euclaise/mathqa_programs huggingface dataset:
Problem: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.267 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 0 , c ) 27 , d ) 54 , e ) can not be determined
Rationale: "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . b"
Answer: b
Python program:
a = 3 * 2
b = 3 * 2
c = a * b
d = 3 * 2
e = c * d
f = e / 4
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 22 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 166 , c ) 86 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 22 = 40 5 * quotient = 40 quotient = 8 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 8 ) + 6 = 166 . b )"
Answer: b
Python program:
a = 6 * 3
b = a + 22 
c = 6 * 3
d = c + 22 
e = d / 5
f = b * e
g = f + 6
Problem: a sum fetched total simple interest of 4016.25 at the rate of 11 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 8925 , b ) 8032.5 , c ) 7302.3 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 55 % of p = 4016.25 or , p = 7302.3 answer c"
Answer: c
Python program:
a = 100 * 4016
b = 11 * 5
c = a / b
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , three boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) 13.5 sec
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 18 = 10 m / s now , length of train = 9 ã — 15 = 135 m â ˆ ´ required time = 135 â  „ 10 = 13.5 sec . answer e"
Answer: e
Python program:
a = 12 * 15
b = a - 15
c = 12 * 15
d = c / 18
e = b / d
Problem: what is the cp of rs 100 stock at 8 discount , with 1 / 5 % brokerage ?
Options: a ) 92.9 , b ) 96.3 , c ) 92.2 , d ) 96.7 , e ) 92.8
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 8 + 1 / 5 92.2 thus the cp is rs 92.2 . answer : c"
Answer: c
Python program:
a = 100 - 8
b = 1 / 5
c = a + b
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 27 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 27 kg zinc , mixture , melted = [ 20 / 9 x 27 ] kg = 60 kg . answer b"
Answer: b
Python program:
a = 11 / 9
b = a * 27
c = b + 27
Problem: if x is an integer such that 3 < x < 10 , 5 < x < 18 , 9 > x > – 2 , 8 > x > 0 , and x + 1 < 9 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "3 < x < 10 , 6 < x < 18 , - 2 < x < 9 0 < x < 8 x < 8 from above : 6 < x < 8 - - > x = 7 . answer : c ."
Answer: c
Python program:
a = 9 - 1
b = a - 1
Problem: if n is a positive integer greater than 1 , then p ( n ) represents the product of all the prime numbers less than or equal to n . the second smallest prime factor of p ( 12 ) + 11 is
Options: a ) 2 , b ) 11 , c ) 13 , d ) 17 , e ) 211
Rationale: p ( 12 ) + 11 = 2 ∗ 3 ∗ 5 ∗ 7 ∗ 11 + 11 = 11 ( 2 ∗ 3 ∗ 5 ∗ 7 + 1 ) = 11 ∗ 211 . both 11 and 211 are primes : 11 is the smallest prime of p ( 12 ) + 11 and 211 is the second smallest prime of p ( 12 ) + 11 . answer : e .
Answer: e
Python program:
a = 4 + 3 
b = 11 * a
c = 4 + 1 
d = b * c
e = d * 3
f = e * 2
g = f + 11 
h = g / 11
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 140 marks , the no of questions he attempts correctly is :
Options: a ) a ) 35 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 40
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 140 = > 5 x = 200 = > x = 40 answer : e"
Answer: e
Python program:
a = 140 + 60 
b = 4 + 1 
c = a / b
Problem: the average ( arithmetic mean ) of 4 different integers is 70 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 13 , e ) 33
Rationale: "total of integers = 70 * 4 = 280 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 280 - ( 90 + 89 + 88 ) = 280 - 267 = 13 answer : d"
Answer: d
Python program:
a = 70 * 4
b = a - 90
c = 90 - 1
d = b - c
e = 90 - 2
f = d - e
Problem: double of quarter of 6 percent written as a decimal is :
Options: a ) 0.03 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 6 % = 0.03 answer : a"
Answer: a
Python program:
a = 6 / 100
b = a / 6
c = b * 2
Problem: p and q can complete a work in 20 days and 12 days respectively . p alone started the work and q joined him after 4 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 20 work done by q in 1 day = 1 / 12 work done by p in 4 days = 4 × ( 1 / 20 ) = 1 / 5 remaining work = 1 – 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 20 + 1 / 12 = 8 / 60 = 2 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 2 / 15 ) = 6 total days = 4 + 6 = 10 answer : option b"
Answer: b
Python program:
a = 4 / 20
b = 1 - a
c = 1/(20)
d = 1/(12)
e = c + d 
f = b / e
g = 4 + f
Problem: if in one hour , a canoe rows at 16 km / hr downstream and 9 km / hr upstream , calculate the speed of a boat in still water ( in km / hr ) .
Options: a ) 18 kmph , b ) 15.5 kmph , c ) 12.5 kmph , d ) 13.5 kmph , e ) 22.5 kmph
Rationale: speed in still water = ( 16 + 9 ) 1 / 2 kmph = 12.5 kmph . answer : c
Answer: c
Python program:
a = 16 + 9 
b = a / 2
Problem: a rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it . one parallel to the length and the other parallel to breadth . the cost of graveling the roads at 75 paise per sq meter is ?
Options: a ) rs . 259 , b ) rs . 252 , c ) rs . 258 , d ) rs . 251 , e ) rs . 252
Rationale: "area of cross roads = 55 * 4 + 35 * 4 - 4 * 4 = 344 sq m cost of graveling = 344 * ( 75 / 100 ) = rs . 258 answer : c"
Answer: c
Python program:
a = 55 + 35 
b = a - 4
c = b * 4
d = c * 75
e = d / 100
Problem: a salesman ` s commission is 5 % on all sales upto rs . 10000 and 4 % on all sales exceeding this . he remits rs . 31100 to his parent company after deducing his commission . find the total sales .
Options: a ) 32500 , b ) 2500 , c ) 22500 , d ) 30000 , e ) 40000
Rationale: let his total sales be rs . x . now ( total sales ) – ( commission ) = rs . 31100 x - [ ( 5 % of 10000 + 4 % of ( x - 10000 ) ] = 31100 x - [ ( ( 5 / 100 ) * 10000 + ( 4 / 100 ) * ( x - 10000 ) ] = 31100  x - 500 - ( ( x - 10000 ) / 25 ) = 31100  x - ( x / 25 ) = 31200  24 x / 25 = 31200  x = [ ( 31200 * 25 ) / 24 ) = 32500 . total sales = rs . 32500 answer a
Answer: a
Python program:
a = 31100 + 100 
b = 100 / 4
c = a * b
d = 12 + 12 
e = c / d
Problem: approximately how many revolutions will be made by a car tire with a 15 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 669 , b ) 660 , c ) 360 , d ) 720 , e ) 1,440
Rationale: diameter of car tire = 15 inches radius of car tire = 7.5 inches = 7.5 * 2.54 cm = 19.05 cm circumference of the car tire = 2 * pi * 19.05 = 2 * 3.14 * 19.05 = 119.63 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 119.63 = 668.73 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer a
Answer: a
Python program:
a = 1 / 2
b = 3 * 2
c = b / 10
d = c + 1 
e = d / 10
f = e + 4 
g = f / 10
h = g + 1 
i = h / 10
j = i + 3 
k = j * 15
l = 3 * 2
m = l * 10
n = m + 3 
o = n * 10
p = o + 3 
q = p * 10
r = q + 3 
s = r + 2 
t = s * 10
u = k / t
v = a / u
Problem: 16 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 ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 240
Rationale: 2 * 16 c 2 = 2 * 120 = 240 the answer is e .
Answer: e
Python program:
a = 16 - 1
b = 16 * a
Problem: the grade point average of one third of the classroom is 30 ; the grade point average of the rest is 33 . what is the grade point average of the whole class ?
Options: a ) 44 , b ) 41 , c ) 38 , d ) 35 , e ) 32
Rationale: "let n = total students in class total points for 1 / 3 class = 30 n / 3 = 10 n total points for 2 / 3 class = 33 * 2 n / 3 = 22 n total points for whole class = 10 n + 22 n = 32 n 32 n total class points / n total students = 32 grade point average for total class answer : e"
Answer: e
Python program:
a = 33 / 3
b = a * 2
c = 30 / 3
d = b + c
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 4,4 ) , ( 7,4 ) , ( 5,9 ) , ( 8,9 ) ?
Options: a ) 21 .
b ) 28 .
c ) 5 .
d ) 49 .
e ) 52 .
Rationale: delta x will give us the dimension of one side of the parallelogram = 5 - 4 = 1 unit delta y will give us the dimension of the other side of parallelogram = 9 - 4 = 5 unit area of parallelogram = 1 * 5 = 5 answer is c
Answer: c
Python program:
a = 3 + 2
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 18 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 36 , e ) 96
Rationale: "a 54 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 54 miles"
Answer: a
Python program:
a = 36 / 2
b = a / 6
c = 18 * b
Problem: average expenditure of a person for the first 3 days of a week is rs . 360 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 400 , e ) none
Rationale: "explanation : assumed mean = rs . 360 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 360 + rs . 40 = rs . 400 correct option : d"
Answer: d
Python program:
a = 420 - 360
b = 4 * a
c = 3 + 4 
d = b / c
e = 360 + d
Problem: what approximate value will come in place of the question mark ( ? ) in the below question ? ( 47 % of 1442 - 36 % of 1412 ) + 63 = ?
Options: a ) 237 , b ) 278 , c ) 278 , d ) 252 , e ) 271
Rationale: explanation : since there are 5 cups of each kind , prepared with milk or tea leaves added first , are identical hence , total number of different people ways of presenting the cups to the expert is 10 ! / ( 5 ! x 5 ! ) = 252 answer : d ) 252
Answer: d
Python program:
a = 10 + 4 
b = a + 4 
c = b + 1 
d = 36 + 10 
e = d + 12 
f = e / 100
g = c + f 
h = 47 / 100
i = h * 1442
j = 36 / 100
k = j * 1412
l = i - k
m = 63 + l 
n = g + m
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 47 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 47 has the form 4 k + 3 , so the units digit of 93 ^ 47 is 7 . the units digit if powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a
Python program:
a = reminder * (
b = reminder + (
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 400,000 ?
Options: a ) 200 , b ) 216 , c ) 300 , d ) 400 , e ) 2,500
Rationale: "first digit = last digit = 4 or 6 or 8 so three possibilities . . second = fifth = any of ten digits third = fourth = any of ten digits . . so total integers = 3 * 10 * 10 = 300 answer : c"
Answer: c
Python program:
a = 6 - 4
b = a * 10
c = b * 10
Problem: multiplication of 2 numbers is 9375 and the quotient , when the larger one is divided by the smalleris 15 . find the sum of the numbers ?
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600
Rationale: let the numbers be x and y . then , xy = 9375 and x = 15 . y xy = 9375 ( x / y ) 15 y 2 = 625 . y = 25 . x = 15 y = ( 15 x 25 ) = 375 . sum of the numbers = x + y = 375 + 25 = 400 . c
Answer: c
Python program:
a = 9375 / 15
b = math.sqrt(a)
c = 9375 / 15
d = math.sqrt(c)
e = 9375 / d
f = b + e
Problem: a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) 452000 , b ) 562000 , c ) 800000 , d ) 500000 , e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 40000 100 % = 40000 * 100 / 5 = $ 800000 answer is c"
Answer: c
Python program:
a = 20 * 3
b = a + 30 
c = b + 5 
d = 100 - c
e = 40000 / d
f = e * 100
Problem: a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 7 / 19 , b ) 6 / 19 , c ) 5 / 19 , d ) 4 / 19 , e ) none of these
Rationale: "explanation : please remember that maximum portability is 1 . so we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs . so here we go , total cases of non defective bulbs 16 c 2 = 16 ∗ 15 / 2 ∗ 1 = 120 total cases = 20 c 2 = 20 ∗ 19 / 2 ∗ 1 = 190 probability = 120 / 190 = 12 / 19 p of at least one defective = 1 − 12 / 19 = 7 / 19 option a"
Answer: a
Python program:
a = 20 - 4
b = math.comb(a, 2)
c = math.comb(20, 2)
d = b / c
e = 1 - d
Problem: after decreasing 24 % in the price of an article costs rs . 988 . find the actual cost of an article ?
Options: a ) 1667 , b ) 6789 , c ) 1300 , d ) 6151 , e ) 1421
Rationale: "cp * ( 76 / 100 ) = 988 cp = 13 * 100 = > cp = 1300 answer : c"
Answer: c
Python program:
a = 24 / 100
b = 1 - a
c = 988 / b
Problem: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 846 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 638 , c ) s . 650 , d ) s . 762 , e ) s . 735
Rationale: "s . i . for 1 year = ( 846 - 825 ) = rs . 29 s . i . for 3 years = 21 * 3 = rs . 63 principal = ( 825 - 63 ) = rs . 762 . answer : d"
Answer: d
Python program:
a = 846 - 825
b = a * 3
c = b / 4
d = 825 - c
Problem: of the votes cast on a certain proposal , 58 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 230 , b ) 245 , c ) 260 , d ) 275 , e ) 290
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 58 0.2 x = 58 x = 290 the answer is e ."
Answer: e
Python program:
a = 40 / 100
b = 1 - a
c = 40 / 100
d = b - c
e = 58 / d
Problem: the s . i . on a certain sum of money for 3 years at 10 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 1267 , c ) 1750 , d ) 2267 , e ) 1400
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 10 ) = rs . 1400 answer : e"
Answer: e
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 4000 * c
e = d - 4000
f = e / 2
g = 10 / 100
h = 3 * g
i = f / h
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.45 – 6.45 * ?
Options: a ) 0.45 , b ) 0.5 , c ) 6.45 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.45 * = 6 ( the greatest positive even integer less than or equal to 6.45 is 6 ) . hence , 6.45 – 6.45 * = 6.45 - 6 = 0.45 answer : a ."
Answer: a
Python program:
a = math.floor(6, 45)
b = 6 - 45
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 54 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the distance traveled by maxwell ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "after the 1 st hour , maxwell has travelled 4 km . and brad just left home . so the distance between them = 54 - 4 = 50 . relative speed = 4 + 6 = 10 kmph . now to cover these 50 kms , they will take 50 / 10 = 5 hrs . so in 5 hrs , maxwell walks 5 * 4 = 20 kms . so total distance travelled by maxwell = 4 + 20 = 24 . answer : d"
Answer: d
Python program:
a = 54 + 6 
b = 4 + 6 
c = a / b
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2
Options: a ) 31 , b ) 22 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 7 x 11 ^ 2 = 2 ^ 22 x 7 ^ 7 x 11 ^ 2 total number of prime factors = ( 22 + 7 + 2 ) = 31 . answer is a ."
Answer: a
Python program:
a = 2 * 11
b = a + 7 
c = b + 2
Problem: at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 10 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 48 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 cents ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let number of apples = a number of oranges = b a + b = 10 - - - 1 . 48 = ( . 4 a + . 6 b ) / 10 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 4 let the number of oranges put back = c 45 * ( 10 - c ) = 40 * 6 + 60 ( 4 - c ) = > c = 2 answer b"
Answer: b
Python program:
a = 48 * 10
b = 45 * 10
c = a - b
d = 60 - 45
e = c / d
Problem: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area q covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads q = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Python program:
a = rectangle_area + (
Problem: by approximately what percent is x greater than 4 / 5 if ( 4 / 5 ) ( x ) = 1 ?
Options: a ) 73 % , b ) 56 % , c ) 41 % , d ) 37 % , e ) 29 %
Rationale: 4 / 5 = 80 % , 5 / 4 = 125 % increase by 45 percentage points 45 / 80 = 56 % , hence b
Answer: b
Python program:
a = 4 / 5
b = 5 - a
c = 4 / 5
d = b / c
e = d * 100
Problem: a train 120 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 22 , b ) 48.2 , c ) 99 , d ) 288 , e ) 12
Rationale: speed of the train relative to man = ( 120 / 10 ) m / sec = ( 12 ) m / sec . [ ( 12 ) * ( 18 / 5 ) ] km / hr = 43.2 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 43.2 = = > x = 48.2 km / hr . answer : b
Answer: b
Python program:
a = 10 * const_0_2778
b = a * 10
c = 120 - b
d = c / 5
e = d / const_0_2778
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 15 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 43.75 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 115 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 115 - 80 ) / 80 * 100 = ~ 43.75 % answer : d ."
Answer: d
Python program:
a = 100 + 15 
b = 100 - 20
c = a - b
d = c * 100
e = 100 - 20
f = d / e
Problem: a field is 90 metre long and 50 metre broad . a 25 metre long , 20 metre broad and 4 metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field . how much the level of field will rise ?
Options: a ) 0.5 metre , b ) 0.3 metre , c ) 0.8 metre , d ) 0.6 metre , e ) 0.7 metre
Rationale: area of field = 90 x 50 = 4500 m 2 area of field dug out = 25 x 20 = 500 m 2 therefore , area of remaining field = 4500 m 2 - 500 m 2 = 4000 m 2 volume of the earth dug out = 25 x 20 x 4 = 2000 m 3 therefore , field will rise by 2000 / 4000 = 0.5 metre answer a
Answer: a
Python program:
a = 25 * 20
b = a * 4
c = 90 * 50
d = 25 * 20
e = c - d
f = b / e
Problem: how many odd numbers between 10 and 800 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 12 numbers . answer : a ."
Answer: a
Python program:
a = 10 + 4
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 106 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 47 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 106 ) / ( 3 / 20 ) = 30 / 54 = 56,6 % it means that 9 / 106 represents only 56,6 % . therefore a decrease of 47 % . answer b"
Answer: b
Python program:
a = 3 / 20
b = a * 100
Problem: the price of lunch for 15 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.8 , d ) 14 , e ) 15.87
Rationale: "x - > price without gratuity 207 = x + 0.15 x = > x = 207 / 1.15 = 180 so average price per person , excluding the gratuity = 180 / 15 = 12 the answer is b ."
Answer: b
Python program:
a = 100 - 15
b = 207 * a
c = b / 100
d = c / 15
Problem: a soft drink company had 6000 small and 15000 big bottles in storage . if 11 % of small 12 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 15360 , b ) 16010 , c ) 15060 , d ) 14930 , e ) 18540
Rationale: "6000 + 15000 - ( 0.11 * 6000 + 0.12 * 15000 ) = 18540 . answer : e ."
Answer: e
Python program:
a = 6000 + 15000 
b = 11 / 100
c = 6000 * b
d = 12 / 100
e = d * 15000
f = c + e 
g = a - f
Problem: solve the equation for x : 6 x - 27 + 3 x = 4 + 9 - x ?
Options: a ) 4 , b ) 5 , c ) 3 , d ) 9 , e ) 6
Rationale: "9 x + x = 13 + 27 10 x = 40 = > x = 4 answer : a"
Answer: a
Python program:
a = 27 + 4 
b = 6 + 6 
c = a / b
Problem: a sum of money at simple interest amounts to rs . 840 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 798 , c ) 654 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 840 ) = rs . 14 . s . i . for 3 years = rs . ( 14 x 3 ) = rs . 42 . principal = rs . ( 840 - 42 ) = rs . 798 . answer : b"
Answer: b
Python program:
a = 854 - 840
b = a * 3
c = b / 4
d = 840 - c