euclaise/mathqa_programs huggingface dataset:
Problem: the angle between the minute hand and the hour hand of a clock when the time is 8 : 30
Options: a ) 80 deg , b ) 40 deg , c ) 35 deg , d ) 75 deg , e ) 60 deg
Rationale: "angle traced hr hand 17 / 2 hrs = 300 / 12 * 17 / 2 = 255 angle by min 30 min ( 360 / 60 * 30 ) = 180 req = 255 - 180 = 75 answer d"
Answer: d
Python program:
a = 3 * 4
b = 3 * 4
c = b - 1
d = a / c
e = 4 + 1 
f = 3 * 4
g = f - 1
h = e * g
i = d * h
j = const_60 / 2
k = i - j
l = 3 * 4
m = l - 1
n = k * m
o = n / 2
Problem: a large tank can filled by a and b in 30 minutes and 45 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ?
Options: a ) 30 min , b ) 20 min , c ) 25 min , d ) 40 min , e ) 45 min
Rationale: "part filled by a + b in 1 minute = 1 / 30 + 1 / 45 = 1 / 45 suppose the tank is filled in x minutes then , x / 2 ( 1 / 45 + 1 / 45 ) = 1 x / 2 * 2 / 45 = 1 x = 45 min answer is e"
Answer: e
Python program:
a = 1 / 30
b = 1 / 45
c = a + b 
d = 1 / 45
e = c + d 
f = 1 / e
g = f * 2
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 13 a – d = 3 a + d = 13 2 d = 10 d = 5 answer : b"
Answer: b
Python program:
a = 3 * 6
b = 13 - 6
c = b + 3 
d = a - c
e = d - 6
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 4136 cm is ?
Options: a ) 22 , b ) 28 , c ) 17 , d ) 12 , e ) 47
Rationale: "2 * 22 / 7 * 14 * x = 4136 = > x = 47 answer : e"
Answer: e
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 4136 / g
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 36 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 23.56 , b ) 23.59 , c ) 44.0 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 36 + 20 ) = 112 cm parameter of the square = 112 cm i . e . 4 a = 112 a = 28 diameter of the semicircle = 28 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 28 ) = 1 / 2 ( 22 / 7 ) ( 28 ) = 44 cm to two decimal places answer : c"
Answer: c
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: on selling 15 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 45 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 72
Rationale: "( c . p . of 15 balls ) - ( s . p . of 15 balls ) = ( c . p . of 5 balls ) c . p . of 10 balls = s . p . of 15 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 10 = rs . 72 . answer : option e"
Answer: e
Python program:
a = 15 - 5
b = 720 / a
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 3 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 179 : 2 , b ) 178 : 3 , c ) 179 : 1 , d ) 179 : 54 , e ) 179 : 45
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 3 = 15 / 8 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 8 + 7 / 2 = 43 / 8 = 5.375 litres as 7 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 5.375 : 1.625 = 179 : 54 . answer : d"
Answer: d
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 3 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k 
m = e / l
Problem: x and y are positive integers . when x is divided by 6 , the remainder is 3 , and when x is divided by 16 , the remainder is 5 . when y is divided by 9 , the remainder is 5 , and when y is divided by 7 , the remainder is 4 . what is the least possible value of x / y ?
Options: a ) 2.5 , b ) 3 , c ) 2 , d ) 1.3 , e ) 1.5
Rationale: "when x is divided by 6 , the remainder is 3 : so , the possible values of x are : 3 , 9 , 15 , 21 , etc . when x is divided by 16 , the remainder is 5 : so , the possible values of x are : 5,21 . . . stop . since both lists include 21 , the smallest possible value of x is 21 . when y is divided by 9 , the remainder is 5 : so , the possible values of y are : 5 , 14 , 23,32 etc . when y is divided by 7 , the remainder is 4 : so , the possible values of y are : 6 , 14 , . . . stop . since both lists include 14 , the smallest possible value of y is 14 since the smallest possible values of x and y are 21 and 14 respectively , the smallest possible value of x / y is 1.5 . so , e is the correct answer to the original question ."
Answer: e
Python program:
a = 9 * 2
b = a + 5 
c = 3 + 6 
d = b - c
Problem: in what time will a train 600 meters long cross an electric pole , if its speed is 144 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 15 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 600 / 40 = 15 seconds answer : d"
Answer: d
Python program:
a = 144 * const_0_2778
b = 600 / a
Problem: a certain class of students is being divided into teams . the class can either be divided into 10 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 120 , d ) 60 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 10 24 so , lets find the least common multiple of 10 24 , ie 120 so our answer is ( c ) 120"
Answer: c
Python program:
a = math.lcm(10, 24)
Problem: a man took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 15,000 , d ) rs . 20,000 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 12 x 3 ) = rs . 15000 . answer c"
Answer: c
Python program:
a = 5400 * 100
b = 3 * 12
c = a / b
d = const_60 / 4
e = d * 100
f = c / e
Problem: the ratio of the present age of sandy to that of molly is 7 : 2 . twelve years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 39 , b ) 45 , c ) 51 , d ) 57 , e ) 63
Rationale: "let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 12 ) / ( 2 x + 12 ) = 5 / 2 4 x = 36 x = 9 six years ago , sandy ' s age was 7 ( 9 ) - 6 = 57 the answer is d ."
Answer: d
Python program:
a = 10 + 6 
b = 5 * a
c = 10 + 6 
d = 2 * c
e = b - d
f = e * 7
g = 2 + 2 
h = f / g
i = h - 6
Problem: the sides of a triangle are in the ratio 3 : 5 : 7 . if the pereimeter is 60 cms , the longest side is
Options: a ) 7 , b ) 30 , c ) 28 , d ) 25 , e ) 16
Rationale: "3 x + 5 x + 7 x = 60 15 x = 60 x = 4 longest side = 7 * 4 = 28 answer : c"
Answer: c
Python program:
a = 3 + 5 
b = a + 7 
c = 60 / b
d = 60 * c
Problem: how many positive integers between 5 and 5000 ( both are inclusive ) are there such that they are multiples of 5 ?
Options: a ) 1500 , b ) 1000 , c ) 999 , d ) 1001 , e ) 1005
Rationale: "multiples of 5 = 5 , 10,15 - - - - - , 5000 number of multiples of 5 = > 5000 - 5 / 5 + 1 = 1000 answer is b"
Answer: b
Python program:
a = 5000 - 5
b = a / 5
Problem: the sale price sarees listed for rs . 528 after successive discount is 20 % and 10 % is ?
Options: a ) 288 , b ) 277 , c ) 380 , d ) 290 , e ) 262
Rationale: "528 * ( 80 / 100 ) * ( 90 / 100 ) = 380 answer : c"
Answer: c
Python program:
a = 528 * 20
b = a / 100
c = 528 - b
d = 528 * 20
e = d / 100
f = 528 - e
g = f * 10
h = g / 100
i = c - h
Problem: a train covers a distance of 9 km in 6 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 100 , b ) 105 , c ) 110 , d ) 120 , e ) 125
Rationale: "speed = ( 9 / 6 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 5 = 125 m . answer : option e"
Answer: e
Python program:
a = 9 / 6
b = a - 5
c = 9 / b
Problem: the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 52 black cars in the lot , how many red cars are there in the lot ?
Options: a ) 11 , b ) 20 , c ) 24 , d ) 27 , e ) 32
Rationale: "b is correct r / b = 3 / 8 and b = 52 r = 52 * 3 / 8 = 20"
Answer: b
Python program:
a = 3 / 8
b = a * 52
c = math.floor(b)
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 5 : 9 . if the shop carries 204 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 51 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: let us assume the number of dogs , cats and bunnies to be 3 x , 5 x and 9 x total dogs and bunnies = 12 x . and we are given that 12 x = 204 . hence x = 17 . dogs = 3 x = 3 * 17 = 51 ( option a )
Answer: a
Python program:
a = 3 + 9 
b = 204 / a
c = b * 3
Problem: a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 900 . how many workers were part of the latter production run ?
Options: a ) a ) 6 , b ) b ) 10 , c ) c ) 11 , d ) d ) 15 , e ) e ) 34
Rationale: "the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 900 . . thus for the current period = 900 - 500 = 400 ( 5 n + 45 ) k = 400 k = 400 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 400 / 5 n + 45 500 ( 5 n + 45 ) = 400 ( 5 n + 20 ) 25 n + 225 = 20 n + 80 5 n = 145 n = 29 thus n + 5 = 34 hence e"
Answer: e
Python program:
a = 20 + 5
Problem: there are 5 guys who have equal number of bullets . all of them shoot 4 bullets . the remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division . what was the original number of bullets each one had ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 25
Rationale: let initially each was having x bullets they shot 4 bullets so 5 x - 20 = x x = 5 so each was having 5 bullets . total was 25 . answer : e
Answer: e
Python program:
a = 4 * 5
b = 5 - 1
c = a / b
d = c * 5
Problem: the cost price of an article is 55 % of the marked price . calculate the gain percent after allowing a discount of 15 % .
Options: a ) 40.5 % , b ) 48.7 % , c ) 54.5 % , d ) 55.6 % % , e ) none
Rationale: sol . let marked price = rs . 100 . then , c . p . = rs . 55 . s . p = rs . 85 . â ˆ ´ gain % = [ 30 / 55 * 100 ] % = 54.5 % . answer c
Answer: c
Python program:
a = 100 - 15
b = a / 55
c = b - 1
d = c * 100
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 4 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 1.6 , b ) 1 , c ) 0.4 , d ) 0.16 , e ) 0.016
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 16 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 160 / 10,000 = 16 / 1000 = 0.016 ft the answer is e ."
Answer: e
Python program:
a = volume_cylinder / (
Problem: peter and tom shared the driving on a certain trip . if peter and tom both drove for the same amount of time , but peter only drove 2 / 5 of the total distance , what was the ratio of tom ' s average speed to peter ' s average speed ?
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 1 : 2 , d ) 3 : 2 , e ) 2 : 3
Rationale: the answer is suppose to be d . 3 : 2 . it ' s from the gmatprep option d is answer
Answer: d
Python program:
a = 2 / 5
b = 1 - a
c = 2 / 5
d = b / c
Problem: a grocery shop has a sale of rs . 6735 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4691 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6735 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6735 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34309 + x = 39000 = > x = 39000 − 34309 = 4691 answer : d"
Answer: d
Python program:
a = 5 + 1 
b = 6500 * a
c = 6735 + 6927 
d = 6855 + c 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 6
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 12 t = 12 / 2 = 6 answer : e"
Answer: e
Python program:
a = 4 - 2
b = 12 / a
Problem: 1 / 4 of all the juniors and 2 / 3 of all the seniors are going on a trip . if there are 2 / 3 as many juniors as seniors , what fraction of the students are not going on the trip ?
Options: a ) 4 / 9 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 / 3 , e ) 5 / 6
Rationale: j be the number of juniors and s be the number of seniors . there are 2 / 3 as many juniors as seniors 23 ∗ s = j j / s = 23 going on trip = j 4 + 23 ∗ s fraction = ( j 4 + 23 s ) / ( j + s ) = ( 2 / 3 * 1 / 4 + 2 / 3 ) / ( 2 / 3 + 1 ) = 1 / 2 fraction not on trip = 1 / 2 answer : b
Answer: b
Python program:
a = 2 / 3
b = 4 * 3
c = a * b
d = 2 / 3
e = 4 * 3
f = d * e
g = 1 / 4
h = f * g
i = c + h 
j = 4 * 3
k = 2 / 3
l = 4 * 3
m = k * l
n = j + m 
o = i / n
Problem: sonika deposited rs . 4500 which amounted to rs . 8400 after 2 years at simple interest . had the interest been 4 % more . she would get how much ?
Options: a ) 9680 , b ) 8790 , c ) 8760 , d ) 9020 , e ) 5000
Rationale: "( 4500 * 2 * 4 ) / 100 = 360 8400 - - - - - - - - 8760 answer : c"
Answer: c
Python program:
a = 4 / 100
b = 8400 - 4500
c = b / 2
d = c / 4500
e = a + d 
f = e * 4500
g = f * 2
h = g + 4500
Problem: a grocer has a sale of rs . 4000 , rs . 6524 , rs . 5689 , rs . 7230 and rs . 6000 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?
Options: a ) s . 12557 , b ) s . 14993 , c ) s . 15560 , d ) s . 12589 , e ) s . 12500
Rationale: "total sale for 5 months = rs . ( 4000 + 6524 + 5689 + 7230 + 6000 ) = rs . 29443 required sale = rs . [ ( 7000 x 6 ) - 29443 ] = rs . ( 42000 - 29443 ) = rs . 12557 . option a"
Answer: a
Python program:
a = 5 + 1 
b = a * 7000
c = 4000 + 6524 
d = c + 5689 
e = d + 7230 
f = e + 6000 
g = b - f
Problem: at a contest with 2000 participants , 1 / 2 of the people are aged 16 to 18 . next year , the number of people aged 16 to 18 will increase by 1 / 4 . after this change , what percentage of the total 2000 people will the 16 - to 18 - year - olds represent ?
Options: a ) 62.50 % , b ) 60 % , c ) 70 % , d ) 65 % , e ) 66 / 3 %
Rationale: i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2000 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 4 , we are multiplying it by 1 + 1 / 4 = 5 / 4 , so the answer here must be ( 1 / 2 ) * ( 5 / 4 ) = 5 / 8 = 62.50 % . answer : a
Answer: a
Python program:
a = 2000 / 2
b = 1 / 4
c = 1 + b 
d = a * c
e = d / 2000
f = e * 100
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 26 sec , b ) 28 sec , c ) 12 sec , d ) 77 sec , e ) 66 sec
Rationale: "d = 250 m + 250 m = 500 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 500 * 3 / 125 = 12 sec answer : c"
Answer: c
Python program:
a = 80 * const_0_2778
b = 250 / a
Problem: the closest approximation of f ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: f ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c
Answer: c
Python program:
a = 0 / 4
b = a * 69
Problem: there are 9 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 97 , b ) 99 , c ) 101 , d ) 103 , e ) 105
Rationale: the total number of ways to form a team of 4 is 9 c 4 = 126 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 7 c 2 = 21 . the number of ways to form an acceptable team is 126 - 21 = 105 . the answer is e .
Answer: e
Python program:
a = 9 - 4
b = math.factorial(a)
c = 4 * 3
d = c + 3 
e = b - d
Problem: the average of first 11 prime numbers is ?
Options: a ) 14.55 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11
Rationale: "sum of 11 prime no . = 160 average = 160 / 11 = 14.55 answer : a"
Answer: a
Python program:
a = 11 + 1
Problem: if 12 men or 20 women can do a piece of work in 108 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "d 80 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 108 days . so , 27 women can do it in ( 20 * 108 ) / 27 = 80 days ."
Answer: d
Python program:
a = 12 * 108
b = 9 / a
c = 20 * 108
d = 12 / c
e = b + d 
f = 1/(e)
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 7500 , brokerage being 1 / 4 % , is :
Options: a ) 103.92 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 7500 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 7500 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 104.17 = market value of rs . 100 stock = rs . 104.17 - re . 0.25 . = market value of rs . 100 stock = rs . 103.92 . answer : a"
Answer: a
Python program:
a = 7500 / 756
b = a * 10
c = 1 / 4
d = b - c
Problem: a bag contains 6 black and 5 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 5 / 11 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 5 ) = 11 . number of white balls = 5 p ( drawing a white ball ) = 5 / 11 option b ."
Answer: b
Python program:
a = math.factorial(5)
b = 5 - 2
c = math.factorial(b)
d = a / c
e = math.factorial(2)
f = d / e
g = math.factorial(6)
h = 6 - 2
i = math.factorial(h)
j = g / i
k = math.factorial(2)
l = j / k
m = f + l 
n = 6 + 5 
o = math.factorial(n)
p = 6 + 5 
q = p - 2
r = math.factorial(q)
s = o / r
t = math.factorial(2)
u = s / t
v = m / u
Problem: in what ratio water be mixed with milk costing rs . 12 per liter to obtain a mixture worth of rs . 8 per litre ?
Options: a ) 2 : 7 , b ) 1 : 2 , c ) 2 : 9 , d ) 2 : 2 , e ) 2 : 6
Rationale: answer with explanation : by the rule of allegation , i . c . p of 1 liter of water = 0 ii . c . p of 1 liter of milk = 12 iii . mean price ( p ) = 8 iv . d – m = 12 - 8 = 4 v . m – c = 8 - 0 = 8  ratio of water and milk = 4 : 8 = 1 : 2 answer : b
Answer: b
Python program:
a = 8 / 12
b = 1 - a
c = 8 / 12
d = b / c
Problem: a reindeer chased by a cheetah passed a certain tree at a constant speed of 50 miles per hour while being chased by a cheetah . then , 2 minutes later , the cheetah passed the same tree at a constant speed of 60 miles per hour . if both animals maintained their speeds , how long after the cheetah passed the tree did the cheetah catch up with the reindeer ?
Options: a ) 30 min , b ) 45 min , c ) 1 hr , d ) 3 min , e ) 1 min
Rationale: when the cheetah is at the tree , the reindeer is 50 / 30 miles ahead on the highway . ( the distance covered in 2 min ) every hour , cheetah runs 10 miles more than the deer . how many hours will it takes it to cover 50 / 30 miles more ? the answer is ( 50 / 30 ) / 10 = 1 / 60 = 1 min answer e
Answer: d
Python program:
a = 60 - 50
b = 2 / const_60
c = 50 * b
d = a / c
e = d / 2
Problem: if the numbers 1 to 100 are written on 100 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 100 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 74 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 100 . answer : c"
Answer: c
Python program:
a = 1 / 100
Problem: a fort had provision of food for 150 men for 45 days . after 10 days , 25 men left the fort . find out the number of days for which the remaining food will last
Options: a ) 44 , b ) 42 , c ) 40 , d ) 38 , e ) 36
Rationale: "explanation : given that fort had provision of food for 150 men for 45 days hence , after 10 days , the remaining food is sufficient for 150 men for 35 days remaining men after 10 days = 150 - 25 = 125 assume that after 10 days , the remaining food is sufficient for 125 men for x days more men , less days ( indirect proportion ) ⇒ men 150 : 125 } : : x : 35 ⇒ 150 × 35 = 125 x ⇒ 6 × 35 = 5 x ⇒ x = 6 × 7 = 42 ⇒ the remaining food is sufficient for 125 men for 42 days . answer : option b"
Answer: b
Python program:
a = 25 + 10 
b = 150 * a
c = 150 - 25
d = b / c
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 2 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 3 , d ) 4 / 3 , e ) 5 / 2
Rationale: "b work 1 / 8 * 2 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 3 / 4 * remaining work = 4 / 3 * 1 / 4 = 1 / 3 answer : c"
Answer: c
Python program:
a = 2 / 6
b = 2 / 8
c = a + b
Problem: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and sandy will make a basket but jill will miss ?
Options: a ) 1 / 8 , b ) 3 / 8 , c ) 3 / 28 , d ) 5 / 28 , e ) 1 / 56
Rationale: "the probability that jack and sandy will make a basket but jill will miss is 1 / 6 * 6 / 7 * 1 / 8 = 1 / 56 . the answer is e ."
Answer: e
Python program:
a = 1 / 7
b = 1 / 8
c = a * b
d = 1 / 6
e = 1 - d
f = c * e