options: a ) 36 , b ) 232 , c ) 216 , d ) 455 , e ) 363
Rationale: "number of cubes = ( 18 x 18 x 18 ) / ( 3 x 3 x 3 ) = 216 answer : c"
Answer: c
Python program:
a = volume_cube / (
Problem: 600 x 223 + 600 x 77 = ?
Options: a ) 180000 , b ) 138800 , c ) 658560 , d ) 116740 , e ) none of them
Rationale: "= 600 x ( 223 + 77 ) ( by distributive law ) = 600 x 300 = 180000 answer is a"
Answer: a
Python program:
a = 223 ** 600
b = 600 * a
Problem: a volume of 10976 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 2744 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10976 l can be kept in ( 10976 / 4 ) hemispheres ans . 2744 answer : d"
Answer: d
Python program:
a = 10976 / 4
Problem: at the end of the day , february 14 th , a florist had 150 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 15 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 50 % , b ) 25 % , c ) 250 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 150 s + l = 150 1 / 3 * 150 = 50 short - stemmed white = 20 short - stemmed pink = 15 = > short - stemmed red = 15 15 / p = 15 / r = > r = p so total long stemmed = 100 and long stemmed red + long stemmed pink = 100 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 150 = > r = 130 and r = 65 long stemmed r = 65 - 15 = 50 so long stemmed red / r = 50 / 100 = 50 % answer - a"
Answer: a
Python program:
a = 150 / 3
b = 150 - a
c = 150 / 3
d = c - 20
e = d - 15
f = b * e
g = 150 / 3
h = g - 20
i = h - 15
j = 15 + i 
k = f / j
l = 150 / 3
m = 150 - l
n = k / m
o = n * 100
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 260 before any discount ?
Options: a ) $ 130.00 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 210.00
Rationale: "original price : 260 $ max first discount = - 30 % thus : 260 ∗ ( 1 − 30 / 100 ) = 182 second discount on the discounted price = - 20 % thus : 182 ∗ ( 1 − 20 / 100 ) = 145,6 answer b ."
Answer: b
Python program:
a = 30 + 20 
b = a / 100
c = 260 * b
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 11 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 27,720
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , 2 * 5 , and 11 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 * 11 = 27,720 the answer is e ."
Answer: e
Python program:
a = math.lcm(1, 11)
Problem: carl bought 16 gumballs , lewis bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?
Options: a ) 20 , b ) 16 , c ) 22 , d ) 18 , e ) 24
Rationale: smallest gumballs = ( 19 - 16 ) + ( 19 - 12 ) + 19 = 29 largest gumballs = ( 25 - 16 ) + ( 25 - 12 ) + 25 = 47 difference = 47 - 29 = 18 d
Answer: d
Python program:
a = 25 * 3
b = 19 * 3
c = a - b
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 28 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 35
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 28 days whole work will be done by y in 28 * 5 / 4 = 35 days answer is e"
Answer: e
Python program:
a = 8 / 40
b = 1 - a
c = 1/(b)
d = 28 * c
Problem: find the principle on a certain sum of money at 7 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 939.6 , b ) 958.9 , c ) 927.78 , d ) 926.82 , e ) 902.1
Rationale: "1120 = p [ 1 + ( 7 * 12 / 5 ) / 100 ] p = 958.90 answer : b"
Answer: b
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 7
e = d / 100
f = e + 1 
g = 1120 / f
Problem: find the simple interest on rs . 69,600 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8700 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500
Rationale: "p = rs . 69600 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 69,600 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8700 answer is b ."
Answer: b
Python program:
a = 2 * 3
b = a * 100
c = b * 100
d = 3 * 3
e = d * 100
f = 3 + 2 
g = f * 2
h = e * g
i = c + h 
j = 16 * 3
k = j + 2 
l = k / 3
m = i * l
n = 3 * 3
o = 2 * 3
p = 2 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
Problem: the lcm and hcf of two numbers are 60 and 2 respectively . find the larger of the two numbers if their sum is 22 .
Options: a ) 12 , b ) 2 , c ) 4 , d ) 54 , e ) 56
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 60 * 2 = 120 so the answer which we are looking for has to be a factor of 120 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 120 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Python program:
a = 60 * 2
b = a / 22
Problem: excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 20 , e ) 22
Rationale: "due to stoppages , it covers 9 km less . time taken to cover 9 km = ( 9 / 54 x 60 ) min = 10 min . answer : b"
Answer: b
Python program:
a = 54 - 45
b = a / 54
c = const_60 * b
Problem: the number of stamps that p and q had were in the ratio of 7 : 2 respectively . after p gave q 15 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 2 : 1 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "p started with 7 k stamps and q started with 2 k stamps . ( 7 k - 15 ) / ( 2 k + 15 ) = 2 / 1 3 k = 45 k = 15 p has 7 ( 15 ) - 15 = 90 stamps and q has 2 ( 15 ) + 15 = 45 stamps . the answer is c ."
Answer: c
Python program:
a = 15 * 2
b = 15 * 1
c = a + b 
d = 2 + 1 
e = c / d