euclaise/mathqa_programs huggingface dataset:
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 33 ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "first , let ' s translate the expression 21 # 33 , using the definition given : 21 # 33 = 21 × 24 × 27 × 30 × 33 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 33 = 3 ^ 6 ( 7 × 8 × 9 × 10 × 11 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 33 = 3 ^ 5 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 ) let ' s group the prime bases : 21 # 33 = 2 ^ 4 × 3 ^ 7 × 5 × 7 × 11 the sum of the exponents is 4 + 7 + 1 + 1 + 1 = 14 the answer is c ."
Answer: c
Python program:
a = 2 + 2 
b = 3 + a 
c = 2 + 2 
d = b + c 
e = 2 + 2 
f = 3 + e 
g = d + f
Problem: after decreasing 20 % in the price of an article costs rs . 620 . find the actual cost of an article ?
Options: a ) 775 , b ) 620 , c ) 750 , d ) 800 , e ) 720
Rationale: "cp * ( 80 / 100 ) = 620 cp = 7.75 * 100 = > cp = 775 answer : a"
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 620 / b
Problem: 90 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 32256 , b ) 24000 , c ) 24936 , d ) 25600 , e ) none
Rationale: "answer ∵ 90 % of p = 23040 ∴ p = ( 23040 x 100 ) / 90 = 25600 correct option : d"
Answer: d
Python program:
a = 100 / 90
b = a * 23040
Problem: if y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "i just tried plugging in the numbers and found out that 5 * 8820 = 44 , 100 , which is a square of 210 b"
Answer: b
Python program:
a = 2 + 3 
b = a * 2
Problem: a train 100 m long crosses a platform 125 m long in 40 sec ; find the speed of the train ?
Options: a ) 36.21 , b ) 77.11 , c ) 54.12 , d ) 33.0 , e ) 20.25
Rationale: "d = 100 + 125 = 225 t = 40 s = 225 / 40 * 18 / 5 = 20.25 kmph answer : e"
Answer: e
Python program:
a = const_60 * 0
b = 40 * a
c = b - 100
Problem: a group of men decided to do a work in 15 days , but 8 of them became absent . if the rest of the group did the work in 18 days , find the original number of men ?
Options: a ) 15 , b ) 48 , c ) 54 , d ) 33 , e ) 45
Rationale: "original number of men = 8 * 18 / ( 18 - 15 ) = 48 answer is b"
Answer: b
Python program:
a = 8 * 18
b = 18 - 15
c = a / b
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 5 , 6 , 7 , 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 7 , d ) 2 / 15 , e ) 3 / 28
Rationale: "p ( x is prime ) = 3 / 7 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 3 / 7 * 1 / 4 = 3 / 28 the answer is e ."
Answer: e
Python program:
a = 2 / 5
b = 1 / 4
c = a * b
Problem: a and b can do a piece of work in 2 days , b and c in 3 days , c and a in 4 days . how long will c take to do it ?
Options: a ) 14 days , b ) 20 days , c ) 22 days , d ) 24 days , e ) 26 days
Rationale: "2 c = 1 / 3 + 1 / 4 – 1 / 2 = 1 / 12 c = 1 / 24 = > 24 days answer : d"
Answer: d
Python program:
a = 2 * 3
b = 2 * 3
c = b / 4
d = 2 * 3
e = d / 2
f = 2 * 3
g = f / 3
h = e + g 
i = c + h 
j = i / 2
k = 2 * 3
l = k / 2
m = j - l
n = a / m
Problem: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 12 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 134.40
Rationale: "correct answer : e the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.12 ( $ 1120 ) = $ 134.40 . the correct answer is e ."
Answer: e
Python program:
a = 1720 - 600
b = a * 12
c = b / 100
Problem: the area of one square is x ^ 2 + 10 x + 25 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 36 , what is the value of x ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "the areas are ( x + 5 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 5 and 2 x - 5 . if we add the two perimeters : 4 ( x + 5 ) + 4 ( 2 x - 5 ) = 36 12 x = 36 x = 3 the answer is a ."
Answer: a
Python program:
a = 10 / 2
b = 4 * a
c = b - 10
d = 36 - c
e = d / 10
Problem: when magnified 1000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0003 , e ) 0.0002
Rationale: it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d
Answer: d
Python program:
a = 0 / 3
Problem: a group of n students can be divided into equal groups of 4 with 3 student left over or equal groups of 5 with 3 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 66 , b ) 46 , c ) 49 , d ) 53 , e ) 86
Rationale: "4 x + 3 = 5 y + 3 . . . . . . . . . . . ie : 4 x - 5 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x = fraction ( not possible ) if y = 4 thus x = 5 n = 23 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 43 23 + 43 = 66 . . . . . a"
Answer: a
Python program:
a = 5 * 2
b = a + 3 
c = 2 * 3
d = 5 * c
e = d + 3 
f = b + e
Problem: q - 1 : how many two digit numbers of distinct digits can be formed by using digits 1 , 2 , 3 , 4 , 5 , 6 and 7 such that the numbers are divisible by 5 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "6 two digit numbers divisible by 5 must end in either 0 or 5 . since there is no 0 , all correct answers are a combination of the other digits and 5 . there are six other numbers plus the 5 so there are 6 correct answers . correct answer is d ."
Answer: d
Python program:
a = 1 + 1 
b = a + 1 
c = b + 3 
d = c + 4 
e = d + 1
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 9 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 585 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 9 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 = 9 × 65 = 585 miles correct answer is c ) 585 miles"
Answer: c
Python program:
a = 65 * 9
Problem: how many of the integers between 45 and 105 are even ?
Options: a ) 21 , b ) 30 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 45 to 105 is 60 numbers half of them is even . . which is 30 answer : b"
Answer: b
Python program:
a = 105 - 45
b = a / 2
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 50 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 470
Rationale: "total cost 940 940 * 50 / 100 = 470 so the cut in amount is 470 the less amount to be spend is 940 - 470 = 470 answer : e"
Answer: e
Python program:
a = 100 - 50
b = a / 100
c = b * 940
Problem: price of a book increases 15 % successively ( 2 times ) what is the new price of the book more compared to that of the old price :
Options: a ) 32.25 % , b ) 23.34 % , c ) 36 % , d ) 39 % , e ) 29 %
Rationale: new price is 1.15 * 1.15 * old price = 1.3225 * old price increase in price = 0.3225 * old price % increase = 100 * 0.3225 * old price / old price = 32.25 % answer : a
Answer: a
Python program:
a = 100 + 15 
b = a / 100
c = 100 + 15 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: there are 7 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 315 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 7 c 2 number of ways of selecting 2 non fiction books = 6 c 2 7 c 2 * 6 c 2 = 21 * 15 = 315 answer : c"
Answer: c
Python program:
a = 7 * 4
b = 6 * 7
c = a * b
d = math.factorial(2)
e = d ** 2
f = c / e
Problem: andrew purchased 6 kg of grapes at the rate of 74 per kg and 9 kg of mangoes at the rate of 59 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 975 , c ) 980 , d ) 1020 , e ) 1080
Rationale: cost of 6 kg grapes = 74 × 6 = 444 . cost of 9 kg of mangoes = 59 × 9 = 531 . total cost he has to pay = 444 + 531 = 975 b
Answer: b
Python program:
a = 6 * 74
b = 9 * 59
c = a + b
Problem: the ratio of the incomes of uma and bala is 4 : 3 and the ratio of their expenditure is 3 : 2 . if at the end of the year , each saves $ 5000 then the income of uma is ?
Options: a ) $ 24000 , b ) $ 23000 , c ) $ 22000 , d ) $ 21000 , e ) $ 20000
Rationale: "let the income of uma and bala be $ 4 x and $ 3 x let their expenditures be $ 3 y and $ 2 y 4 x - 3 y = 5000 - - - - - - - 1 ) 3 x - 2 y = 5000 - - - - - - - 2 ) from 1 ) and 2 ) x = 5000 uma ' s income = 4 x = 4 * 5000 = $ 20000 answer is e"
Answer: e
Python program:
a = 4 * 5000
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5040 = ?
Options: a ) 392 , b ) 229 , c ) 756 , d ) 493 , e ) 540
Rationale: c 756 ? = 5040 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 756
Answer: c
Python program:
a = 3 / 4
b = 1 / 2
c = a * b
d = 2 / 5
e = c * d
f = e * 5040
Problem: there are 17 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 156 , b ) 167 , c ) 157 , d ) 342 , e ) 380
Rationale: "the total number of stations = 19 from 19 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 19 p ₂ ways . ² ⁰ p ₂ = 19 * 18 = 342 . answer : d"
Answer: d
Python program:
a = 17 + 1 
b = 17 + 1 
c = b + 1 
d = a * c
Problem: there are 18 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 800 , b ) 380 , c ) 360 , d ) 478 , e ) 566
Rationale: "the total number of stations = 20 from 20 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 20 p 2 ways . 20 p 2 = 20 * 19 = 380 answer : b"
Answer: b
Python program:
a = 18 + 2 
b = 18 + 2 
c = b - 1
d = a * c
Problem: tickets numbered 1 to 30 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?
Options: a ) 2 / 15 , b ) 7 / 15 , c ) 10 / 30 , d ) 7 / 30 , e ) 8 / 30
Rationale: "here , the sample space s = ( 1 , 2 , 3 , 4 , 5 , . . . , 29 , 30 ) . let e = the event of getting a multiple of 3 or 5 . e = ( 3 , 6 , 9 , 12 , 15 , 18 , 5 , 10 , 20 , 21 , 24 , 25 , 27 , 30 ) p ( e ) = n ( e ) / n ( s ) = 14 / 30 = 7 / 15 answer : b"
Answer: b
Python program:
a = 3 / 10
Problem: a 160 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 94 kmph , c ) 92 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: s = 160 / 6 * 18 / 5 = 96 kmph answer : a
Answer: a
Python program:
a = 160 / 6
b = a * const_3_6
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 6 : 4 . another alloy of copper and zinc contains copper and zinc in the ratio 3 : 7 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 12 : 1 , b ) 1 : 2 , c ) 4 : 1 , d ) 2 : 5 , e ) 2 : 6
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 6 x / 10 , and fraction of zinc in alloy _ 1 = 4 x / 10 similarly , fraction of copper in alloy _ 2 = 3 y / 10 , and fraction of zinc in alloy _ 2 = 7 y / 10 . mixing them , we get copper = 6 x / 10 + 3 y / 10 ; zinc = 4 x / 10 + 7 y / 10 so , 6 x + 3 y = 4 x + 7 y - > 2 x = 4 y - > x / y = 2 / 4 = 1 / 2 so , they must be mixed in the ratio 1 : 2 answer : b"
Answer: b
Python program:
a = 3 + 7 
b = 6 / a
c = 3 / 7
d = b - c
e = 3 / 7
f = 3 + 7 
g = 3 / f
h = e - g
i = d / h
Problem: a tank contains 7,500 gallons of a solution that is 6 percent sodium chloride by volume . if 2,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 5.18 % , b ) 6.18 % , c ) 7.18 % , d ) 8.18 % , e ) . 7 %
Rationale: "we start with 7,500 gallons of a solution that is 6 % sodium chloride by volume . this means that there are 0.06 x 7,500 = 450 gallons of sodium chloride . when 2,000 gallons of water evaporate we are left with 5,500 gallons of solution . from here we can determine what percent of the 5,500 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 450 / 5,500 ) x 100 = ? 0.081 x 100 = ? = 8.18 % answer is d ."
Answer: d
Python program:
a = 100 * 100
b = 6 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 16 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 16 = 404 hence , new average = 404 ⁄ 10 = 40.4 answer b"
Answer: b
Python program:
a = 40 * 2
b = 13 + 16 
c = a + b 
d = c - 31
e = d / 10
Problem: rs . 705 is divided amongst a , b , c so that 3 times a ' s share , 5 times b ' s share and 4 times c ' s share are all equal . find b ' s share ?
Options: a ) 177 , b ) 150 , c ) 180 , d ) 716 , e ) 616
Rationale: a + b + c = 705 3 a = 5 b = 4 c = x a : b : c = 1 / 3 : 1 / 5 : 1 / 4 = 20 : 12 : 15 12 / 47 * 705 = rs . 180 answer : c
Answer: c
Python program:
a = 4 / 3
b = 4 / 5
c = a + b 
d = c + 1 
e = 705 / d
Problem: the sale price sarees listed for rs . 175 after successive discount is 20 % and 5 % is ?
Options: a ) 187 , b ) 133 , c ) 142 , d ) 178 , e ) 175
Rationale: "175 * ( 80 / 100 ) * ( 95 / 100 ) = 133 answer : b"
Answer: b
Python program:
a = 175 * 20
b = a / 100
c = 175 - b
d = 175 * 20
e = d / 100
f = 175 - e
g = f * 5
h = g / 100
i = c - h
Problem: the average salary of all the workers in a workshop is rs . 9500 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12
Rationale: let the total number of workers be x . then , 9500 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3500 x = 42000 = x = 12 . answer : e
Answer: e
Python program:
a = 12000 - 9500
b = 7 * a
c = 9500 - 6000
d = b / c
e = 7 + d
Problem: solve x 2 – 3 x – 4 = 0 .
Options: a ) 1,4 , b ) - 1,4 , c ) 2,3 , d ) 2 , - 3 , e ) 3,4
Rationale: "this one factors easily : x 2 – 3 x – 4 = 0 ( x + 1 ) ( x – 4 ) = 0 x + 1 = 0 or x – 4 = 0 x = – 1 or x = 4 the solution is x = – 1 , 4 answer b - 1,4"
Answer: b
Python program:
a = 4 * 2
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 2 / 5 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 223.78 , b ) 37.78 , c ) 246.0 , d ) 278.88 , e ) 102.5
Rationale: "explanation : capital = rs . x , then 3 / 5 x = 61.5 x = 102.50 answer : e ) rs . 102.50"
Answer: e
Python program:
a = 4 / 5
b = 61 / 50
Problem: a sum of money lent at compound interest for 2 years at 20 % per annum would fetch rs . 482 more , if the interest was payable half yearly than if it was payable annually . the sum is
Options: a ) 200000 , b ) 20000 , c ) 200029 , d ) 288778 , e ) 277789
Rationale: explanation : let sum = rs . x c . i . when compounded half yearly = c . i . when compounded annually = = > x = 20000 answer : b ) 20000
Answer: b
Python program:
a = 20 / 2
b = a / 100
c = b + 1 
d = c ** 4
e = 20 / 100
f = e + 1 
g = f ** 2
h = d - g
i = 482 / h
Problem: a monkey start climbing up a tree 20 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 17 hrs it wil be 17 ft . bt since the height of the tree is 20 ft , so if the monkey hops up the tree in the next hr i . e 18 th hr then it reaches at the top of the tree . hence it takes 18 hrs for monkey to reach at the top answer : b
Answer: b
Python program:
a = 3 - 2
b = 20 / a
c = b - 2
Problem: 1 / 0.06 is equal to
Options: a ) 25.5 , b ) 16.7 , c ) 25 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.06 = ( 1 * 100 ) / 6 = 100 / 6 = 16.7 option b"
Answer: b
Python program:
a = 1 / 0
Problem: rs 3600 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 2800 , c ) s 1800 , d ) s 3500 , e ) s 3100
Rationale: "explanation : average rate = ( 144 / 3600 ) * 100 = 4 ratio = 1 : 1 so , first part = ( 1 / 2 ) * 3600 = rs 1800 . answer : c"
Answer: c
Python program:
a = 5 / 100
b = 3600 * a
c = b - 144
d = 5 / 100
e = 3 / 100
f = d - e
g = c / f
Problem: without stoppages , a train travels certain distance with an average speed of 200 km / h , and with stoppages , it covers the same distance with an average speed of 160 km / h . how many minutes per hour the train stops ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "due to stoppages , it covers 40 km less . time taken to cover 40 km = 40 â  „ 200 h = 1 â  „ 5 h = 1 â  „ 5 ã — 60 min = 12 min answer e"
Answer: e
Python program:
a = 160 / 200
b = a * const_60
c = const_60 - b
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 56 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.8 $ , b ) 387.8 $ , c ) 420.8 $ , d ) 457.8 $ , e ) 480.8 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 56 ) = 457.8 hence answer will be ( d )"
Answer: d
Python program:
a = 0 * 65
b = a * 12
Problem: the price of an item is discounted 2 percent on day 1 of a sale . on day 2 , the item is discounted another 12 percent , and on day 3 , it is discounted an additional 25 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 66 % , b ) 67.5 % , c ) 69 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 2 % discount = 980 price in day 2 after 12 % discount = 862.4 price in day 3 after 25 % discount = 646.8 so , price in day 3 as percentage of the sale price on day 1 will be = 646.8 / 980 * 100 = > 66 % answer will definitely be ( a )"
Answer: a
Python program:
a = 25 / 100
b = 1 / 2
c = 1 - b
d = a / c
e = d * 100
f = e + 2
Problem: find the smallest number of four digits exactly divisible by 4 , 5,7 and 8 .
Options: a ) 1150 , b ) 1160 , c ) 1140 , d ) 1152 , e ) 1145
Rationale: "smallest number of four digits is 1000 . required number must be divisible by l . c . m . of 4,5 , 7,8 i . e 280 , on dividing 1000 by 280 , we get 120 as remainder . therefore , required number = 1000 + ( 280 â € “ 120 ) = 1160 . answer is b ."
Answer: b
Python program:
a = 100 * 100
b = 10 * a
c = b - 100
d = c + 5
Problem: a sum fetched a total simple interest of rs . 2700 at the rate of 6 p . c . p . a . in 3 years . what is the sum ?
Options: a ) 25000 , b ) 20000 , c ) 18000 , d ) 14000 , e ) 15000
Rationale: "sol . principal = rs . [ 100 * 2700 / 6 * 3 ] = rs . [ 270000 / 18 ] = rs . 15000 . answer e"
Answer: e
Python program:
a = 2700 * 100
b = a / 6
c = b / 3
Problem: if 20 men can build a water fountain 56 metres long in 21 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 10 m , b ) 14 m , c ) 17 m , d ) 19 m , e ) 20 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 21 : 3 : : 56 : x therefore ( 20 x 21 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 420 = 14 hence , the required length is 14 m . answer : b"
Answer: b
Python program:
a = 20 * 21
b = 56 / a
c = 35 * 3
d = b * c
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 5 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1 , b ) 2 , c ) 10 , d ) 8 , e ) 16
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 5 ( pir ^ 2 ) pir ^ 2 = 10 pir r = 10 answer : c"
Answer: c
Python program:
a = 5 ** 2
b = math.sqrt(a)
c = 2 * b
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 3 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 4 , b ) 2 , c ) 6 , d ) 7 , e ) 8
Rationale: a + b + c = 18 b + c + d = 9 a + d = 13 a – d = 9 a + d = 13 2 d = 4 d = 2 answer : b
Answer: b
Python program:
a = 3 * 6
b = 13 - 6
c = b + 3 
d = a - c
e = d - 6
Problem: a classroom has equal number of boys and girls . 8 girls left to play kho - kho , leaving twice as many boys as girls in the classroom . what was the total number of girls and boys present initially ?
Options: a ) 16 , b ) 24 , c ) 32 , d ) 48 , e ) 54
Rationale: after 8 girls left remaining 8 girls now boys 16 are twice as many as remaining girls . initially boys = 16 and girls = 16 . answer : c
Answer: c
Python program:
a = 2 * 8
b = a * 2
Problem: a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . what is the present age of the mother ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "let present age of the mother = 5 x then , present age of the person = 2 x 5 x + 8 = 2 ( 2 x + 8 ) 5 x + 8 = 4 x + 16 x = 8 present age of the mother = 5 x = 40 answer is d ."
Answer: d
Python program:
a = 2 + 3 
b = 8 - a
c = 1 / 2
d = 2 + 3 
e = 2 / d
f = c - e
g = b / f
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "given : positive integer n is a perfect square and a perfect cube - - > n is of a form of n = x 6 for some positive integer x - - > 0 < x ^ 6 < 10 ^ 3 - - > 0 < x ^ 2 < 10 - - > x can be 1 , 2 or 3 hence nn can be 1 ^ 6 , 2 ^ 6 or 3 ^ 6 . answer : b ."
Answer: b
Python program:
a = 4 + 2 
b = a / 1
Problem: the speed of a boat in still water is 50 kmph and the speed of the current is 20 kmph . find the speed and upstream ?
Options: a ) 30 kmph , b ) 40 kmph , c ) 78 kmph , d ) 15 kmph , e ) 23 kmph
Rationale: speed downstream = 50 + 20 = 70 kmph speed upstream = 50 - 20 = 30 kmph answer : a
Answer: a
Python program:
a = 50 - 20
Problem: if 5 x = 6 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 8 * y ?
Options: a ) 48 / 25 , b ) 36 / 25 , c ) 6 / 5 , d ) 5 / 6 , e ) 25 / 36
Rationale: "5 x = 6 y = > x / y = 6 / 5 1 / 5 * x to 1 / 8 * y = x / y * 8 / 5 = ( 6 / 5 ) * ( 8 / 5 ) = 48 / 25 ans : a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 5
c = a / b
d = 6 / 5
e = c * d
Problem: when a number is divided by 6 & then multiply by 12 the answer is 10 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 6.5
Rationale: "if $ x $ is the number , x / 6 * 12 = 10 = > 2 x = 10 = > x = 5 b"
Answer: b
Python program:
a = 10 / 12
b = a * 6