euclaise/mathqa_programs huggingface dataset:
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 270 . the amount of the bill is
Options: a ) 2200 , b ) 2520 , c ) 2600 , d ) 3354 , e ) none of these
Rationale: "explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 270 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 270 or x = 2250 . p . w . = rs . 2250 sum due = p . w . + t . d . = rs . ( 2250 270 ) = rs . 2520 answer : b"
Answer: b
Python program:
a = 4 * 3
b = 9 / a
c = b * 16
d = c / 100
e = 270 / d
f = e + 270
Problem: for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 25 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
Options: a ) 0.05 , b ) 0.36 , c ) 0.2 , d ) 0.25 , e ) 0.6
Rationale: "index for females = ( 25 - 8 ) / 25 = 17 / 25 = 0.68 index for males = ( 25 - 17 / 25 = 8 / 25 = 0.32 index for females exceeds males by 0.68 - 0.32 = 0.36 answer : b"
Answer: b
Python program:
a = 25 - 8
b = a / 25
c = 8 / 25
d = b - c
Problem: at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 62 , b ) 171 , c ) 475 , d ) 513 , e ) 684
Rationale: "total automobile instalment credit = 57 * 3 = 171 total consumer instalment credit = 171 ∗ 100 / 36 = 475 ; answer = c . 475"
Answer: c
Python program:
a = 57 * 3
b = 36 / 100
c = a / b
Problem: the perimeter of a semi circle is 122 cm then the radius is ?
Options: a ) 17 , b ) 28 , c ) 24 , d ) 11 , e ) 12
Rationale: "36 / 7 r = 122 = > r = 24 answer : c"
Answer: c
Python program:
a = 2 + math.pi 
b = 122 / a
Problem: what is the units digit of ( 493 ) ( 915 ) ( 381 ) ( 756 ) ( 28 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 1 . imo b ."
Answer: b
Python program:
a = math.factorial(493)
b = math.factorial(915)
c = a * b
d = math.factorial(493)
e = math.factorial(756)
f = d * e
g = c + f 
h = g / 493
Problem: if the average ( arithmetic mean ) of a and b is 150 , and the average of b and c is 90 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 120 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 300 b + c = 180 a - c = 120 . imo option c ."
Answer: c
Python program:
a = 90 * 2
b = 150 * 2
c = a - b
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of e is less than the square root of e . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "e = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b
Problem: claire has a total of 92 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 68 , c ) 54 , d ) 57 , e ) 60
Rationale: "g + h = 92 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 92 - h or 3 ( 92 - h ) + 4 h = 300 h = 300 - 276 = 24 then g = 92 - 24 = 68 b"
Answer: b
Python program:
a = 92 - 25
b = a + 1
Problem: a car ferry can hold up to 60 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 5 tons ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20
Rationale: "the weight of one car and one truck is 5.75 tons . 60 / 5.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is e ."
Answer: e
Python program:
a = 0 + 75 
b = 60 / a
c = 0 + 75 
d = 60 / c
e = b + d
Problem: if a man walks at the rate of 4 kmph , he misses a train by only 6 min . however , if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train . the distance covered by him to reach the station is
Options: a ) 3 km , b ) 4 km , c ) 5 km , d ) 6 km , e ) 7 km
Rationale: let the distance covered be d and time taken to reach the station in time t d / 4 = t + 6 / 60 - - - ( 1 ) d / 5 = t - 6 / 60 - - - ( 2 ) ( 1 ) - ( 2 ) gives d / 4 - d / 5 = ( 6 + 6 ) / 60 d / 20 = 12 / 60 d = 12 * 20 / 60 = 4 km answer : b
Answer: b
Python program:
a = 4 * 6
b = 5 * 6
c = a + b 
d = c + 6 
e = d / const_60
f = 4 * e
Problem: what is the sum of all even integers between 99 and 301 ?
Options: a ) 20200 , b ) 20000 , c ) 40400 , d ) 40000 , e ) 44000
Rationale: "a = 100 , tn = 300 a + ( n - 1 ) d = 300 = > n = 101 sn = n / 2 ( a + l ) = 101 / 2 ( 100 + 300 ) sn = 20200 answer : a"
Answer: a
Python program:
a = 301 - 99
b = a - 2
c = b / 2
d = c + 99 
e = 301 - 99
f = e + 2 
g = f / 2
h = d * g
Problem: a person was asked to state his age in years . his reply was , ` ` take my age 4 years hence , multiply it by 4 and subtract 4 times my age 4 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 32 , c ) 27 , d ) 26 , e ) 19
Rationale: "explanation : let the present age of person be x years . then , 4 ( x + 4 ) - 4 ( x - 4 ) = x < = > ( 4 x + 16 ) - ( 4 x - 16 ) = x < = > x = 32 . . answer : b"
Answer: b
Python program:
a = 4 * 4
b = 4 * 4
c = a + b
Problem: the average ( arithmetic mean ) of the even integers from 24 to 48 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 12 to 24 inclusive ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "so , according to a mean of a set of even numbers from 24 to 48 = ( 24 + 48 ) / 2 = 36 and mean of a set of even numbers from 12 to 24 = ( 12 + 24 ) / 2 = 18 difference = 36 - 18 = 18 answer : c ."
Answer: c
Python program:
a = 24 + 12 
b = a / 2
c = 48 + 24 
d = c / 2
e = b - d
Problem: 2 friends a and b running up hill and then to get down length of road - 440 yads a on his return journey met b going up at 20 yards from top if a has finished race 5 minute earlier than b then how much time a had taken to complete the race ?
Options: a ) 100 minute , b ) 110 minute , c ) 120 minute , d ) 130 minute , e ) 140 minute
Rationale: total journey = 440 * 2 = 880 a meet b 20 yards from top in getting down it means he has covered 440 + 20 = 460 yards while b is 420 yards . so he is 40 yards ahead of b which is equals to 5 minute . so 40 yards in 5 min 880 yards will be in 5 * 880 / ( 40 ) = 110 minute answer : b
Answer: b
Python program:
a = 440 / 10
b = a - 4
c = 5 / b
d = 440 * 2
e = c * d
Problem: a train speeds past a pole in 25 seconds and a platform 500 m long in 35 seconds . its length is :
Options: a ) 1150 m , b ) 2250 m , c ) 1450 m , d ) 1350 m , e ) 1250 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 x + 500 / 35 = x / 25 x = 1250 m . answer : option e"
Answer: e
Python program:
a = 2 - 1
b = 500 * a
Problem: the average age of 40 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 22 , b ) 27 , c ) 28 , d ) 26 , e ) 56
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 40 ) = 56 years answer : e"
Answer: e
Python program:
a = 40 * 15
b = a + 16 
c = b + 40 
d = 40 * 15
e = c - d
Problem: 14 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 2548
Rationale: "no . of ways of picking 2 biology books ( from 14 books ) = 14 c 2 = ( 14 * 13 ) / 2 = 91 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 91 * 28 = 2548 ( option e )"
Answer: e
Python program:
a = math.factorial(14)
b = 14 - 2
c = math.factorial(b)
d = a / c
e = d / 2
f = math.factorial(8)
g = 8 - 2
h = math.factorial(g)
i = f / h
j = i / 2
k = e * j
Problem: the average of non - zero number and its square is 5 times the number . the number is :
Options: a ) 9 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: let the number be x . then , ( x + x 2 ) / 2 = 5 x = > x 2 - 9 x = 0 = > x ( x - 9 ) = 0 = > x = 0 or x = 9 so , the number is 9 . answer : a
Answer: a
Python program:
a = 5 * 2
b = a - 1
Problem: evaluate : 50 - 12 ÷ 4 × 2 =
Options: a ) 44 , b ) 54 , c ) 16 , d ) 27 , e ) 30
Rationale: "according to order of operations , 12 ÷ 4 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 4 × 2 = 3 × 2 = 6 hence 50 - 12 ÷ 4 × 2 = 50 - 6 = 44 correct answer a ) 44"
Answer: a
Python program:
a = 12 * 4
b = a * 2
c = 50 - b
Problem: if 40 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 150 , c ) 75 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 40 % of 3 / 5 of x = 36 40 / 100 * 3 / 5 * x = 36 x = ( 36 * 50 / 12 ) = 150 required number = 150 . correct option : b"
Answer: b
Python program:
a = 40 / 100
b = 3 / 5
c = a * b
d = 36 / c
Problem: the sum and the product of two numbers are 24 and 23 respectively , the difference of the number is ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 22
Rationale: explanation : x + y = 24 xy = 23 ( x - y ) 2 = ( x + y ) 2 - 4 xy ( x - y ) 2 = 576 - 92 = > ( x - y ) = 22 answer : e
Answer: e
Python program:
a = 24 ** 2
b = 23 * 2
c = a - b
d = 23 * 2
e = c - d
f = math.sqrt(e)
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 7 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 7 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 7 is p ( 7 ) = 9.50 + 0.25 ( 7 – 1 ) = 9.50 + 0.25 * 6 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 7 ) - p ( 1 ) = 9.50 + 0.25 * 6 - 9.50 = 1.5 . answer : d ."
Answer: d
Python program:
a = 7 - 1
b = 0 * 25
c = b + 0
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 2800 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 2800 envelopes b will take 2800 / 1400 hrs = 2 hrs so the answer is choice a"
Answer: a
Python program:
a = 6000 / 2
b = 3000 / 1
c = 6000 / 3
d = b - c
e = a - d
f = 2800 / e
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units d digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : d . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Python program:
a = 9 * 2
b = a + 2 
c = b ** 2
Problem: ron has had 3 pay cuts in her salary in the past 6 months . if the first pay cut was 5 % , the second pay cut was 10 % and the third was 15 % . what will be the percentage decrease , if the salary is decreased in a single shot ?
Options: a ) 29.33 % , b ) 27.33 % , c ) 17.33 % , d ) 27.99 % , e ) 29.33 %
Rationale: let rs . 100 be initial salary . salary after 1 st decrease , 5 % = 95 salary after 2 nd decrease , 10 % = 85.5 i . e . reduced by 10 percent of 95 salary after 3 rd decrease , 15 % = 72.675 i . e . reduced by 15 percent of 85.5 so if its decreased in single shot = i = ( ( b - a ) / b ) * 100 = 27.33 % answer : b
Answer: b
Python program:
a = 100 - 5
b = 100 - 5
c = 10 / 100
d = b * c
e = a - d
f = 100 - 5
g = 100 - 5
h = 10 / 100
i = g * h
j = f - i
k = 15 / 100
l = j * k
m = e - l
n = 100 - m
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 50 .
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 50 , remainder will be - 4 i . e . n will be 4 less than a multiple of 50 . so you must add 12 to n to make it a multiple of 50 c"
Answer: c
Python program:
a = 50 - reminder
Problem: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 222 marks in the second test and failed by 39 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 232 , c ) 246 , d ) 625 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 36 marks in the second test . pass mark in the second test = 222 + 39 = 252 45 / 100 m = 261 pass mark in the first test = 40 / 100 m = 40 / 45 * 261 = 232 answer : b"
Answer: b
Python program:
a = 222 + 39
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 60 , b ) 277 , c ) 48 , d ) 99 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.4 = 2.5 km = 2500 m . required time = 2500 * 3 / 125 = 60 sec . answer : a"
Answer: a
Python program:
a = 1 * 10
b = 60 * 1000
c = b / 3600
d = a / c
e = 1 * 4
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: if x # y is defined to equal x ^ 2 / y for all x and y , then ( - 1 # 2 ) # 2 =
Options: a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 12 , d ) 1 / 8 , e ) - 4 / 3
Rationale: "( - 1 ) ^ 2 / 2 = 1 / 2 ( 1 / 2 ) ^ 2 / 2 = 1 / 8 so d is my answer"
Answer: d
Python program:
a = negate ** (
b = a / 2
c = b ** 2
d = c / 2
Problem: a can do a piece of work in 4 days . b can do it in 6 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 12 days , c ) 66 days , d ) 77 days , e ) 44 days
Rationale: c = 1 / 2 - 1 / 4 - 1 / 6 = 1 / 12 = > 12 days answer : b
Answer: b
Python program:
a = 4 * 6
b = 4 * 6
c = 4 * 6
d = c / 4
e = 4 * 6
f = e / 6
g = d + f 
h = g * 2
i = b - h
j = i / 2
k = a / j
Problem: how many seconds will a 800 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 48 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 800 * 3 / 50 = 48 sec answer : d"
Answer: d
Python program:
a = 63 - 3
b = const_0_2778 * a
c = 800 / b
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.52 , d ) 2.72 , e ) none of these
Rationale: "1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each ` ` part ' ' is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 850 * 2 * ( 4 / 5 ) = 1360 2160 + 1360 = 3520 solving for units gives us 3.52 so the answer is c"
Answer: c
Python program:
a = 3 * 900
b = 2 * 850
c = a + b 
d = 4 * c
e = 3 + 2 
f = d / e
g = f / 1000
Problem: at veridux corporation , there are 210 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 55
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 210 â € “ 90 = 120 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 210 â € “ 40 = 170 must be associates . now , in the â € œ associate â €  row , 135 + e = 170 , which means e = 35 â € ” the other 35 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 35 = 90 , which means b = 55 . there are fifteen female managers in this company . thus , the answer = ( e ) ."
Answer: e
Python program:
a = 40 * 1
Problem: 7 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 40 , b ) 48 , c ) 45 , d ) 42 , e ) 22
Rationale: "though 2 * ( 7 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 6 , so he ' ll play 12 matches . similarly , second guy has to play with the rest of 5 as his 2 games with the first guy are already played . so he plays 10 matches . this continues like this and the total matches are 12 + 10 + 8 . . . + 2 12 + 10 + . . . + 2 = 2 ( 6 + 5 + . . . + 1 ) = 2 ( ( 6 * 7 ) / 2 ) = 6 * 7 = 42 . answer : d"
Answer: d
Python program:
a = 7 - 1
b = 7 * a
Problem: what is value of x if 32 - y = 16 x - y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 2 , e ) 6
Rationale: "32 - y = 16 x - y 32 = 16 x - y + y 16 x = 32 x = 2 answer is option d"
Answer: d
Python program:
a = 32 + 1 
b = 32 - 1
c = a / b
Problem: find the cost of fencing around a circular field of diameter 18 m at the rate of rs . 2.50 a meter ?
Options: a ) 138 , b ) 132 , c ) 150 , d ) 140 , e ) 222
Rationale: "2 * 22 / 7 * 9 = 56 56 * 2 1 / 2 = rs . 140 answer : d"
Answer: d
Python program:
a = 18 / 2
b = circumface * (
Problem: what is the least value of x . so that 23 x 58 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 8 = 18 + x least value of x may be 0 therefore 18 + 0 = 18 is divisible by 3 . answer : option b"
Answer: b
Python program:
a = math.lcm(23, 58)
b = a / 58
c = b / 4
d = c / 4
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 22 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 288 , b ) 210 , c ) 881 , d ) 1277 , e ) 121
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 22 = 330 m . let the length of the platform be x m . then , ( x + 330 ) / 36 = 15 = > x = 210 m . answer : b"
Answer: b
Python program:
a = 54 * const_0_2778
b = 22 * a
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.55 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 7 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.55 9.9 - 45 x + 36 x = 8.55 9 x = 1.35 x = 0.15 the answer is e ."
Answer: e
Python program:
a = 22 / 100
b = 22 / 100
c = 18 * 2
d = b * c
e = 8 - 55
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: the average age of a , b and c is 29 years . if the average age of a and c is 32 years , what is the age of b in years ?
Options: a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 23
Rationale: "age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 29 ã — 3 â € “ 32 ã — 2 = 87 â € “ 64 = 23 years e"
Answer: e
Python program:
a = 29 * 3
b = 32 * 2
c = a - b
Problem: the number of sailors on a ship is 88 % 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 ) 97 : 50
Rationale: "sailor = 1 / 88 * officer sailor / officer = 1.88 / 1 = 188 / 100 = 47 / 25 answer will be c"
Answer: c
Python program:
a = 88 + 100 
b = a / 100
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 300 m , its area is ?
Options: a ) 3000 sq m
b ) 1878 sq m
c ) 2789 sq m
d ) 26811 sq m
e ) 29762 sq m
Rationale: 5 x + 12 x + 13 x = 300 = > x = 10 a = 50 , b = 120 , c = 130 s = ( 50 + 120 + 130 ) / 2 = 150 3000 sq m answer : a
Answer: a
Python program:
a = 5 + 12 
b = a + 13 
c = 300 / b
d = 300 * c
Problem: a coin is tossed 7 times . what is the probability of getting exactly 6 heads ?
Options: a ) 7 / 32 , b ) 3 / 64 , c ) 5 / 64 , d ) 3 / 128 , e ) 7 / 128
Rationale: "the number of possible outcomes is 2 ^ 7 = 128 there are 7 ways to get exactly 6 heads . p ( exactly 6 heads ) = 7 / 128 the answer is e ."
Answer: e
Python program:
a = 1 / 2
b = a ** 6
c = math.comb(7, 6)
d = 1 / 2
e = c * d
f = b * e
Problem: how many integer values r are there for x such that 1 < 3 x + 5 < 17 ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: 1 < 3 x + 5 < 17 = > - 4 < 3 x < 12 = > - 4 / 3 < x < 4 x can take integer values r - 1,0 , 1 , 2 , 3 answer d
Answer: d
Python program:
a = 5 * 1
Problem: find the missing value : 8597 - ? = 7429 - 4358
Options: a ) 5526 , b ) 5426 , c ) 5326 , d ) 5226 , e ) none of them
Rationale: "let 8597 - x = 7429 - 4358 . then , x = ( 8597 + 4358 ) - 7429 = 12955 - 7429 = 5526 . answer is a ."
Answer: a
Python program:
a = 8597 / 100
b = 7429 / a