euclaise/mathqa_programs huggingface dataset:
Problem: in measuring the sides of a rectangle , one side is taken 7 % in excess , and the other 6 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.58 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 61 / 57 ) x ( 47 / 50 ) y = ( 867 / 862 ) ( xy ) error in measurement = ( 867 / 862 ) xy - xy = ( 5 / 862 ) xy error percentage = [ ( 5 / 862 ) xy ( 1 / xy ) 100 ] % = ( 29 / 50 ) % = 0.58 % . answer is e ."
Answer: e
Python program:
a = 7 - 6
b = 7 * 6
c = b / 100
d = a - c
Problem: how many squares are there between 2011 to 2300 ? ? ? ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: nos . are 2025 , 2116 , 2209 answers is 3 answer : a
Answer: a
Python program:
a = math.sqrt(2300)
b = math.floor(a)
c = math.sqrt(2011)
d = math.floor(c)
e = b - d
Problem: the average age of a group of 10 students is 14 years . if 5 more students join the group , the average age rises by 1 year . the average age of the new students is :
Options: a ) 22 , b ) 38 , c ) 11 , d ) 17 , e ) 91
Rationale: explanation : total age of the 10 students = 10 × 14 = 140 total age of 15 students including the newly joined 5 students = 15 × 15 = 225 total age of the new students = 225 − 140 = 85 average age = 85 / 5 = 17 years answer : d
Answer: d
Python program:
a = 14 + 1 
b = 14 + 1 
c = a * b
d = 14 * 10
e = c - d
f = e / 5
Problem: average expenditure of a person for the first 3 days of a week is rs . 310 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 ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 310 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 . 310 + rs . 40 = rs . 350 correct option : a"
Answer: a
Python program:
a = 420 - 310
b = 4 * a
c = 3 + 4 
d = b / c
e = 310 + d
Problem: if the perimeter of a rectangular garden is 800 m , its length when its breadth is 100 m is ?
Options: a ) 286 m , b ) 899 m , c ) 300 m , d ) 166 m , e ) 187 m
Rationale: "2 ( l + 100 ) = 800 = > l = 300 m answer : c"
Answer: c
Python program:
a = 800 / 2
b = a - 100
Problem: two equal sums of money were invested , one at 4 % and the other at 4.5 % . at the end of 7 years , the simple interest received from the latter exceeded to that received from the former by 31.50 . each sum was :
Options: a ) 1200 , b ) 600 , c ) 750 , d ) 900 , e ) none of these
Rationale: difference of s . i . = √ 31.50 let each sum be x . then x × 4 1 / 2 × 7 / 100 − x × 4 × 7 / 100 = 31.50 or 7 ⁄ 100 x × 1 ⁄ 2 = 63 ⁄ 2 or x = 900 answer d
Answer: d
Python program:
a = 4 - 5
b = 31 / 5
c = b * 100
d = c / 7
Problem: shekar scored 76 , 65 , 82 , 67 and 75 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 73
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 75 ) / 5 = 365 / 5 = 73 hence average = 73 answer : e"
Answer: e
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 75 
e = 1 + 4 
f = d / e
Problem: tickets for all but 100 seats in a 10000 - seat stadium were sold . of the tickets sold , 30 % were sold at half price and the remaining tickets were sold at the full price of $ 2 . what was the total revenue from ticket sales ?
Options: a ) $ 16,830 , b ) $ 17,820 , c ) $ 18,000 , d ) $ 19,800 , e ) $ 21,780
Rationale: 10000 seats - - > full price : half price = 7000 : 3000 price when all seats are filled = 14000 + 3000 = 17000 100 seats are unsold - - > loss due to unfilled seats = 30 + 2 * 70 = 170 revenue = 17000 - 170 = 16830 answer : a
Answer: a
Python program:
a = 10000 - 100
b = 10000 - 100
c = b * 30
d = c / 100
e = a - d
f = 2 * e
g = 10000 - 100
h = g * 30
i = h / 100
j = f + i 
k = j / 1000
l = math.floor(k)
Problem: a and b started a business investing rs . 10,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 2 , e ) 18 : 4
Rationale: "a : b = 10000 : 20000 = 1 : 2 answer : d"
Answer: d
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 2 
f = 3 * 3
g = f + 1 
h = 2 * g
i = e / h
Problem: rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 9 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 9 : 3 , b ) 9 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 9 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 9 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 9 / 100 ( 6000 - x ) = 540 - 2 x / 100 = > 540 - 1 / 50 x = 450 = > x = 4500 amount lent at 10 % = 1500 required ratio = 4500 : 1500 = 9 : 3 answer : a"
Answer: a
Python program:
a = 450 * 100
b = 6000 * 7
c = a - b
d = 9 - 7
e = c / d
f = 450 * 100
g = 6000 * 7
h = f - g
i = 9 - 7
j = h / i
k = e / j
Problem: a man sitting in a train which is travelling at 15 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 97 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 15 ) kmph = 97 kmph . answer c"
Answer: c
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 15
Problem: there are 35 student in a school . 20 if them speek hindi 19 of them speak eng 9 of them speak both , then how many student neithe speak eng nor speak hindi
Options: a ) 28 , b ) 30 , c ) 32 , d ) 35 , e ) none of these
Rationale: total number of students = 35 no of hindi speaking students ( h ) = 20 no of english speaking students ( e ) = 19 h intersection e = 9 thus h union e = 20 + 19 - 9 = 30 thus number of student neithe speak eng nor speak hindi = 35 - 30 = 5 answer : e
Answer: e
Python program:
a = 20 + 19 
b = a - 9
c = 35 - b
Problem: a student chose a number , multiplied it by 2 , then subtracted 152 from the result and got 102 . what was the number he chose ?
Options: a ) 127 , b ) 100 , c ) 129 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 152 = 102 2 x = 254 x = 127 correct answer a"
Answer: a
Python program:
a = 102 + 152 
b = a / 2
Problem: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 50 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1000 min , b ) 1200 min , c ) 1300 min , d ) 1400 min , e ) 1600 min
Rationale: volume of pool = 50 * 150 * 10 cu . ft , 80 % full = 50 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 50 * 150 * 10 * 0.8 / 60 min = 1000 min a
Answer: a
Python program:
a = 80 / 100
b = 50 * 150
c = b * 10
d = a * c
e = d / 60
Problem: if a is an integer greater than 9 but less than 26 and b is an integer greater than 14 but less than 31 , what is the range of a / b ?
Options: a ) 1 , b ) 1 / 2 , c ) 5 / 6 , d ) 2 / 3 , e ) 4 / 3
Rationale: "range of a / b = max ( a / b ) - min ( a / b ) to get max ( a / b ) = > max ( a ) / min ( b ) = 25 / 15 to get min ( a / b ) = > min ( a ) / max ( b ) = 10 / 30 range = 25 / 15 - 10 / 30 = 4 / 3"
Answer: e
Python program:
a = 26 - 1
b = 14 + 1 
c = a / b
d = 9 + 1 
e = 31 - 1
f = d / e
g = c - f
Problem: if the cost price is 40 % of selling price . then what is the profit percent .
Options: a ) 150 % , b ) 120 % , c ) 130 % , d ) 200 % , e ) none of these
Rationale: "explanation : let the s . p = 100 then c . p . = 40 profit = 60 profit % = ( 60 / 40 ) * 100 = 150 % . answer : a"
Answer: a
Python program:
a = 100 - 40
b = a / 40
c = b * 100
Problem: when positive integer x is divided by positive integer y , the remainder is 12 . if x / y = 75.12 , what is the value of y ?
Options: a ) 84 , b ) 98 , c ) 51 , d ) 65 , e ) 100
Rationale: "when positive integer x is divided by positive integer y , the remainder is 12 - - > x = qy + 12 ; x / y = 75.12 - - > x = 75 y + 0.12 y ( so q above equals to 75 ) ; 0.12 y = 12 - - > y = 100 . answer : e ."
Answer: e
Python program:
a = math.floor(75, 12)
b = 75 - 12
c = 12 / b
Problem: the cost to park a car in a certain parking garage is $ 20.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 3.58 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 20 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 20 + 7 * 1.75 = 32.25 thus the average parking price = 32.25 / 9 = 3.58 $ a is the correct answer ."
Answer: a
Python program:
a = 9 - 2
b = 1 * 75
c = 20 + 0 
d = c / 9
Problem: the unit digit in the product ( 611 * 704 * 912 * 261 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 1 * 4 * 2 * 1 ) = 2 answer : a"
Answer: a
Python program:
a = 611 * 704
b = a * 912
c = b * 261
d = 611 * 704
e = d * 912
f = e * 261
g = 4 + 4 
h = f - g
i = c - h
Problem: two trains are moving in opposite directions with speed of 150 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 48 , c ) 47 , d ) 30 , e ) 25
Rationale: "explanation : relative speed = 150 + 90 = 240 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 240 hr = 1 / 120 hr = 3600 / 120 seconds = 30 seconds answer : option d"
Answer: d
Python program:
a = 1 + 10 
b = 150 + 90 
c = a / b
d = c * 3600
Problem: a train 60 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 2 , e ) 3
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 60 * 3 / 55 = 3 sec . answer e"
Answer: e
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 60 / b
Problem: if the sum and difference of two numbers are 20 and 10 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 200 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 10 = 200 . answer : d"
Answer: d
Python program:
a = 20 + 10 
b = a / 2
c = b ** 2
d = 20 + 10 
e = d / 2
f = 20 - e
g = f ** 2
h = c - g
Problem: a 340 - liter solution of kola is made from 75 % water , 5 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 12 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 19.6 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 340 + 12 + 3.2 + 6.8 = 362 numerator : 340 ( 1 - . 75 - . 05 ) + 3.2 340 ( 0.2 ) + 3.2 68 + 3.2 71.2 ratio : 71.2 / 362 = 0.196 answer : c"
Answer: c
Python program:
a = 75 / 100
b = 340 * a
c = 340 - b
d = 5 / 100
e = 340 * d
f = c - e
g = f + 3 
h = 340 + 3 
i = h + 12 
j = i + 6 
k = g / j
l = k * 100
Problem: the average mark of the students of a class in a particular exam is 90 . if 2 students whose average mark in that exam is 45 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ?
Options: a ) 10 , b ) 40 , c ) 20 , d ) 30 , e ) 25
Rationale: "let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 2 ) students = 95 ( x - 2 ) 90 x - ( 2 * 45 ) = 95 ( x - 2 ) 100 = 5 x = > x = 20 answer : c"
Answer: c
Python program:
a = 95 * 2
b = 2 * 45
c = a - b
d = 95 - 90
e = c / d
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 250 more than a :
Options: a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 250 total earning = \ inline \ frac { 58 xy } { 100 } = 7250 answer : b ) rs . 7250"
Answer: b
Python program:
a = 3 * 6
b = 4 * 5
c = a + b 
d = 5 * 4
e = c + d 
f = 4 * 5
g = 3 * 6
h = f - g
i = 250 / h
j = e * i
Problem: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 11 , the remainder is 9 . what is the smallest positive integer k such that k + n is a multiple of 33 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 11 q + 9 n + 2 = 3 p + 3 = 11 q + 11 n + 2 is a multiple of 3 and 11 , so it is a multiple of 33 . the answer is a ."
Answer: a
Python program:
a = 33 - reminder
Problem: a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 75 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,700 , c ) 3,300 , d ) 5,400 , e ) 324,000
Rationale: "together the two machines make 35 + 75 = 110 copies per minute . so , in half an hour they will make 110 * 30 = 3,300 copies . answer : c ."
Answer: c
Python program:
a = 35 + 75 
b = a * const_60
c = b / 2
Problem: the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 750 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 750 ã — 22 ) = rs . 16500 . answer : option c"
Answer: c
Python program:
a = 5 * 5
b = 750 * a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 950 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 77 % , d ) 5.26 % , e ) 12 %
Rationale: 950 - - - 50 100 - - - ? = > 5.26 % answer : d
Answer: d
Python program:
a = 100 / 950
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: find the compound interest on rs . 25000 in 2 years at 4 % per annum . the interest being compounded half yearly .
Options: a ) rs 2060.808 , b ) rs 2060.801 , c ) rs 2060.804 , d ) rs 2060.802 , e ) rs 2060.805
Rationale: "explanation : given : principal = rs . 25000 , rate = 4 % per half year , time = 2 years = 4 half years therefore , amount = p ( 1 + ( r / 2 ) / 100 ) 2 n amount = rs . [ 25000 * ( 1 + 2 / 100 ) 4 ] = rs . ( 25000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 27060.804 therefore , c . i . = rs . ( 27060.804 – 25000 ) = rs 2060.804 answer : c"
Answer: c
Python program:
a = 2 / 4
b = a / 100
c = 1 + b 
d = c ** 3
e = 4 * 4
f = e * 100
g = math.sqrt(100)
h = f * g
i = d * h
j = 4 * 4
k = j * 100
l = math.sqrt(100)
m = k * l
n = i - m
Problem: ravi covers a distance of 900 mtrs in 180 secs . find his speed in kmph ?
Options: a ) 10 kmph , b ) 18 kmph , c ) 20 kmph , d ) 26 kmph , e ) 28 kmph
Rationale: given distance d = 900 meters and time = 180 seconds speed = distance / time = 900 / 180 = 5 m / s . but speed is asked in kmph , to convert 5 mps to kmph , multiply it by 18 / 5 . speed in kmph = 5 x 18 / 5 = 18 kmph b
Answer: b
Python program:
a = 900 / 180
b = a * const_3_6
Problem: find the value of x from the below equation ? : 3 x ^ 2 - 5 x + 2 = 0
Options: a ) 2 / 3 , b ) - 1 , c ) 0 , d ) - 2 / 3 , e ) 2
Rationale: "a = 3 , b = - 5 , c = 2 x 1,2 = ( 5 â ± â ˆ š ( ( - 5 ) ^ 2 - 4 ã — 3 ã — 2 ) ) / ( 2 ã — 3 ) = ( 5 â ± â ˆ š ( 25 - 24 ) ) / 6 = ( 5 â ± 1 ) / 6 x 1 = ( 5 + 1 ) / 6 = 6 / 6 = 1 x 2 = ( 5 - 1 ) / 6 = 4 / 6 = 2 / 3 a"
Answer: a
Python program:
a = 2 ** 3
b = 5 * 5
c = a - b
d = math.sqrt(c)
e = 2 - d
f = e / 3
Problem: n ^ ( n / 2 ) = 4 is true when n = 4 in the same way what is the value of n if n ^ ( n / 2 ) = 8 ?
Options: a ) 4 , b ) 8 , c ) 2 , d ) 6 , e ) 10
Rationale: n ^ ( n / 2 ) = 8 apply log n / 2 logn = log 8 nlogn = 2 log 8 = log 8 ^ 2 = log 64 logn = log 64 now apply antilog n = 64 / n now n = 8 . answer : b
Answer: b
Python program:
a = 8 ** 2
b = a / 8
Problem: if n = 2 ^ 0.25 and n ^ b = 8 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 12 , d ) 5 / 3 , e ) 80 / 3
Rationale: "25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 3 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 3 b = 12 answer : c"
Answer: c
Python program:
a = math.log(8)
b = 2 ** 0
c = math.log(b)
d = a / c
Problem: [ ( 3.242 x 15 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) 0.04863
Rationale: "answer multiplying 3.242 x 15 = 4.863 now divide 4.863 by 100 so , 4.863 ÷ 100 = 0.04863 ∴ shift the decimal two places to the left as 100 correct option : e"
Answer: e
Python program:
a = 3 * 242
b = a / 100
c = b / 10
Problem: there are 41 students in a class , number of girls is one more than number of guys . we need to form a team of 4 students . all 4 in the team can not be from same gender . number of girls and guys in the team should not be equal . how many ways can such a team be made ?
Options: a ) 50540 ways , b ) 60540 ways , c ) 50840 ways , d ) 40540 ways , e ) 51540 ways
Rationale: boys = 20 and girls = 21 now the combinations are { girl , girl , girl , boy } or { boy , boy , boy , girl } so 21 c 3 * 20 c 1 + 20 c 3 * 21 c 1 = 50540 ways answer : a
Answer: a
Python program:
a = 41 / 2
b = math.floor(a)
c = 41 - b
d = math.factorial(c)
e = 4 - 1
f = math.factorial(e)
g = d / f
h = 41 / 2
i = math.floor(h)
j = 41 - i
k = 4 - 1
l = j - k
m = math.factorial(l)
n = g / m
o = 41 / 2
p = math.floor(o)
q = n * p
r = 41 / 2
s = math.floor(r)
t = math.factorial(s)
u = 41 / 2
v = math.floor(u)
w = 4 - 1
x = v - w
y = math.factorial(x)
z = t / y
A = 4 - 1
B = math.factorial(A)
C = z / B
D = 41 / 2
E = math.floor(D)
F = 41 - E
G = C * F
H = q + G
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2
Options: a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is e ."
Answer: e
Python program:
a = 2 * 11
b = a + 5 
c = b + 2
Problem: pipe p can drain the liquid from a tank in 3 / 4 the time that it takes pipe q to drain it and in 3 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 8 / 23 , c ) 3 / 8 , d ) 3 / 11 , e ) 3 / 4
Rationale: suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 3 / 4 ) rq ] = 4 / 3 also , rp = rr / ( 3 / 3 ) = > 4 / 3 = rr / ( 3 / 3 ) = > rr = 4 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 4 / 3 + 4 / 3 = 11 / 3 = 1 / ( 3 / 11 ) thus running simultaneously , pipe q will drain 3 / 11 of the liquid . thus answer = d .
Answer: d
Python program:
a = 3 * 3
b = 4 * 3
c = b * 2
d = 3 * 3
e = c + d 
f = a / e
Problem: xavier starts from p towards q at a speed of 40 kmph and after every 12 mins increases his speed by 20 kmph . if the distance between p and q is 56 km , then how much time does he take to cover the distance ?
Options: a ) 40 , b ) 48 , c ) 44 , d ) 36 , e ) 30
Rationale: "first 12 min = 40 * 12 / 60 = 8 km 2 nd 12 min = 60 * 12 / 60 = 12 km 3 rd 12 min = 80 * 12 / 60 = 16 km 4 th 12 min = 100 * 12 / 60 = 20 km total time 12.4 = 48 min b"
Answer: b
Python program:
a = 12 + 12 
b = a + 12 
c = b + 12
Problem: in the next cricket world cup t - 20 , team w has decided to score 200 runs only through 4 s and 6 s . in how many ways can the team w score these 200 runs ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: team w can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6 ' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4 ' s and 6 ' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d
Answer: d
Python program:
a = 6 * 4
b = 200 / a
c = 10 + b 
d = c - 1
Problem: in a class of 50 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "total = english + german - both + neither - - > 50 = english + 22 - 12 + 0 - - > english = 40 - - > only english = english - both = 40 - 12 = 28 . answer : d ."
Answer: d
Python program:
a = 50 + 12 
b = a - 22
c = b - 12
Problem: a train 130 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: "speed of train relative to man : 130 / 6 * 18 / 5 km / hr = 78 km / hr let speed of train = x therefore x + 6 = 78 x = 78 - 6 x = 72 km / hr answer : d"
Answer: d
Python program:
a = 6 * const_0_2778
b = a * 6
c = 130 - b
d = c / 6
e = d / const_0_2778
Problem: two pipes can fill a tank in 30 minutes and 20 minutes . an outlet pipe can empty the tank in 15 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 48 , b ) 54 , c ) 60 , d ) 66 , e ) 72
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 30 + v / 20 - v / 15 = v / 60 per minute the tank will be filled in 60 minutes . the answer is c ."
Answer: c
Python program:
a = 1 / 30
b = 1 / 20
c = a + b 
d = 1 / 15
e = c - d
Problem: a barrel full of beer has 2 taps one midway , , which draw a litre in 6 minutes and the other at the bottom , which draws a litre in 4 minutes . the lower tap is lower normally used after the level of beer in the barrel is lower than midway . the capacity of the barrel is 36 litres . a new assistant opens the lower tap when the barrel is full and draws out some beer . as a result the lower tap has been used 24 minutes before the usual time . for how long was the beer drawn out by the new assistant ?
Options: a ) 15 minutes , b ) 16 minutes , c ) 17 minutes , d ) 18 minutes , e ) none of these
Rationale: sol . the top tab is operational till 18 litres is drawn out . ∴ time after which the lower tap is usually open = 18 × 6 = 108 minutes ∴ time after which it is open now = 108 – 24 = 84 minutes ∴ litres drawn = 84 / 6 = 14 litres ∴ 18 – 14 = 4 litres were drawn by the new assistant . ∴ time = 4 × 4 = 16 minutes answer b
Answer: b
Python program:
a = 36 / 2
b = 36 / 2
c = b * 6
d = c - 24
e = d / 6
f = a - e
g = 4 * f
Problem: xy = 1 then what is ( 6 ^ ( x + y ) ^ 2 ) / ( 6 ^ ( x - y ) ^ 2 )
Options: a ) 1296 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 6 ^ 4 = 1296 answer a"
Answer: a
Python program:
a = 4 * 1
b = 6 ** a