euclaise/mathqa_programs huggingface dataset:
Problem: a certain kind of fuel is 1515 high octane and 4545 regular octane . if high octane costs 3 times as much as regular octane , what fraction of the cost of the fuel is due to the high octane ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 3 / 7 , d ) 3 / 5 , e ) 4 / 5
Rationale: let x be the amount of fuel high octane = x / 5 regular = 4 x / 5 price of regular = y price of high octante = 3 y cost of high octane in the fuel = 3 y * x / 5 total cost = 3 y * x / 5 + 4 x / 5 * y % = cost of high octante / total cost = 3 / 7 answer is c
Answer: c
Python program:
a = 3 + 4 
b = 3 / a
Problem: 8 coins are tossed . whats is the probability that one and only one turns up head ?
Options: a ) 1 / 256 , b ) 1 / 32 , c ) 1 / 64 , d ) 1 / 128 , e ) 1 / 189
Rationale: explanation : possible outcomes ( sample space ) when 8 coins are tossed are : ( h , h , h , h , h , h , h , h ) , ( h , h , h , h , h , h , h , t ) , ( h , h , h , h , h , h , t , h ) , ( h , h , h , h , h , h , t , t ) , . . . . . . . ( t , t , t , t , t , t , t , t ) = 28 required outcomes : ( h , t , t , t , t , t , t , t ) , ( t , h , t , t , t , t , t , t ) , ( t , t , h , t , t , t , t , t ) , ( t , t , t , h , t , t , t , t ) , ( t , t , t , t , h , t , t , t ) , ( t , t , t , t , t , h , t , t ) , ( t , t , t , t , t , t , h , t ) , ( t , t , t , t , t , t , t , h ) = 8 so the required probability = 8 / 28 = 1 / 32 answer : b
Answer: b
Python program:
a = 2 ** 8
b = 8 / a
Problem: a rectangular lawn of dimensions 110 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 3988 , b ) s . 4800 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928
Rationale: "area = ( l + b – d ) d ( 110 + 60 – 10 ) 10 = > 1600 m 2 1600 * 3 = rs . 4800 answer : b"
Answer: b
Python program:
a = 110 + 60 
b = a - 10
c = b * 10
d = c * 3
Problem: if you multiply all the numbers on your mobile phone , what is the answer ?
Options: a ) 2 , b ) 6 , c ) 1 , d ) 0 , e ) 7
Rationale: d 0 their is a zero in your phone .
Answer: d
Python program:
a = 1 - 1
b = 1 * a
Problem: if x is 20 percent greater than 12 , then x =
Options: a ) 10.2 , b ) 12.1 , c ) 8.1 , d ) 15.6 , e ) 14.4
Rationale: "x is 20 % greater than 12 means x is 1.2 times 12 ( in other words 12 + 20 / 100 * 12 = 1.2 * 12 ) therefore , x = 1.2 * 12 = 14.4 answer : e"
Answer: e
Python program:
a = 20 / 100
b = a * 12
c = 12 + b
Problem: if 7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ ( 7 ^ 9 ) - 7 ^ k , then k = ?
Options: a ) 11 / 3 , b ) 11 / 2 , c ) 242 , d ) 3 ^ 10 , e ) 7 ^ 11 - 1
Rationale: "7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ 7 ^ 9 - 7 ^ k 7 * ( 7 ^ k ) = 7 ^ ( 49 * 7 ^ 9 ) = 7 ^ ( 7 ^ 2 * 7 ^ 9 ) = 7 ^ ( 7 ^ 11 ) 7 ^ k + 1 = 7 ^ ( 7 ^ 11 ) so k + 1 = 7 ^ 11 so k = 7 ^ 11 - 1 answer is e"
Answer: e
Python program:
a = 9 + 2 
b = 7 ** a
c = b - 1
Problem: find the probability in a group of 10 students sitting in a row , two of them always sit next to each other
Options: a ) 0.5 , b ) 0.4 , c ) 0.3 , d ) 0.2 , e ) 0.1
Rationale: assume that these 2 students are 1 and then u can sit is 9 ! and these 2 students can sit by 2 ways then total ways are 9 ! * 2 and the probability is 9 ! * 2 / 10 ! = 1 / 5 = 0.2 answer : d
Answer: d
Python program:
a = 10 - 1
b = math.factorial(a)
c = math.factorial(2)
d = b * c
e = math.factorial(10)
f = d / e
Problem: a student got 74 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 66 % , b ) 67 % , c ) 68 % , d ) 69 % , e ) 70 %
Rationale: "74 + 81 + x = 3 * 75 x = 70 the answer is e ."
Answer: e
Python program:
a = 3 * 75
b = 74 + 81 
c = a - b
Problem: a leak in the bottom of a tank can empty the full tank in 3 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 1440 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 3 - 1 / 12 ) = 1 / 4 work done by the inlet in 1 min . = ( 1 / 4 × 1 / 60 ) = 0.004167 volume of 0.004167 part = 6 litres . therefore , volume of whole = 0.004167 x 6 ‹ = › 1440 litres . answer d"
Answer: d
Python program:
a = 12 * const_60
b = 6 * a
c = 12 * const_60
d = 3 * const_60
e = c / d
f = e - 1
g = b / f
Problem: the ratio of 2 numbers is 4 : 6 and their h . c . f . is 8 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 52 , d ) 96 , e ) 60
Rationale: "let the numbers be 4 x and 6 x their h . c . f . = 8 so the numbers are 4 * 8 , 6 * 8 = 32,48 l . c . m . = 96 answer is d"
Answer: d
Python program:
a = 6 ** 4
b = 2 ** 4
c = 4 ** 4
d = b + c 
e = a + d 
f = 8 / e
g = math.sqrt(f)
Problem: when positive integer n is divided by 4 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 35 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 4 , the remainder is 1 i . e . , n = 4 x + 1 values of n can be one of { 1 , 5 , 9 , 13 , 17 , . . . . . . . . . . . 29 , 33 , 37 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , . . . . . . . . } combining both the sets we get n = { 5,33 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 35 or 35 x in case of n = 33 p = 2 so for min value of p , we take min value of n . b is the answer ."
Answer: b
Python program:
a = 35 - reminder
Problem: sam invested rs . 12000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 13230.0 , b ) 12300.02 , c ) 16537.5 , d ) 15000.0 , e ) 16537.11
Rationale: "p = rs . 12000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 12000 * ( 1 + 5 / 100 ) 2 ] = ( 12000 * 21 / 20 * 21 / 20 ) = rs . 13230.00 answer : a"
Answer: a
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 12000
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 18 , what was the price before the first discount ?
Options: a ) $ 32 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 67.54 , e ) $ 65.23
Rationale: let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 18 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 18 solve for x x = $ 32 correct answer a
Answer: a
Python program:
a = 100 * 100
b = a * 18
c = 100 - 25
d = c * 100
e = 100 - 25
f = e * 25
g = d - f
h = b / g
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 16 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 36 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 16 = 36 km apart , they take 1 hour to be 1000 m apart , they take 36 * 1000 / 1000 = 36 min . answer is e"
Answer: e
Python program:
a = 20 + 16
Problem: a cube of edge 5 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 10 cm * 5 cm , find the rise in water level ?
Options: a ) 2.5 cm , b ) 3.6 cm , c ) 5 cm , d ) 6.43 cm , e ) 7.56 cm
Rationale: "increase in volume = volume of the cube = 5 * 5 * 5 cm ^ 3 rise in water level = volume / area = 5 * 5 * 5 / 10 * 5 = 2.5 cm answer is a"
Answer: a
Python program:
a = volume_cube / (
Problem: two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 15 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 3 ) ã — ( 2 / 5 ) = 2 / 15 answer : b ) 2 / 15"
Answer: b
Python program:
a = 1 / 3
b = 2 / 5
c = a * b
Problem: 4 men and 12 boys finish a piece of work in 4 days , 7 men and 6 boys do it in 5 days . the ratio between the efficiencies of a man and boy is ?
Options: a ) 18 : 19 , b ) 17 : 19 , c ) 15 : 19 , d ) 18 : 14 , e ) 18 : 11
Rationale: "4 m + 12 b - - - - - 4 days 7 m + 6 b - - - - - - - 5 days 16 m + 48 b = 35 m + 30 b 18 b = 19 m = > 5 m = 6 b m : b = 18 : 19 answer : a"
Answer: a
Python program:
a = 12 * 4
b = 6 * 5
c = a - b
d = 7 * 5
e = 4 * 4
f = d - e
g = c / f
Problem: a boatman trying to cross the river . the width of the river is 400 m . he is selling boat with 10 m / sec . he takes 50 sec to cross the river due to flow of water . calculate the drift .
Options: a ) 500 , b ) 400 , c ) 300 , d ) 200 , e ) 100
Rationale: the distance boatman travel to cross the river = 50 * 10 = 500 m he sell the boat diagonally . so height = 400 m , base be x and hypotenuse = 500 m so by pythagoras theorem , square of 400 + square of x = square of 500 so , square of x = 250000 - 160000 x = â ˆ š 250000 - 160000 , x = â ˆ š 90000 = 300 drift = 300 m answer c
Answer: c
Python program:
a = 50 * 10
b = a ** 2
c = 400 ** 2
d = b - c
e = math.sqrt(d)
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 60 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 25 , d ) 64 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 60 ounces of a substance has a volume of ( 48 / 112 ) * 60 = 25 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 60 will have a volume a little more than 24 , that is 25 c"
Answer: c
Python program:
a = 48 / 112
b = a * 60
Problem: the average speed of a train is 87 kmph . the train was scheduled to start at 9 am in bangalore , and as per schedule it has to reach a destination of 348 km away from bangalore at 1 : 45 pm same day and a halt was scheduled onthe way . for how long was the halt scheduled ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 55 minutes , d ) 60 minutes , e ) none of these
Rationale: speed of train = 87 kmph and distance it covers is 348 km . time taken to cover the distance = distance / speed = 348 / 87 = 4 hours . but total time taken by train to reach destination is = 1 : 45 pm – 9 a . m = 4 hours 45 minutes . time of halt = total time – take taken without halt = 4 hours 45 minutes – 4 hours = 45 minutes a )
Answer: a
Python program:
a = 4 + 2 
b = a * 2
c = 1 + b 
d = c - 9
e = d * const_60
f = e + 45 
g = 348 / 87
h = g * const_60
i = f - h
Problem: the height of the wall is 4 times its width and length of the wall is 3 times its height . if the volume of the wall be 10368 cu . m . its width is
Options: a ) 4 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 4 x and length = 12 x 12 x ã — 4 x ã — x = 10368 x = 6 answer : c"
Answer: c
Python program:
a = 4 * 3
b = a * 4
c = 10368 / b
d = 1 / 3
e = c ** d
Problem: a courtyard is 24 meter long and 14 meter board is to be paved with bricks of dimensions 25 cm by 15 cm . the total number of bricks required is :
Options: a ) 6000 , b ) 8000 , c ) 8960 , d ) 2000 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2400 ã — 1400 / 25 ã — 15 ) = 8960 option c"
Answer: c
Python program:
a = 24 * 100
b = 14 * 100
c = a * b
d = 25 * 15
e = c / d
Problem: when a = x + ( 3 / x ) and b = x - ( 3 / x ) , ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 4096
Rationale: "- - > ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = { ( 2 ) ^ ( a ^ 2 - b ^ 2 ) } = 2 ^ ( a - b ) ( a + b ) . since a - b = 6 / x and a + b = 2 x , 2 ^ ( a - b ) ( a + b ) = 2 ^ ( 6 / x ) ( 2 x ) = 2 ^ 12 = 4096 therefore , the answer is e"
Answer: e
Python program:
a = 3 * 3
b = 3 * 3
c = a + b 
d = 3 ** c
Problem: 20 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 90 %
Rationale: to maximize the percentage of companies offering both , let ' s assume that all 20 % of companies which offer wireless internet also offer snacks . the answer is a .
Answer: a
Python program:
a = 20 * 1
Problem: in how many seconds will a train 180 meters long pass an oak tree , if the speed of the train is 54 km / hr ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: speed = 54 * 5 / 18 = 15 m / s time = 180 / 15 = 12 seconds the answer is b .
Answer: b
Python program:
a = const_0_2778 * 54
b = 180 / a
Problem: if 20 typists can type 40 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 180 , e ) 400
Rationale: "20 typists can type 40 letters , so 30 typists can type = 40 * 30 / 20 40 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 40 * 30 * 60 / 20 * 20 = 180 d is the answer"
Answer: d
Python program:
a = 40 * 3
b = a / 20
c = b * 30
Problem: there are 4 people who has to cross a stretch of 300 km . they normally run at a speed of 10 kmph . one of them has a bike that travels at 50 kmph . the bike first takes one person alone and crosses the stretch while the other two keep running . then he comes back without wasting time and picks up another person from the way , drives him across the stretch , and does the same for the last person . how long does this whole process take ?
Options: a ) 24 hrs , b ) 16 hrs , c ) 56 / 3 hrs , d ) 58 / 3 hrs , e ) 18 hrs
Rationale: expl : time taken to carry 2 nd person = 300 / 50 = 6 hrs . time taken to meet 3 rd person = ( 300 - 6 * 10 ) / ( 50 + 10 ) = 4 hrs time taken to carry 3 rd person = 4 hours time taken to meet 4 th person = ( 300 – 140 ) / 60 = 8 / 3 total time = 6 + 4 + 4 + 8 / 3 + 8 / 3 = 58 / 3 hours answer : d
Answer: d
Python program:
a = 300 / 50
b = 300 / 50
c = b * 10
d = 300 - c
e = 50 + 10 
f = d / e
g = a + f 
h = 300 / 50
i = h * 10
j = 300 - i
k = 50 + 10 
l = j / k
m = g + l 
n = 300 / 50
o = n * 10
p = 300 - o
q = 10 * 10
r = p - q
s = 300 - r
t = 50 + 10 
u = s / t
v = 300 / 50
w = v * 10
x = 300 - w
y = 10 * 10
z = x - y
A = 300 - z
B = 50 + 10 
C = A / B
D = u + C 
E = m + D
Problem: a courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 15 cm by 13 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18078 , c ) 11076 , d ) 11456 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 1800 ã — 1200 / 15 ã — 13 ) = 11076 option c"
Answer: c
Python program:
a = 18 * 100
b = 12 * 100
c = a * b
d = 15 * 13
e = c / d
Problem: if one length of a square is tripled , and the original parameter is 4 y . what is the new length of one of the sides ?
Options: a ) 12 y / 3
b ) 2 y / 2
c ) 6 y / 3
d ) 12 y / 4
e ) 4 y / 3
Rationale: if the original parameter is 4 y , each length of the square is 4 y / 4 . if the parameter is tripled , then each length becomes 3 ( 4 y ) / 4 . this is 12 y / 4 . answer option d .
Answer: d
Python program:
a = 4 * 3
b = square_area / (
Problem: an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the ?
Options: a ) 8 : 6 , b ) 8 : 7 , c ) 8 : 1 , d ) 8 : 2 , e ) 8 : 4
Rationale: "let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer : b"
Answer: b
Python program:
a = 3 * 2
b = a * 4
c = 7 * 3
d = b / c
Problem: 80 % of a number is added to 20 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 270 , d ) 100 , e ) 281
Rationale: ( 80 / 100 ) * x + 20 = x 4 x + 100 = 5 x x = 100 answer : : d
Answer: d
Python program:
a = 20 / 100
b = 20 / a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 780 grams per kg , what is his percent ?
Options: a ) 28 % , b ) 25 % , c ) 55 % , d ) 28 % , e ) 28.2 %
Rationale: "780 - - - 220 100 - - - ? = > 28.2 % answer : e"
Answer: e
Python program:
a = 100 / 780
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: angelina walked 840 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 16 , e ) 30
Rationale: "let the speed be x . . . so time taken from home to grocery = 840 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 840 / x - 240 / x = 40 . . 600 / x = 40 . . x = 15 m / secs . . so grocery to gym = 2 * 15 = 30 m / s . . . e"
Answer: e
Python program:
a = 480 / 2
b = 840 - a
c = b / 40
d = c * 2
Problem: david obtained 74 , 65 , 82 , 67 and 90 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) a ) 87 , b ) b ) 99 , c ) c ) 68 , d ) d ) 82 , e ) e ) 76
Rationale: "average = ( 74 + 65 + 82 + 67 + 90 ) / 5 = 380 / 5 = 76 . answer : e"
Answer: e
Python program:
a = 74 + 65 
b = a + 82 
c = b + 67 
d = c + 90 
e = 2 + 3 
f = d / e
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.8 % , d ) 18 % , e ) 19.5 %
Rationale: "increase = ( 10 / 60 ) * 100 = ( 1 / 6 ) * 100 = 16.66 % . b"
Answer: b
Python program:
a = 70 - 60
b = a / 60
c = b * 100
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many e acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn e = 4 * 94 = 376 correct option - c"
Answer: c
Python program:
a = 1000 * 1
b = 10 * 3
c = b + 4 
d = a + c 
e = 5 + 2 
f = e + 4 
g = d / f
h = g * 4
Problem: at an elementary school , 70 % of the faculty members are women and 60 % of the faculty members are married . if 2 ⁄ 3 of the men are single , what fraction of the men are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 70
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 20 - - - - - 20 - - - - - - - - - 40 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married man / total man , so 10 / 30 = 1 / 3 c"
Answer: c
Python program:
a = 2 / 3
b = 1 - a
Problem: when n is divided by 24 , the remainder is 5 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 6 , e ) 7
Rationale: "let n = 5 ( leaves a remainder of 5 when divided by 24 ) 4 n = 4 ( 5 ) = 20 , which leaves a remainder of 4 when divided by 8 . answer c"
Answer: c
Python program:
a = 5 - reminder
Problem: a train 400 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 277 m , b ) 700 m , c ) 900 m , d ) 187 m , e ) 1678 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 400 + x ) / 60 = 65 / 3 x = 900 m . answer : c"
Answer: c
Python program:
a = 78 - 1
b = a * const_0_2778
c = 400 / b
Problem: ramu bought an old car for rs . 42000 . he spent rs . 8000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 29.8 % , b ) 16 % , c ) 18 % , d ) 82 % , e ) 23 %
Rationale: "total cp = rs . 42000 + rs . 8000 = rs . 50000 and sp = rs . 64900 profit ( % ) = ( 64900 - 50000 ) / 50000 * 100 = 29.8 % answer : a"
Answer: a
Python program:
a = 42000 + 8000 
b = 64900 - a
c = 42000 + 8000 
d = b / c
e = d * 100
Problem: machine p and machine q are each used to manufacture 990 sprockets . it takes machine p 10 hours longer to produce 990 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 990 / x = 990 / 1.1 x + 10 1.1 ( 990 ) = 990 + 11 x 11 x = 99 x = 9 the answer is e ."
Answer: e
Python program:
a = 10 / 100
b = a + 1 
c = 990 / b
d = 990 - c
e = d / 10
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 40 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 105 , e ) 110
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 40 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 40 = ( 2 ^ 2 * 5 ^ 2 ) ^ 40 = 2 ^ 80 * 5 ^ 80 answer : a"
Answer: a
Python program:
a = 100 / 40
b = 2 ** a
c = b - 1
d = 100 - c
Problem: if the product of 2 integers is negative , at most how many of the integers can be negative ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the product of 2 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 1 correct option : a"
Answer: a
Python program:
a = 2 - 1
Problem: what will be the difference between simple and compound interest @ 10 % per annum on the sum of rs 1000 after 4 years
Options: a ) rs 62.10 , b ) rs 63.10 , c ) rs 64.10 , d ) rs 65.10 , e ) none of these
Rationale: explanation : s . i . = 1000 ∗ 10 ∗ 4 / 100 = 400 c . i . = [ 1000 ( 1 + 10 / 100 ) 4 − 1000 ] = 464.10 so difference between simple interest and compound interest will be 464.10 - 400 = 64.10 option c
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = b ** 4
d = 1000 * c
e = d - 1000
f = 10 / 100
g = 1000 * f
h = g * 4
i = e - h
Problem: find k if 16 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 16 / k = 4 and 16 / 4 = 4 , then k = 4 correct answer d"
Answer: d
Python program:
a = 16 / 4
Problem: the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 sq . ft , how much will it cost to paint outside of a cube having 8 feet each side
Options: a ) rs . 962 , b ) rs . 672 , c ) rs . 546 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 82 = 384 sq . ft quantity of paint required = ( 384 / 16 ) = 24 kg cost of painting = 36.5 x 24 = rs . 876 answer : d"
Answer: d
Python program:
a = surface_cube / (
b = a * 16