euclaise/mathqa_programs huggingface dataset:
Problem: beginning in town a , biker bob rides his bike 10 miles west , 5 miles north , 5 miles east , and then 15 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 22 miles , b ) 20.62 miles , c ) 25 miles , d ) 26 miles , e ) 28 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 15 + 5 = 20 m other being the base ie distance traveled west - distance traveled eat = 10 - 5 = 5 m now this third side or the distance between town a and town b = 20 ^ 2 + 5 ^ 2 = sq root 425 = 20.62 mile answer : b"
Answer: b
Python program:
a = 5 + 15 
b = a ** 2
c = 5 ** 2
d = b + c 
e = math.sqrt(d)
Problem: a , b and c have rs . 400 between them , a and c together have rs . 300 and b and c rs . 150 . how much does c have ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100
Rationale: "a + b + c = 400 a + c = 300 b + c = 150 - - - - - - - - - - - - - - a + b + 2 c = 450 a + b + c = 400 - - - - - - - - - - - - - - - - c = 50 answer : b"
Answer: b
Python program:
a = 300 + 150 
b = a - 400
Problem: 0.0002152 / 0.000205 x 12.05 = ?
Options: a ) 19.64 , b ) 14.64 , c ) 12.6 , d ) 15.64 , e ) 13.64
Rationale: "explanation : ? = 0.0002152 / 0.000205 x 12.05 = 12.6 answer : option c"
Answer: c
Python program:
a = 0 / 2152
Problem: city x has a population 8 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 16 : 1
Rationale: "x = 8 y , y = 2 * z x : y , y : z 8 : 1 , 2 : 1 16 : 2 , 2 : 1 so , x : z = 16 : 1 ( e )"
Answer: e
Python program:
a = 8 * 2
Problem: in digging a pond 20 m * 10 m * 8 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1600 , c ) 2866 , d ) 2787 , e ) 1121
Rationale: "20 * 10 * 8 = 1600 answer : b"
Answer: b
Python program:
a = 20 * 10
b = a * 8
Problem: a man took loan from a bank at the rate of 12 % p . a . s . i . after 10 years he had to pay rs . 1500 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 1502 , b ) 1900 , c ) 1250 , d ) 1750 , e ) 2000
Rationale: "principal = ( 100 * 1500 ) / ( 12 * 10 ) = rs . 1250 answer : c"
Answer: c
Python program:
a = 1500 * 100
b = a / 10
c = b / 12
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 8 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 89
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 8 total people can seat = 81 + 8 = 89 answer : e"
Answer: e
Python program:
a = 15 - 3
b = 15 + a 
c = b * 3
d = c + 8
Problem: if a town of 45,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 46000 , b ) b . 47000 , c ) c . 48000 , d ) d . 49000 , e ) e . 50000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Python program:
a = 3 + 4 
b = 5 * a
c = b * 100
d = 3 + 4 
e = d + 3 
f = c * e
Problem: a computer wholesaler sells 10 different computers and each is priced differently . if the wholesaler chooses 3 computers for display at a trade show , what is the probability ( all things being equal ) that the two most expensive computers will be among the 3 chosen for display ?
Options: a ) 15 / 56 , b ) 3 / 28 , c ) 1 / 28 , d ) 1 / 15 , e ) 1 / 168
Rationale: since , two of the choices are prefixed , we are free to choose 1 from the rest of the 8 avilable . so 8 c 1 is the numerator . total no of ways we can choose 3 from 10 is 10 c 3 , which is the denominator . so , the probability : 8 c 1 / 10 c 3 = 1 / 15 ans is d .
Answer: d
Python program:
a = 3 - 1
b = a / 10
c = 10 - 1
d = 1 / c
e = b * d
f = 3 * e
Problem: how many internal diagonals does a octagon ( eight sided polygon ) have ?
Options: a ) 90
b ) 85
c ) 70
d ) 35
e ) 20
Rationale: number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 8 no . of diagonals = 8 ( 8 - 3 ) / 2 = 20 ans e
Answer: e
Python program:
a = 2 * 4
b = a - 3
c = 2 * 4
d = c / 2
e = b * d
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 17 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 17 = 83 jade handled = 83 transactions . answer : d"
Answer: d
Python program:
a = 90 / 100
b = 10 + 100 
c = a * b
d = c * 2
e = d / 3
f = e + 17
Problem: among 600 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 180
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 180 using your analysis : we see that the total number of students who study either maths or sociology = 264 + 336 - 180 = 420 so , in the image we know that the number of students in the zone with the black boundary = 420 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 600 , we can write : 420 + b + w = 600 or , b + w = 600 - 420 = 180 that is , b = 180 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 180 e"
Answer: e
Python program:
a = 600 / 100
b = a * 56
c = 600 / 100
d = c * 44
e = b + d 
f = 600 / 100
g = f * 30
h = e - g
i = 600 - h
Problem: if a farmer sells 15 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 20 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 60 , e ) 55
Rationale: "say farmer has n goat and he is good for d days . : - we have 3 equations given in question : - ( n - 15 ) * d + 4 = ( n + 20 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 20 d - 3 n = 60 4 n - 15 d = 60 = > n = 60 ans d it is !"
Answer: d
Python program:
a = 3 * 4
b = a - 20
c = b * 20
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 3 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 60 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 3 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 3 * ( 2 / 3 ) ) days = > 60 days answer : a"
Answer: a
Python program:
a = 15 * 21
b = a * 8
c = 21 * 3
d = 2 / 3
e = c * d
f = b / e
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 72 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 8 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 72,000 m : c is the circumference c = 3 meters correct answer e"
Answer: e
Python program:
a = 2 * 3
b = a * 10
c = b * 400
d = 72 / c
e = d * 1000
Problem: a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 , c receives :
Options: a ) s . 14,000 , b ) s . 14,200 , c ) s . 4,400 , d ) s . 8,400 , e ) s . 4,800
Rationale: let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 x 12 / 50 ) = rs . 8,400 . d
Answer: d
Python program:
a = 4000 + 5000 
b = a + 5000 
c = 50000 - b
d = c / 3
e = d / 50000
f = e * 35000
g = f / 4
h = g - 100
i = h / 10
Problem: the sum of number of boys and girls in a school is 900 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 90 , e ) 70
Rationale: we have x + x % of 900 = 900 x + x / 100 * 900 = 900 10 * x = 900 x = 90 answer is d
Answer: d
Python program:
a = 900 / 100
b = a + 1 
c = 900 / b
Problem: one half of a two digit number exceeds its one fourth by 3 . what is the sum of the digits of the number ?
Options: a ) 3 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: explanation : x / 2 – x / 4 = 3 = > x = 12 1 + 2 = 3 a
Answer: a
Python program:
a = 3 * 4
b = reminder + (
Problem: a student chose a number , multiplied it by 2 , then subtracted 200 from the result and got 110 . what was the number he chose ?
Options: a ) 168 , b ) 100 , c ) 155 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 200 = 110 2 x = 310 x = 155 correct answer c"
Answer: c
Python program:
a = 110 + 200 
b = a / 2
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 .
Rationale: "total work = 20 * 3 = 60 beaver hours 12 beaver * x = 60 beaver hours x = 60 / 12 = 5 answer : d"
Answer: d
Python program:
a = 3 * 20
b = a / 12
Problem: the average expenditure of a labourer for 6 months was 90 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 81
Rationale: income of 6 months = ( 6 × 90 ) – debt = 540 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 810 average monthly income = 810 ÷ 10 = 81 answer e
Answer: e
Python program:
a = 90 * 6
b = 60 * 4
c = a + b 
d = c + 30 
e = 6 + 4 
f = d / e
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 1 hours , it must travel at a speed of :
Options: a ) 300 kmph , b ) 360 kmph , c ) 600 kmph , d ) 720 kmph , e ) 750 kmph
Rationale: "explanation : distance = ( 240 x 5 ) = 1200 km . speed = distance / time speed = 1200 / ( 5 / 3 ) km / hr . required speed = ( 1200 x 3 / 5 ) km / hr = 720 km / hr . answer is d"
Answer: d
Python program:
a = 240 * 5
b = 2 / 3
c = 1 + b 
d = a / c
e = d / 2
Problem: the length of rectangle is thrice its breadth and its perimeter is 48 m , find the area of the rectangle ?
Options: a ) 432 , b ) 108 , c ) 252 , d ) 992 , e ) 212
Rationale: "2 ( 3 x + x ) = 48 l = 18 b = 6 lb = 18 * 6 = 108 answer : b"
Answer: b
Python program:
a = 3 * 2
b = 1 * 2
c = a + b 
d = 48 / c
e = d * 3
f = 3 * 2
g = 1 * 2
h = f + g 
i = 48 / h
j = e * i
Problem: find the value of ( √ 1.1 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 2.879 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: "( √ 1.1 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) = > 2.879 answer is b"
Answer: b
Python program:
a = math.sqrt(1)
b = math.sqrt(0)
c = a / b
d = math.sqrt(1)
e = math.sqrt(0)
f = d / e
g = c + f
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 6 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 9490 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 6 = 9490 answer : d"
Answer: d
Python program:
a = 100 + 4 
b = a / 100
c = 100 + 4 
d = c / 100
e = b * d
f = 7500 * e
Problem: if x ^ 2 + y ^ 2 = 15 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 9 , c ) 14 , d ) 17 , e ) 20
Rationale: but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 15 - 2 * 3 = 9 . . answer b
Answer: b
Python program:
a = 3 ** 2
Problem: if h = { 1 , 7 , 18 , 20 , 29 , 33 } , how much less is the mean of the numbers in h than the median of the numbers in h ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 1 + 7 + 18 + 20 + 29 + 33 ) / 6 = 18 median = ( 18 + 20 ) / 2 = 19 difference = 1 option a
Answer: a
Python program:
a = 7 + 1 
b = a + 20 
c = 29 - b
Problem: what will be the cost of house to paint which area equal to 484 sq ft , if the price per foot of building is rs . 20
Options: a ) 1800 , b ) 1760 , c ) 1400 , d ) 2600 , e ) 3600
Rationale: let the side of the square plot be a ft . a 2 = 484 = > a = 22 length of the fence = perimeter of the plot = 4 a = 88 ft . cost of building the fence = 88 * 20 = rs . 1760 . answer : b
Answer: b
Python program:
a = math.sqrt(484)
b = a * 4
c = b * 20
Problem: x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 0 , d ) 1 / 9 , e ) 1 / 5
Rationale: "given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d"
Answer: d
Python program:
a = 2 ** 2
b = 1 * a
c = 6 ** 2
d = b / c
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability r that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability r = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Python program:
a = math.comb(4, 1)
b = a * 2
c = math.comb(6, 3)
d = b / c
e = 5 * 5
f = e * 4
g = d * f
Problem: there are , in a certain league , 50 teams , and each team face another team for a total of 4 times . how many games are played in the season ?
Options: a ) 6660 , b ) 3600 , c ) 2400 , d ) 4900 , e ) 5400
Rationale: by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 4900 option d .
Answer: d
Python program:
a = 50 - 1
b = a * 4
c = 50 / 2
d = b * c
Problem: a cycle is bought for rs . 1000 and sold for rs . 2000 , find the gain percent ?
Options: a ) 11 , b ) 20 , c ) 100 , d ) 77 , e ) 12
Rationale: "1000 - - - - 1000 100 - - - - ? = > 100 % answer : c"
Answer: c
Python program:
a = 2000 - 1000
b = a / 1000
c = b * 100
Problem: a 360 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 57.6 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 360 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 880 m time = distance / speed = 880 x 18 / ( 5 x 55 ) = 57.6 sec ans is : a"
Answer: a
Python program:
a = 360 + 520 
b = 55 * const_0_2778
c = a / b
Problem: 5 x 1.6 - 2 x 1.4 / 1.3 = ?
Options: a ) 3 , b ) 0 , c ) 5 , d ) 4 , e ) 2
Rationale: "given expression = ( 8 - 2.8 ) / 1.3 = 5.2 / 1.3 = 52 / 1.3 = 4 . answer is d ."
Answer: d
Python program:
a = 5 * 1
b = 2 * 1
c = a - b
d = c / 1
Problem: the speed of a car is 98 km in the first hour and 70 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 87 kmph , d ) 56 kmph , e ) 84 kmph
Rationale: "s = ( 98 + 70 ) / 2 = 84 kmph answer : e"
Answer: e
Python program:
a = 98 + 70 
b = a / 2
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 10 days , working 12 hours a day , the number of men required ?
Options: a ) 10 days , b ) 9 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 12 × 10 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 12 × 10 = 8 days d )"
Answer: d
Python program:
a = 12 * 10
b = a * 8
c = 10 * 12
d = b / c
Problem: divide rs . 1301 between a and b , so that the amount of a after 7 years is equal to the amount of b after 9 years , the interest being compounded at 4 % per annum .
Options: a ) 625 , b ) 367 , c ) 288 , d ) 209 , e ) 198
Rationale: explanation : let the two parts be rs . x and rs . ( 1301 - x ) . 625 x = 676 ( 1301 - x ) 1301 x = 676 x 1301 x = 676 . so , the parts are rs . 676 and rs . ( 1301 - 676 ) i . e rs . 676 and rs . 625 answer : a ) rs . 625
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 9
d = 4 / 100
e = 1 + d 
f = e ** 7
g = c / f
h = 1 + g 
i = 1301 / h
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 40 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 40 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 5 liters . answer : c"
Answer: c
Python program:
a = 100 - 90
b = a / 100
c = b * 40
d = 100 - 20
e = d / 100
f = c / e
Problem: david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 4 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 4 / 5 , d ) 1 / 5 , e ) 6 / 5
Rationale: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 4 x total tips for all months = 6 * x + 4 x = 10 x tips for august / total tips for all months = 4 x / 10 x = 2 / 5 answer : b
Answer: b
Python program:
a = 10 - 4
b = a + 4 
c = 4 / b
Problem: a train 330 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 44 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 330 × 2 / 15 ) sec = 44 sec answer : e"
Answer: e
Python program:
a = 330 / 1000
b = 25 + 2 
c = a / b
d = 3600 * c
Problem: walking at 4 / 5 of her normal speed , a worker is 15 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 65
Rationale: "let v be her normal speed and let t be her normal time . d = ( 4 / 5 ) v * ( t + 15 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 4 / 5 ) v * ( t + 15 ) t / 5 = 12 t = 60 the answer is d ."
Answer: d
Python program:
a = 4 * 15
Problem: a cylinder of height h is 8 / 9 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 68 % , d ) 80 % , e ) 100 %
Rationale: basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 8 / 9 new cylinder 3 / 5 so 3 / 5 / 8 / 9 = 3 / 5 * 9 / 8 = 12 / 15 = 4 / 5 = 0.680 or 68 % . answer c
Answer: c
Python program:
a = 3 / 5
b = 8 / 9
c = a / b
d = c * 100
Problem: mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 2 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 , d ) 4 , e ) 5
Rationale: "d = rt m : r = 40 mph , t = t + 1 / 4 hr d = 40 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 40 t + 40 / 4 = 60 t 20 t = 40 / 4 t = 1 / 2 or 1 / 2 hr a"
Answer: a
Python program:
a = 15 / const_60
b = 40 * a
c = 60 - 40
d = b / c
e = const_60 * d
Problem: a can do a job in 15 days and b in 30 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 30 a + b 1 day work = 1 / 15 + 1 / 30 = 3 / 30 = 1 / 10 a + b 4 days work = 1 / 10 * 4 = 2 / 5 remaining work = 1 - 2 / 5 = 3 / 5 answer is b"
Answer: b
Python program:
a = 1 / 15
b = 1 / 30
c = a + b 
d = 4 * c
e = 1 - d
Problem: the population of a city increases by 9 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 25.97 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 8 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 8 / 100 ) ^ 3 = 125.97 ∴ required percentage = 25.97 % answer : c"
Answer: c
Python program:
a = 9 - 1
b = 100 + a 
c = 9 - 1
d = b * c
e = d / 100
f = 9 - 1
g = e + f 
h = 100 + g 
i = 9 - 1
j = h * i
k = j / 100
l = 9 - 1
m = 100 + l 
n = 9 - 1
o = m * n
p = o / 100
q = 9 - 1
r = p + q 
s = k + r
Problem: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.5 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 5 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 150 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 150 - x ) = 8000 × 1000 = > ( 150 - x ) = 8000 × 1000 / 320 = 100 = > x = 50 cm = 5 dm . answer : b"
Answer: b
Python program:
a = 3 * 3
b = a * 1
c = 8000 / 1000
d = b - c
Problem: if k is the greatest positive integer such that 3 ^ k is a divisor of 18 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "18 / 3 = 6 18 / 9 = 2 6 + 2 = 8 k = 8 answer : e"
Answer: e
Python program:
a = 18 / 3
b = 1 + a
Problem: if 18888 – n is divisible by 11 , and 0 < n < 11 , what is n ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 18,888 / 11 = 1717 with a remainder of 1 . we need to subtract the remainder to get a multiple of 11 . the answer is a .
Answer: a
Python program:
a = math.gcd(18888, 11)