euclaise/mathqa_programs huggingface dataset:
Problem: at a small company , 61 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 / 16 , b ) 1 / 3 , c ) 9 / 20 , d ) 47 / 61 , e ) 5 / 7
Rationale: "lets take total employees are 100 . given that , total women = 61 and total married = 60 . total men = 100 - 61 = 39 and single men = 2 / 3 * 39 = 26 . married men = total men - single men = 39 - 26 = 13 . married women = total married - married men = 60 - 13 = 47 . fraction of women are married = married women / total women = 47 / 61 = 5 / 7 . ans d"
Answer: d
Python program:
a = 60 / 100
b = 61 / 100
c = 1 - b
d = 2 / 3
e = 1 - d
f = c * e
g = a - f
h = 61 / 100
i = g / h
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 39 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 156 , c ) 144 , d ) 128 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 39 4 / x = 1 / 39 = > x = 156 min . answer : b"
Answer: b
Python program:
a = 1 + 4 
b = a * 39
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 252 runs ?
Options: a ) 6.25 , b ) 6.22 , c ) 5.5 , d ) 6.39 , e ) 6.13
Rationale: "required run rate = [ 252 - ( 3.2 * 10 ) ] / 40 = 220 / 40 = 5.5 answer : c"
Answer: c
Python program:
a = 10 * 3
b = 252 - a
c = b / 40
Problem: at what price must an article costing rs . 85.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 122.5 , b ) 142.5 , c ) 162.5 , d ) 182.5 , e ) 112.5
Rationale: "cp = 85.50 sp = 85.5 * ( 125 / 100 ) = 106.875 mp * ( 95 / 100 ) = 106.875 mp = 112.5 answer : e"
Answer: e
Python program:
a = 85 * 5
b = a / 100
c = 85 + 5 
d = c * 100
e = 100 - 5
f = d / e
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 12 , and the difference between the total number of strawberries and the total number of blueberries would increase by 76 . each blue box contains how many blueberries ?
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "let x be the number of blueberries in each blue box . then there are x + 12 strawberries in each red box . x + ( x + 12 ) = 76 x = 32 the answer is d ."
Answer: d
Python program:
a = 76 - 12
b = a / 2
Problem: 15 men take 20 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 27.57 , b ) 28.57 , c ) 29.57 , d ) 30.57 , e ) 32
Rationale: 3 w = 2 m 15 m - - - - - - 20 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 15 * 20 * 8 = 14 * x * 6 x = 28.57 answer : b
Answer: b
Python program:
a = 20 * 8
b = 15 * 3
c = a * b
d = 21 * 2
e = d * 6
f = c / e
g = math.floor(f)
h = g + 1
Problem: an association of mathematics teachers has 1,500 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 36 percent of the votes cast ?
Options: a ) 7.5 % , b ) 5.8 % , c ) 4.2 % , d ) 34.5 % , e ) 12.6 %
Rationale: "total umber of members = 1500 number of members that cast votes = 525 since , winning candidate received 36 percent of the votes cast number of votes for winning candidate = ( 36 / 100 ) * 525 = 189 percent of total membership that voted for winning candidate = ( 189 / 1260 ) * 100 = 12.6 % answer e"
Answer: e
Python program:
a = 36 / 100
b = a * 525
c = 4 ** 2
d = 100 * c
e = b / d
f = e * 100
Problem: how many multiples of 10 are there between 81 and 358 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "10 * 9 = 90 10 * 35 = 350 total no of multiples = ( 35 - 9 ) + 1 = 27 answer d"
Answer: d
Python program:
a = 358 - 81
b = a / 10
c = b + 1
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . states b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7600 , b ) 8000 , c ) 8400 , d ) data inadequate , e ) none of these
Rationale: "solution let the number of candidates appeared from each state be x . then , 7 % of x - 6 % of x = 80 ⇔ 1 % of x = 80 ⇔ x = 80 × 100 = 8000 . answer b"
Answer: b
Python program:
a = 7 - 6
b = a / 100
c = 80 / b
Problem: a train leaves mumabai at 9 am at a speed of 45 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 90 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 287 , b ) 279 , c ) 90 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 45 * 1 = 45 km so , the distance between first train and second train is 45 km at 10.00 am time taken by the trains to meet = distance / relative speed = 45 / ( 90 - 45 ) = 1 hours so , the two trains meet at 2 p . m . the two trains meet 1 * 90 = 90 km away from mumbai . answer : c"
Answer: c
Python program:
a = 45 * 1
b = 90 - 45
c = a / b
d = c * 90
Problem: in 1990 the budgets for projects q and v were $ 660,000 and $ 860,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 660 + 30 x = 860 - 10 x - - > 40 x = 200 and x = 5 . thus , it happens in 1995 . d ."
Answer: d
Python program:
a = 2 * 3
b = 10 * a
c = 1990 + b
Problem: a train 100 m long crosses a platform 200 m long in 15 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 72 kmph , d ) 94 kmph , e ) 59 kmph
Rationale: "d = 100 + 200 = 300 t = 15 s = 300 / 15 * 18 / 5 = 72 kmph answer : c"
Answer: c
Python program:
a = 200 * const_0_2778
b = 15 * a
c = b - 100
Problem: the average salary of 15 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 20,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 15,800 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: "total salary . . . 15 * 20 k = 300 k 5 emp @ 25 k = 125 k 4 emp @ 20 k = 80 k remaing 6 emp sal = 300 k - 125 k - 80 k = 95 k average = 95 k / 6 = 15800 ans : b"
Answer: b
Python program:
a = 5 * 4
b = 4 * 4
c = a * b
d = 5 * 5
e = d * 5
f = c - e
g = 4 * 15
h = f - g
i = 2 + 5 
j = h / i
Problem: if 0.10 of a number is equal to 0.070 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 7 : 10 , d ) 20 : 3 , e ) 30 : 7
Rationale: "0.10 a = 0.070 b - > a / b = 0.07 / 0.10 = 7 / 10 : . a : b = 7 : 10 answer : c"
Answer: c
Python program:
a = 0 * 70
b = 0 * 10
c = a / b
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 600 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 1500 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 100 = 1500 answer : b"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 1 / 3
d = 1 - c
e = d / 5
f = b - e
g = 1 / 3
h = 1 - g
i = 1 / 3
j = 1 - i
k = j / 5
l = h - k
m = l / 4
n = f - m
o = 600 / n
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 15 percent of the drink is orange juice and 60 percent is watermelon juice . if the drink is made with 30 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 120 , b ) 160 , c ) 190 , d ) 200 , e ) 400
Rationale: let the total number of ounces in the drink be x . % of orange = 15 % % of watermelon = 60 % % of grape = 100 % - 75 % = 25 % 0.25 x = 30 x = 120 therefore there are a total of 120 ounces in the drink . the answer is a .
Answer: a
Python program:
a = 30 * 15
b = 60 + 15 
c = 100 - b
d = a / c
e = 30 + d 
f = 30 * 60
g = 60 + 15 
h = 100 - g
i = f / h
j = e + i
Problem: sam invested rs . 3000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 2554.0 , b ) 3387.0 , c ) 2503.0 , d ) 3307.5 , e ) 16537.11
Rationale: "p = rs . 3000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 3000 * ( 1 + 5 / 100 ) 2 ] = ( 3000 * 21 / 20 * 21 / 20 ) = rs . 3307.50 answer : d"
Answer: d
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 3000
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 7.5 cm and breadth 6.5 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 10.2 , b ) 10.27 , c ) 10.23 , d ) 10.21 , e ) 10.25
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 7.5 + 5.5 ) = 26 cm parameter of the square = 26 cm i . e . 4 a = 26 a = 6.5 diameter of the semicircle = 6.5 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 6.5 ) = 1 / 2 ( 22 / 7 ) ( 6.5 ) = 143 / 14 = 10.21 cm to two decimal places answer : d"
Answer: d
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: a space shuttle orbits the earth at about 12 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 4,800 , d ) 28,800 , e ) 43,200
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 12 * 3600 = 43,200 answer : e"
Answer: e
Python program:
a = 12 * 3600
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 1.50 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 180 , b ) $ 135 , c ) $ 108 , d ) $ 60 , e ) $ 54
Rationale: since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 1.50 ) or $ 108 . the best answer is therefore c .
Answer: c
Python program:
a = 2 / 3
b = 36 * a
c = 1 / 3
d = b / c
e = 2 * d
Problem: if 213 × 16 = 3408 , then 0.16 × 2.13 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 0.16 × 2.13 = ( 16 / 100 x 213 / 100 ) = ( 16 x 213 / 10000 ) = 3408 / 10000 = 0.3408 . answer a"
Answer: a
Python program:
a = 0 * 16
Problem: what is the smallest positive integer x such that 80 - x is the cube of a positive integer
Options: a ) 16 , b ) 12 , c ) 47 , d ) 9 , e ) 12
Rationale: "given 80 - x is a perfect cube so we will take 64 = 4 * 4 * 4 80 - x = 64 x = 80 - 64 = 16 correct option is a"
Answer: a
Python program:
a = 3 + 4
Problem: the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 10 , then their difference is :
Options: a ) 10 , b ) 46 , c ) 70 , d ) 90 , e ) 100
Rationale: "let the numbers be x and ( 100 - x ) . then , x ( 100 - x ) = 5 * 495 x 2 - 100 x + 2475 = 0 ( x - 55 ) ( x - 45 ) = 0 x = 55 or 45 the numbers are 45 and 55 . required difference = 55 - 45 = 10 . answer : a"
Answer: a
Python program:
a = 5 * 495
b = a / 10
Problem: if two dice are thrown together , the probability of getting a square number on both the dice is
Options: a ) 5 / 12 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 12 , e ) 2 / 3
Rationale: the number of exhaustive outcomes is 36 . let e be the event of getting a sqaure number on both the dice . p ( e ) = 3 / 36 = 1 / 12 . d )
Answer: d
Python program:
a = 6 * 6
b = 6 / a
Problem: what is the area of a square field whose diagonal of length 28 m ?
Options: a ) 288 , b ) 289 , c ) 200 , d ) 112 , e ) 392
Rationale: "d 2 / 2 = ( 28 * 28 ) / 2 = 392 answer : e"
Answer: e
Python program:
a = square_area / (
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 13.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 61 1 / 9 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 12 = 3.6 million $ profit in 1983 = 18.8 - 13 = 5.8 million $ percentage increase in profit = ( 5.8 - 3.6 ) / 3.6 * 100 % = 61 1 / 9 % answer b"
Answer: b
Python program:
a = 13 - 0
b = a * 100
c = 18 - 8
d = b / c
e = 100 - d
Problem: 16 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 16 * 10 / 40 = 4 answer is c"
Answer: c
Python program:
a = 16 * 10
b = a / 40
Problem: the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 15000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8800 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 15000 + 7000 + 9000 / 5 = rs . 8800 correct option : c"
Answer: c
Python program:
a = 8000 + 5000 
b = a + 15000 
c = b + 7000 
d = c + 9000 
e = 4 + 1 
f = d / e
Problem: if n is a prime number greater than 19 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 19 , square it and see what would be the remainder upon division of it by 12 . n = 23 - - > n ^ 2 = 529 - - > remainder upon division 529 by 12 is 1 . answer : b ."
Answer: b
Python program:
a = 19 + 2 
b = a ** 2
c = 12 * 4
d = b - c
Problem: total number of 4 digit number do not having the digit 3 or 6 .
Options: a ) 22 , b ) 28 , c ) 27 , d ) 19 , e ) 11
Rationale: answer : d
Answer: d
Python program:
a = 6 + 3 
b = a + 4 
c = b + 3 
d = c + 3
Problem: the average weight of a , b and c is 43 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 129 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 37 . b ' s weight = 37 kg . e"
Answer: e
Python program:
a = 40 * 2
b = 43 * 2
c = a + b 
d = 43 * 3
e = c - d
Problem: the length of rectangle is thrice its breadth and its perimeter is 80 m , find the area of the rectangle ?
Options: a ) 360 , b ) 376 , c ) 299 , d ) 276 , e ) 111
Rationale: "2 ( 3 x + x ) = 80 l = 36 b = 10 lb = 36 * 10 = 360 a"
Answer: a
Python program:
a = 3 * 2
b = 1 * 2
c = a + b 
d = 80 / c
e = d * 3
f = 3 * 2
g = 1 * 2
h = f + g 
i = 80 / h
j = e * i
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability r that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability r of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"
Answer: c
Python program:
a = 5 / 6
Problem: a train running at the speed of 60 km / hr crosses a pole in 21 seconds . what is the length of the train ?
Options: a ) 350 m , b ) 278 m , c ) 876 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 21 ) m = 350 m . answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 21
Problem: a number when divided by 214 gives a remainder 35 , what remainder will be obtained by dividing the same number 14 ?
Options: a ) 7 , b ) 10 , c ) 11 , d ) 2 , e ) 3
Rationale: "explanation : 214 + 35 = 249 / 14 = 11 ( remainder ) answer : c"
Answer: c
Python program:
a = 14 * 2
b = 35 - a
Problem: a number whose fifth part increased by 3 is equal to its fourth part diminished by 3 is ?
Options: a ) 120 , b ) 180 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 3 = ( n / 4 ) - 3 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 6 â ‡ ’ ( 5 n - 4 n ) / 20 = 6 â ˆ ´ n = 120 option : a"
Answer: a
Python program:
a = 3 + 3 
b = 1 / 3
c = 1 + 3 
d = 1 / c
e = b - d
f = a / e
Problem: a military camp has a food reserve for 250 personnel for 40 days . if after 15 days 50 more personnel are added to the camp , find the number of days the reserve will last for ?
Options: a ) 25 , b ) 67 , c ) 26 , d ) 29 , e ) 18
Rationale: explanation : as the camp has a reserve for 250 personnel that can last for 40 days , after 10 days the reserve left for 250 personnel is for 30 days . now 50 more personnel are added in the camp . hence , the food reserve for 300 personnel will last for : 250 : 300 : : x : 30 … … . . ( it is an indirect proportion as less men means more days ) x = ( 250 * 30 ) / 300 x = 25 days answer : a
Answer: a
Python program:
a = 40 - 15
b = 250 * a
c = 250 + 50 
d = b / c
e = d + 3
Problem: what is x if x + 2 y = 12 and y = 3 ?
Options: a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
Rationale: "x = 12 - 2 y x = 12 - 6 . x = 6 answer : c"
Answer: c
Python program:
a = 2 * 3
b = 12 - a
Problem: in how many years rs 200 will produce the same interest at 10 % as rs . 1000 produce in 2 years at 12 %
Options: a ) 13 , b ) 9 , c ) 11 , d ) 12 , e ) 10
Rationale: explanation : clue : firstly we need to calculate the si with prinical 1000 , time 2 years and rate 12 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 200 * 10 ) = 12 option d
Answer: d
Python program:
a = 1000 * 12
b = a / 100
c = b * 2
d = 10 / 100
e = d * 200
f = c / e
Problem: a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 60 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2560 , d ) $ 2732 , e ) $ 2800
Rationale: "1.4 x = 2240 x = 2240 / 1.4 so , 1.6 x = 2240 * 1.6 / 1.4 = 2560 answer : - c"
Answer: c
Python program:
a = 100 + 60 
b = 100 + 40 
c = a / b
d = 2240 * c
Problem: a person buys 18 local tickets for rs 110 . each first class ticket costs rs 10 and each second class ticket costs rs 3 . what will another lot of 18 tickets in which the numbers of first class and second class tickets are interchanged cost ?
Options: a ) 112 , b ) 118 , c ) 121 , d ) 124 , e ) none of these
Rationale: explanation : let , there are x first class ticket and ( 18 - x ) second class tickets . then , 110 = 10 x + 3 ( 18 − x ) . = > 110 = 10 x + 54 − 3 x . = > 7 x = 56 . = > x = 8 . if the number of the first class and second class tickets are interchanged , then the total cost would be 10 × 10 + 3 × 8 = 124 . answer : d
Answer: d
Python program:
a = 18 * 3
b = 110 - a
c = 10 - 3
d = b / c
e = d * 3
f = 10 * 10
g = e + f
Problem: a train 250 m long running at 72 kmph crosses a platform in 40 sec . what is the length of the platform ?
Options: a ) 450 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 40 = 800 â € “ 250 = 450 m answer : a"
Answer: a
Python program:
a = 72 * const_0_2778
b = 40 * a
c = b - 250
Problem: out of 3 given numbers , the first one is twice the second and 3 times the third . if the average of these numbers is 88 , then the difference between first and third is .
Options: a ) 92 , b ) 39 , c ) 87 , d ) 96 , e ) none
Rationale: sum of three number is = 88 * 3 = 264 let three numbers are a , b , c and a is the highest and c is the lowest then , 2 b = a so b = a / 2 and 3 c = a so c = a / 3 we can write , a + b + c = 264 a + a / 2 + a / 3 = 264 11 a / 6 = 264 a = 144 so , c = 144 / 3 = 48 so there difference is = 144 - 48 = 96 answer d
Answer: d
Python program:
a = 4 + 4 
b = 88 + a
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 32 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 70.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 40 % , thus he must pay slightly more than $ 60 . only answer choice e fits . answer : e ."
Answer: e
Python program:
a = 32 * 8
b = a / 100
c = 10 - b
d = c * 10
Problem: r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 1,3 , 5,7 , 9,11 , 13,15 . . . s = 1 , 9,25 , 49,81 . . . numbers : 1 , 9 , 25 , 49 , 81 , 121 , and 169 are odd integers ( less than 200 ) that are in both sets . solution : seven answer : e"
Answer: e
Python program:
a = 200 - 4
b = a - 4
Problem: the cost to park a car in a certain parking garage is $ 9.00 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 ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.36 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 9 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 9 + 7 * 1.75 = 21.25 thus the average parking price = 21.25 / 9 = 2.36 $ d is the correct answer ."
Answer: d
Python program:
a = 9 - 2
b = 1 * 75
c = 9 + 0 
d = c / 9