euclaise/mathqa_programs huggingface dataset:
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 14 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 112 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,14 = 14 / 100 x = 80 * 14 / 100 x = 11.2 11.2 / 10 = 1,12 = 112 % , answer b"
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 14 * b
d = c / 10
e = d * 100
Problem: what is the 100 th digit of ( 3 ! * 5 ! + 4 ! * 3 ! ) / 2 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 7 , e ) 6
Rationale: ( 3 ! * 5 ! + 4 ! * 3 ! ) / 2 = 3 ! ( 5 ! + 4 ! ) / 2 = 6 ( 120 + 24 ) / 2 = 432 100 th digit of the above product will be equal to 4 answer a
Answer: a
Python program:
a = math.factorial(3)
b = math.factorial(5)
c = a * b
d = math.factorial(4)
e = math.factorial(3)
f = d * e
g = c + f 
h = g / 2
i = h / 100
j = math.floor(i)
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 9408 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50
b ) rs . 67.50
c ) rs . 86.50
d ) rs . 98.00
e ) none of these
Rationale: solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 9408 ⇔ 12 x 2 = 9408 ⇔ x 2 = 784 ⇔ x = 28 . so , length = 84 m and breadth = 112 m . perimeter = [ 2 ( 84 + 112 ) ] m = 392 m . ∴ cost of fencing = rs . ( 0.25 × 392 ) = rs . 98.00 . answer d
Answer: d
Python program:
a = 3 * 4
b = 9408 / a
c = math.sqrt(b)
d = 3 * c
e = 3 * 4
f = 9408 / e
g = math.sqrt(f)
h = 4 * g
i = rectangle_perimeter * (
j = i / 25
Problem: at a certain university , 70 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 50 , d ) 62.5 , e ) 75
Rationale: "answer is 75 % total women = 70 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 20 % but question wants to know the percent of men that are tenured 20 % / 40 % = 50 % c"
Answer: c
Python program:
a = 100 - 70
b = 90 - 70
c = a + b
Problem: if p and t are positive integers such that p > t > 1 , what is the remainder when 92 p × 5 p + t + 11 t × 6 pt is divided by 10 ?
Options: a ) a . 0 , b ) b . 1 , c ) c . 3 , d ) d . 4 , e ) e . 5
Rationale: 92 p × 5 p + t + 11 t × 6 pt - - 1 = b
Answer: b
Python program:
a = 6 - 5
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 50 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 ) 1 , c ) 3 / 4 , d ) 2 , e ) 3
Rationale: "d = rt m : r = 40 mph , t = t + 1 / 4 hr d = 40 ( t + 1 / 4 ) p : r = 50 , t = t d = 50 t since they went the same distance : 40 t + 40 / 4 = 50 t 10 t = 10 t = 1 hr , b"
Answer: b
Python program:
a = 15 / const_60
b = 40 * a
c = 50 - 40
d = b / c
e = const_60 * d
Problem: a person buys an article at rs . 350 . at what price should he sell the article so as to make a profit of 30 % ?
Options: a ) 455 , b ) 277 , c ) 269 , d ) 261 , e ) 281
Rationale: "cost price = rs . 350 profit = 30 % of 350 = rs . 105 selling price = cost price + profit = 350 + 105 = 455 answer : a"
Answer: a
Python program:
a = 30 / 100
b = 350 * a
c = 350 + b
Problem: two trains 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 12.24 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 200 = 340 m . required time = 340 * 9 / 250 = 12.24 sec . answer : e"
Answer: e
Python program:
a = 140 + 200 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: how many cubes of 5 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 1770 cm , b ) 8000 cm , c ) 7860 cm , d ) 6170 cm , e ) 1870 cm
Rationale: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 5 * 5 * 5 = 8000 note : 1 m = 100 cm answer : b"
Answer: b
Python program:
a = volume_cube / (
Problem: the average of first seven multiples of 4 is :
Options: a ) 9 , b ) 16 , c ) 15 , d ) 8 , e ) 10
Rationale: "explanation : ( 4 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 4 x 28 / 7 = 16 answer : b"
Answer: b
Python program:
a = 4 + 1
Problem: there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120
Rationale: "method 1 : take the first amateur . he plays a game with each of the other four i . e . 4 games . now take the second one . he has already played a game with the first one . he plays 3 games with the rest of the 3 amateurs i . e . 3 more games are played . now take the third amateur . he has already played a game each with the first and the second amateur . now he plays 2 games with the remaining 2 amateurs so 2 more games are played . now go on to the fourth amateur . he has already played 3 games with the first 3 amateurs . he just needs to play a game with the last one i . e . 1 more game is played . the last amateur has already played 4 games . total no of games = 4 + 3 + 2 + 1 = 10 method 2 : each person is one participant of 4 games . so there are in all 4 * 5 = 20 instances of one participant games . but each game has 2 participants so total number of games = 20 / 2 = 10 answer : a ."
Answer: a
Python program:
a = 5 * 4
b = a / 2
Problem: in a urban village of india named ` ` owlna ' ' , 75 % people have refrigerator , 90 % people have television , 85 % people got computers and 75 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 25 %
Rationale: "e 10 % 100 - [ ( 100 - 75 ) + ( 100 - 90 ) + ( 100 - 85 ) + ( 100 - 75 ) ] = 100 - ( 25 + 10 + 15 + 25 ) = 100 - 75"
Answer: e
Python program:
a = 100 - 75
b = 100 - 90
c = a + b 
d = 100 - 85
e = c + d 
f = 100 - 75
g = e + f 
h = 100 - g
Problem: a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 67 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 20 , c ) 32 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 67 - x ounces of q is present in the mixture ( as the total = 67 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 67 - x ) = 15 = > x = 35 = > 67 - 35 = 32 ounces of q is present in the mixture . answer is c ."
Answer: c
Python program:
a = 20 / 100
b = a * 67
c = 15 - b
d = 25 / 100
e = 20 / 100
f = d - e
g = c / f
Problem: if $ 5,000 is invested in an account that earns 8 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.08 / 2 ) ^ 2 = 5408 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 8 / 100 ) = 5400 difference = 5408 - 5400 = 8 $ answer : b"
Answer: b
Python program:
a = 8 * 1
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 675 square meters , then what is the width of the rectangular garden ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "let x be the width of the garden . 3 x ^ 2 = 675 x ^ 2 = 225 x = 15 the answer is b ."
Answer: b
Python program:
a = 675 / 3
b = math.sqrt(a)
Problem: how many odd 3 - digit integers smaller than 500 are there such that all their digits are different ?
Options: a ) 72 , b ) 88 , c ) 112 , d ) 122 , e ) 144
Rationale: case 1 : numbers starting with 1 1 _ _ the unit digit can take 4 numbers ( 3,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 2 : numbers starting with 2 2 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 case 3 : numbers starting with 3 3 _ _ the unit digit can take 4 numbers ( 1,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 4 : numbers starting with 4 4 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 hence 32 + 40 + 32 + 40 = 144 , correct answer is e
Answer: e
Python program:
a = 10 - 1
b = math.factorial(a)
c = 10 - 1
d = 3 - 1
e = c - d
f = math.factorial(e)
g = b / f
h = 500 - 100
i = h / 100
j = g * i
k = j / 2
Problem: a van takes 5 hours to cover a distance of 435 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 50 , b ) 52 , c ) 54 , d ) 56 , e ) 58
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 435 / 7.5 = 58 kph the answer is e ."
Answer: e
Python program:
a = 3 / 2
b = a * 5
c = 435 / b
Problem: if the price of a tv is first decreased by 20 % and then increased by 50 % , then the net change in the price will be :
Options: a ) 20 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 150 % of ( 80 % of 100 ) = rs . 150 / 100 * 80 / 100 * 100 = rs . 120 . . ' . increase = 20 % answer : a"
Answer: a
Python program:
a = 100 - 20
b = 100 + 50 
c = a * b
d = c / 100
e = d - 100
Problem: 18 % of 680 - ? = 68.7
Options: a ) 44.1 , b ) 32.4 , c ) 66.5 , d ) 75.2 , e ) 53.7
Rationale: "e 53.7 ( 18 * 680 ) / 100 - ? = 68.7 ? = 122.4 - 68.7 ? = 53.7"
Answer: e
Python program:
a = 68 * 7
b = a / 100
c = b * 18
d = c / 100
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 241 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 12200 , b ) 11897 , c ) 18799 , d ) 10000 , e ) 12782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 241 p = 10000 answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 20 + 1 
c = a * b
d = 20 + 1 
e = c + d
Problem: a , b and c can do a piece of work in 24 , 30 and 40 days respectively . they start the work together but c leaves 4 days before the completion of the work . in how many days is the work done ?
Options: a ) 11 , b ) 5 , c ) 70 , d ) 11 , e ) 13
Rationale: x / 24 + x / 30 + x / 40 = 1 x = 11 days answer : d
Answer: d
Python program:
a = 40 - 30
b = 24 - a
c = b - 4
d = c + 1
Problem: of the 120 passengers on flight 750 , 45 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 48 , c ) 46 , d ) 52 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 45 * 120 = 54 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 54 - 8 = 46 answer c"
Answer: c
Python program:
a = 45 / 100
b = 120 * a
c = 10 / 100
d = 120 * c
e = 10 / 100
f = 120 * e
g = f / 3
h = d - g
i = b - h
Problem: what is the smallest positive integer x , such that 6000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 36 , d ) 12 , e ) 18
Rationale: "take out the factors of 6000 that will come 2 * 3 * 10 ^ 3 . for perfect cube you need every no . raise to the power 3 . for 6000 x to be a perfect cube , need two 2 and 2 3 that means 36 or 6 ^ 2 c is the answer ."
Answer: c
Python program:
a = 3 + 4
Problem: if x is equal to the sum of the integers from 10 to 20 , inclusive , and y is the number of even integers from 10 to 20 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 175 , c ) 180 , d ) 190 , e ) 200
Rationale: sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 10 + ( 11 - 1 ) * 1 } = 11 * 15 = 165 = x number of even number = ( 20 - 10 ) / 2 + 1 = 6 = y x + y = 165 + 6 = 171 a
Answer: a
Python program:
a = 10 + 20 
b = a / 2
c = 20 - 10
d = c + 1 
e = b * d
f = 20 - 10
g = f / 2
h = g + 1 
i = e + h
Problem: 49 * 49 * 49 * 49 = 7 ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 8
Rationale: "sol . 49 * 49 * 49 * 49 = ( 72 * 72 * 72 * 72 ) = 7 ( 2 + 2 + 2 + 2 ) = 78 . so , the correct answer is 8 . answer d"
Answer: d
Python program:
a = 49 * 49
Problem: find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case .
Options: a ) 266 , b ) 268 , c ) 270 , d ) 272 , e ) 274
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 33 , 8 ) + 2 = 266 . answer : a"
Answer: a
Python program:
a = math.lcm(33, 8)
b = 2 + a
Problem: 50 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 240 , b ) 288 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 50 / 100 ) * x + 120 = x x = 240 answer : a"
Answer: a
Python program:
a = 120 / 100
b = 120 / a
Problem: there are 4 runners on a track team who run an average of 4.5 seconds per 40 yards . if another runner joins their team who runs 4.3 seconds per 40 yards , what will the new average 40 yard time be ?
Options: a ) 4.46 , b ) 4.39 , c ) 4.42 , d ) 4.49 , e ) 4.33
Rationale: ( sum of the 4 times ) / 4 = 4.5 sum of the 4 times = 18 new sum = 18 + 4.3 = 22.3 new average = 22.3 / 5 = 4.46 ans : a
Answer: a
Python program:
a = 4 + 5 
b = a / 2
Problem: a train is moving at 4 / 5 of its usual speed . the train is 30 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "new time = d / ( 4 v / 5 ) = 5 / 4 * usual time 30 minutes represents 1 / 4 of the usual time . the usual time is 2 hours . the answer is c ."
Answer: c
Python program:
a = 4 / 5
b = 30 * a
c = 4 / 5
d = 1 - c
e = 1/(d)
f = b * e
g = f / const_60
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 50 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 732 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 50 + 52 + 54 + . . . . . upto 12 terms ) this is an a . p with first term , a = 50 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 50 + { 12 - 1 ) x 2 ] = 6 ( 122 ) = 732 kms . answer : c"
Answer: c
Python program:
a = 2 * 50
b = 12 - 1
c = b * 2
d = a + c 
e = 12 / 2
f = d * e
Problem: what is the least integer greater than – 3 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 3 ) + ( 0.5 ) = - 2.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 3 to - 2.5 ) . next , the question asks for the least integer that is greater than - 2.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 2.5 is - 2 . final answer : a"
Answer: a
Python program:
a = 0 + 5
Problem: if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 90 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 50 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
Options: a ) $ 60 , b ) $ 70 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 3 x + 4 y + 2 z = 90 7 x + 2 y + 2 z = 50 adding both the equations = 10 x + 6 y + 4 z = 140 5 x + 3 y + 2 z = 70 ans b"
Answer: b
Python program:
a = 50 + 90 
b = a / 2
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 8 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23.9 % , c ) 24 % , d ) 25 % , e ) 34 %
Rationale: "since 8 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.92 = 0.22 ; { % of customers who sample candy } = 0.239 . answer : b ."
Answer: b
Python program:
a = 100 - 8
b = a / 100
c = 22 / b
Problem: | x + 3 | – | 4 - x | = | 8 + x | how many u solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Python program:
a = 4 + 3 
b = a * 2
c = b / 8
Problem: a sum of money is sufficient to pay a ' s wages for 21 days and b ' s wages for 28 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 12 days , b ) 12 1 / 4 days , c ) 14 days , d ) 24 1 / 2 days , e ) none of these
Rationale: let total money be rs . x a ' s 1 day ' s wages = rs . x / 21 , b ' s 1 day ' s wages = rs . x / 28 ( a + b ) ' s 1 day ' s wages = rs . ( x / 21 + x / 28 ) = rs . x / 12 ; money is sufficient to pay the wages of both for 12 days . correct option : a
Answer: a
Python program:
a = 1 / 21
b = 1 / 28
c = a + b 
d = 1 / c
Problem: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 24 . what is the total number of students in the school ?
Options: a ) 50 , b ) 80 , c ) 120 , d ) 150 , e ) 100
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 24 + 2 / 3 of 24 80 / 100 x = 40 x = 50 . answer : option a"
Answer: a
Python program:
a = 2 / 3
b = 24 * a
c = 24 + b 
d = 20 / 100
e = 1 - d
f = c / e
Problem: the l . c . m . of two numbers is 48 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 40 , d ) 53 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : option c"
Answer: c
Python program:
a = 2 * 3
b = 48 / a
c = b * 3
d = 2 * 3
e = 48 / d
f = e * 2
g = c + f
Problem: if x + ( 1 / x ) = 5 , what is the value of r = x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) r = 21 , b ) r = 22 , c ) r = 23 , d ) 24 , e ) 27
Rationale: "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c"
Answer: c
Python program:
a = 5 ** 2
b = a - 2
Problem: how many multiples of 2 are there between 1 and 56 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 27 , d ) 26 , e ) 28
Rationale: "27 multiples of 2 between 1 and 56 exclusive . from 2 * 1 upto 2 * 27 , ( 1,2 , 3,4 , . . . , 27 ) . hence , 27 multiples ! correct option is c"
Answer: c
Python program:
a = 56 - 1
b = a / 2
c = b + 1
Problem: the average of marks obtained by 120 boys was 39 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 39 24 x = 4680 - 1800 = > x = 2880 / 24 x = 120 . hence , the number of boys passed = 120 . answer : c"
Answer: c
Python program:
a = 39 * 120
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
Problem: the area of a circular place is 17.56 hectares . find the cost of fencing it at the rate of rs . 3 / meter approximately .
Options: a ) rs . 4233
b ) rs . 4350
c ) rs . 4457
d ) rs . 4670
e ) rs . 4756
Rationale: area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c
Answer: c
Python program:
a = 1000 * 10
b = a * 17
c = b / math.pi
d = math.sqrt(c)
e = circumface * (
Problem: from a pack of 52 cards , two cards are drawn at random together at random what is the probability of both the cards being kings ?
Options: a ) 1 / 221 , b ) 8 / 221 , c ) 4 / 589 , d ) 4 / 587 , e ) 7 / 654
Rationale: "let s be the sample space then n ( s ) = 52 c 2 = ( 52 * 51 ) / ( 2 * 1 ) = 1326 let e be the event of getting 2 kings out of 4 n ( e ) = 4 c 2 = ( 4 * 3 ) / ( 2 * 1 ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 1326 = 1 / 221 answer ( a )"
Answer: a
Python program:
a = 52 / 4
b = 52 / 4
c = a * b
d = math.comb(52, 2)
e = c / d
Problem: the length of a rectangle is halved , while its breadth is tripled . wat isthe % change in area ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 67 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Python program:
a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
Problem: 3 , 7,12 , 18,25 . . . . . . . . . . . . . . 10 th terms
Options: a ) 43 , b ) 53 , c ) 63 , d ) 65 , e ) 74
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 42 + 10 = 52 52 + 11 = 63 63 + 11 = 74 answer : e"
Answer: e
Python program:
a = negate - (
Problem: 10 men and 15 women together can complete a work in 5 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 127 days , b ) 150 days , c ) 177 days , d ) 187 days , e ) 225 days
Rationale: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 5 15 women ' s 1 day work = ( 1 / 5 - 10 / 100 ) = 1 / 10 1 woman ' s 1 day work = 1 / 150 1 woman alone can complete the work in 150 days . answer : b"
Answer: b
Python program:
a = 1 * 100
b = 1 * 100
c = 10 * 5
d = b - c
e = a / d
f = 15 * 5
g = e * f
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 25 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 25 s = ( 27 x + 17 y ) / ( x + y ) = 25 = ( 27 x + 17 y ) / = 25 ( x + y ) = 2 x = 8 y = x / y = 8 / 2 = 4 / 1 i . e 4 : 1 answer : b"
Answer: b
Python program:
a = 27 - 25
b = 25 - 17
c = a / b