euclaise/mathqa_programs huggingface dataset:
Problem: tom drives from town w to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between w and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point w to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Python program:
a = 3 / 36
b = 2 / 60
c = a - b
d = 1/(c)
Problem: the average of first 12 natural numbers is ?
Options: a ) 5.2 , b ) 6.5 , c ) 5.3 , d ) 5.9 , e ) 5.1
Rationale: "sum of 12 natural no . = 156 / 2 = 78 average = 78 / 12 = 6.5 answer : b"
Answer: b
Python program:
a = 12 + 1
Problem: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 65 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 55 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 65 - { both correctly } + 5 { both correctly } = 55 . answer : b ."
Answer: b
Python program:
a = 85 + 65 
b = a + 5 
c = b - 100
Problem: what is the average of 12 , 13 , 14 , 51 , 52 , 53 , 1 , 11.5 , 1 , 1.20 , and 11.25 ?
Options: a ) 21.06 , b ) 23 , c ) 26 , d ) 23.69 , e ) 22.56
Rationale: "add 12 , 13 , 14 , 51 , 52 , 53 , 1 , 11.5 , 1,12 , and 11.25 grouping numbers together may quicken the addition sum = 231.75 231.75 / 11 = 21.06 a"
Answer: a
Python program:
a = 12 + 13 
b = a + 14 
c = b + 51 
d = c + 52 
e = d + 53 
f = e + 12 
g = 3 + 4 
h = f / g
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 5 % ?
Options: a ) 20 % , b ) 29 % , c ) 10 % , d ) 80 % , e ) 42.5 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 95 2 / 3 sp 1 = 95 sp 1 = 142.5 100 - - - 42.5 = > 42.5 % answer : e"
Answer: e
Python program:
a = 100 - 5
b = 2 / 3
c = a / b
d = c - 100
Problem: a jewelry store purchased a pair of earrings for $ 240 and was selling it at a price that equaled the purchase price of the earrings plus a markup that was 25 percent of the selling price . after some time a jewelry store owner decided to decrease the selling price by 20 percent . what was the jewelry store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 2 , c ) $ 10 , d ) $ 16 , e ) $ 18
Rationale: sale price ( sp ) = 240 + markup ( mp ) - - > mp = sp - 240 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 240 3 sp / 4 = 240 sp = 320 now a discount of 20 % is given so new sp is . 8 * 320 = 256 profit = 256 - 240 = 16 answer is d
Answer: d
Python program:
a = 25 / 100
b = a * 240
c = 25 / 100
d = 1 - c
e = b / d
f = 240 + e 
g = 20 / 100
h = 1 - g
i = f * h
j = i - 240
Problem: if 1 / 4 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 12 are from africa , 1 / 6 are from asia and the remaining 36 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108
Rationale: "1 / 4 + 1 / 8 + 1 / 12 + 1 / 6 = ( 6 + 3 + 2 + 4 ) / 24 = 15 / 24 let x be the number of passengers on the ship . 36 = ( 9 / 24 ) x = 3 x / 8 x = 96 the answer is b ."
Answer: b
Python program:
a = 1 / 4
b = 1 / 8
c = a + b 
d = 1 / 12
e = c + d 
f = 1 / 6
g = e + f 
h = 1 - g
i = 36 / h
Problem: a hare and a tortoise have a race along a circle of 100 yards diameter . the tortoise goes in one direction and the hare in the other . the hare starts after the tortoise has covered 1 / 5 of its distance and that too leisurely . the hare and tortoise meet when the hare has covered only 1 / 8 of the distance . by what factor should the hare increase its speed so as to tie the race ?
Options: a ) 37.9 , b ) 37.2 , c ) 37.1 , d ) 37.82 , e ) 37.8
Rationale: assume the circumference of the circle is 200 meters . hare and tortoise started at the same point but moves in the opposite direction . it is given that by that time tortoise covered 40 m ( 1 / 5 th of the distance ) , hare started and both met after hare has covered 25 . this implies , in the time hare has covered 25 m , hare has covered 200 - 40 - 25 = 135 meters . so hare : tortoise speeds = 25 : 135 = 5 : 27 now hare and tortoise has to reach the starting point means , hare has to cover 175 meters and tortoise has to cover only 25 meters in the same time . as time = distancespeed = 2527 = 1755 × kdistancespeed = 2527 = 1755 × k ie . , hare has to increase its speed by a factor k . solving we get k = 37.8 answer : e
Answer: e
Python program:
a = 8 - 1
b = 100 / 5
c = 100 - b
d = 100 / 8
e = c - d
f = 100 / 8
g = e / f
h = a * g
Problem: a certain rectangular crate measures 20 feet by 20 feet by 20 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 20 x 20 i . e . of radius 20 / 2 = 10 e"
Answer: e
Python program:
a = 20 / 2
b = volume_cylinder / (
c = math.pi * 20
d = math.sqrt(b)
Problem: jack got paid today for his part - time job as a juggler , and noticed that 20 % of his paycheck went to taxes . jack wants to spend 80 % of what ' s left on a new bike , and put the rest into savings . if jack puts $ 20 into savings , how much was his original paycheck before taxes ?
Options: a ) $ 125 , b ) $ 135 , c ) $ 145 , d ) $ 155 , e ) $ 165
Rationale: let p be jack ' s original paycheck value . the value after taxes t is given by t = p - 20 % p let s be the amount put into savings , given by s = t - 80 % t for s = $ 20 , solve for p $ 20 = ( p - 20 % p ) - 80 % ( p - 20 % p ) p = $ 125 correct answer a
Answer: a
Python program:
a = 100 - 80
b = a / 100
c = 20 / b
d = 80 / 100
e = c / d
Problem: find a sum for 1 st 5 prime no . ' s ?
Options: a ) 23 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 ) = 28 note : 1 is not a prime number option b"
Answer: b
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b 
d = 2 + 3 
e = d + 2 
f = c + e 
g = 5 + 2 
h = f + g 
i = 5 + 2 
j = i + 2 
k = h + j 
l = 5 + 2 
m = l + 2 
n = m + 4 
o = k + n 
p = 5 + 2 
q = p + 2 
r = q + 4 
s = r + 2 
t = o + s 
u = 5 + 2 
v = u + 2 
w = v + 4 
x = w + 2 
y = x + 4 
z = t + y
Problem: a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability w that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer w : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Python program:
a = 3 / 5
b = 3 / 5
c = a * b
d = 3 / 5
e = 2 / 5
f = d * e
g = 3 / 5
h = 2 / 5
i = g * h
j = f + i 
k = c + j
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel two times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 9 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 2 and w = 2 s then we have 1 / ( 2 * s ) + 1 / s = 1 / 2 < = > 3 / ( 2 * s ) = 1 / 2 < = > s = 3 ans : b"
Answer: b
Python program:
a = 2 * 4
b = 1/(a)
c = b + 1 
d = c * 3
e = 2 * 4
f = d * e
Problem: if a train , travelling at a speed of 90 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 135 m , b ) 125 m , c ) 129 m , d ) 120 m , e ) 165 m
Rationale: "explanation : d = 90 * 5 / 18 * 5 = 125 m answer : option b"
Answer: b
Python program:
a = 90 * const_0_2778
b = a * 5
Problem: karthik read 7 / 13 th of a book in 1 st week and 5 / 9 th of the remaining book in 2 nd week . if there were 96 pages unread after 2 nd week , how many pages were there in the book ?
Options: a ) 518 , b ) 452 , c ) 468 , d ) 502 , e ) 396
Rationale: solution 96 pages were unread so on second week have 5 / 9 so unread pages = 1 - 5 / 9 = 4 / 9 96 * 9 / 4 = 216 then , on first week unread pages were 216 total pages = 216 * 13 / 6 = 468 so answer is c
Answer: c
Python program:
a = 5 / 9
b = 1 - a
c = 96 / b
d = c * 13
e = 7 - 1
f = d / e
Problem: find the quotient : 0.0204 / 17
Options: a ) 0.012 , b ) 0.12 , c ) 0.0012 , d ) 0.00012 , e ) none of them
Rationale: 204 / 17 = 12 . dividend contains 4 places of decimal . 0.2040 / 17 = 0.0012 . answer is c .
Answer: c
Python program:
a = 0 / 204
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 50 kmph its consumption is 1 litre per hour . if each litre costs $ 30 and other expenses per hous is $ 20 , then what would be the minimum expenditure required to cover a distance of 400 km ?
Options: a ) 300 , b ) 400 , c ) 250 , d ) 350 , e ) 450
Rationale: "50 kmph consumption is 1 lt / hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance . 1 lt costs $ 30 so 8 lt costs $ 240 extra expenses for 1 hr - $ 20 8 hrs - $ 160 total expense - $ 240 + $ 160 = $ 400 answer : b"
Answer: b
Python program:
a = 400 / 50
b = a * 30
c = 400 / 50
d = c * 20
e = b + d
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 59.29 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 59.29 x 100 ) paise = 5929 paise . number of members = 5929 = 77 . answer : c"
Answer: c
Python program:
a = 59 * 29
b = math.sqrt(a)
Problem: if a ^ 2 + b ^ 2 = 30 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 30 - 20 = 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 30 + 20 = 50 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 50 + 10 = 60 d"
Answer: d
Python program:
a = math.sqrt(30)
b = a * 10
c = b + 3
Problem: a can do a work in 30 days , b can do it in 20 days . they together under took to do a piece of work for rs . 1000 , what is the share of b ?
Options: a ) rs . 500 , b ) rs . 400 , c ) rs . 800 , d ) rs . 600 , e ) rs . 200
Rationale: explanation : share of their work days = 30 : 20 share of their work = 20 : 30 share of b ’ s money = 3 / 5 * 1000 = 600 answer : option d
Answer: d
Python program:
a = 30 * 20
Problem: 3 x ^ 2 - 6 x + 3 = 0 find the above equation find the value of x
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: a = 3 , b = - 6 , c = 3 x 1,2 = ( 6 ± √ ( ( - 6 ) 2 - 4 × 3 × 3 ) ) / ( 2 × 3 ) = ( 6 ± √ ( 36 - 36 ) ) / 6 = ( 6 ± 0 ) / 6 x 1 = x 2 = 1 b
Answer: b
Python program:
a = 6 / 3
b = a / 2
Problem: the income of a broker remains unchanged though the rate of commission is increased from 4 % to 5 % . the percentage of slump in business is :
Options: a ) 8 % , b ) 1 % , c ) 20 % , d ) 80 % , e ) none
Rationale: "explanation : let the business value changes from x to y . then , 4 % of x = 5 % of y or 4 / 100 × x = 5 / 100 × y or y = 4 / 5 x change in business = ( x − 4 / 5 x ) = 1 / 5 x percentage slump in business = ( 1 / 5 x × 1 / x × 100 ) % correct option : c"
Answer: c
Python program:
a = 4 / 100
b = 5 / 100
c = a / b
d = 1 - c
e = d * 100
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 45 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: equate the fat : 0.1 x + 0.45 * 8 = 0.2 ( x + 8 ) - - > x = 20 . answer : e .
Answer: e
Python program:
a = 45 - 20
b = a * 8
c = b / 10
Problem: if the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm , a square with the same area as the original rectangle would result . find the perimeter of the original rectangle .
Options: a ) 40 cm
b ) 45 cm
c ) 50 cm
d ) 52 cm
e ) 57 cm
Rationale: explanation : let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( 1 ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( 2 ) solving 1 & 2 , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : option c
Answer: c
Python program:
a = 3 + 4 
b = a * 3
c = 4 * 3
d = b - c
e = 3 + 4 
f = e * 3
g = 4 * 3
h = f - g
i = 3 + 4 
j = h + i 
k = d + j 
l = k * 2
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 110 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 7 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 70 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 110 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 7 + 4 = 11 kms / hr time taken = 110 / 11 = 10 hrs distance traveled by brad = brad ' s speed * time taken = 7 * 10 = 70 kms . . . answer - d"
Answer: d
Python program:
a = 4 + 7 
b = 110 / a
c = 4 * b
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 15 % . staff are allowed a further 10 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.75 d , b ) 0.76 d , c ) 0.765 d , d ) 0.775 d , e ) 0.805 d
Rationale: "successive doscounts = - a - b + ab / 100 putting the values , total discount = - 15 - 10 + 150 / 100 = - 25 + 1.5 = 23.5 % discount hence the final price of the dress = d - 0.235 d = 0.765 d correct option : c"
Answer: c
Python program:
a = 100 - 15
b = a / 100
c = 100 - 15
d = c / 100
e = 10 / 100
f = d * e
g = b - f
Problem: in a simultaneous throw of a pair of dice , find the probability of getting a total more than 11
Options: a ) 11 / 25 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 6 / 17
Rationale: total number of cases = 10 * 10 = 100 favourable cases = [ ( 2,10 ) , ( 3,9 ) , ( 3,10 ) , ( 4,8 ) , ( 4,9 ) , ( 4,10 ) , ( 5,7 ) , ( 5,8 ) , ( 5,9 ) , ( 5,10 ) , ( 6,6 ) , ( 6,7 ) , ( 6,8 ) , ( 6,9 ) , ( 6,10 ) , ( 7,5 ) , ( 7,6 ) , ( 7,7 ) , ( 7,8 ) , ( 7,9 ) , ( 7,10 ) , ( 8,4 ) , ( 8,5 ) , ( 8,6 ) , ( 8,7 ) , ( 8,8 ) , ( 8,9 ) , ( 8,10 ) , ( 9,3 ) , ( 9,4 ) , ( 9,5 ) , ( 9,6 ) , ( 9,7 ) , ( 9,8 ) , ( 9,10 ) , ( 10,2 ) , ( 10,3 ) , ( 10,4 ) , ( 10,5 ) , ( 10,6 ) , ( 10,7 ) , ( 10,8 ) , ( 10,9 ) , ( 10,10 ) ] = 44 so probability = 44 / 100 = 11 / 25 answer is a
Answer: a
Python program:
a = 2 * 3
b = 11 - a
c = b / 11
Problem: sandy had $ 210 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 240 , b ) $ 300 , c ) $ 360 , d ) $ 420 , e ) $ 480
Rationale: "let the money sandy took for shopping be x . 0.7 x = 210 x = 300 the answer is b ."
Answer: b
Python program:
a = 100 - 30
b = a / 100
c = 210 / b
Problem: if a ã — b = 2 a - 3 b + ab , then 2 ã — 5 + 5 ã — 2 is equal to :
Options: a ) 18 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "explanation : 2 ã — 5 + 5 ã — 2 = ( 2 ã — 2 - 3 ã — 5 + 2 ã — 5 ) + ( 2 ã — 5 - 3 ã — 2 + 5 ã — 3 ) = ( 4 - 15 + 10 + 10 - 6 + 15 ) = 18 . answer : a"
Answer: a
Python program:
a = 2 * 2
b = 3 * 2
c = a - b
d = 2 * 2
e = c + d 
f = 2 * 2
g = 3 * 2
h = f - g
i = 2 * 2
j = h + i 
k = e + j
Problem: if ( n + 2 ) ! / n ! = 156 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 156 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 156 from here , we might just test the answer choices . since ( 13 ) ( 12 ) = 156 , we can see that n = 11 d"
Answer: d
Python program:
a = 4 + 4 
b = a - 1
Problem: 18 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 230 , b ) 274 , c ) 306 , d ) 354 , e ) 424
Rationale: "2 * 18 c 2 = 2 * 153 = 306 the answer is c ."
Answer: c
Python program:
a = 18 - 1
b = 18 * a
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 3 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 3 + 3 = 28 meter answer is d ."
Answer: d
Python program:
a = 12 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: a 6 - liter solution is 40 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4
Rationale: let x be the amount of pure alcohol required . 0.4 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 2.4 x = 1.2 liters the answer is a .
Answer: a
Python program:
a = 6 * 40
b = a / 100
c = b * 2
d = 6 - c
Problem: the present population of a town is 2100 . population increase rate is 5 % p . a . find the population of town before 1 years ?
Options: a ) 1500 , b ) 1600 , c ) 2000 , d ) 2100 , e ) 2500
Rationale: "p = 2100 r = 5 % required population of town = p / ( 1 + r / 100 ) ^ t = 2100 / ( 1 + 5 / 100 ) = 2100 / ( 21 / 20 ) = 2000 ( approximately ) answer is c"
Answer: c
Python program:
a = 2100 * 5
b = a / 100
c = 2100 + b
Problem: a math teacher has 25 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 25 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 25 - 17 = 8 answer ( a )"
Answer: a
Python program:
a = 25 * 8
b = a / 10
c = b / 2
d = c - const_0_25
e = d - const_0_25
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.4 * 48 + 0.3 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 34 = 66 . answer : b ."
Answer: b
Python program:
a = 40 / 100
b = 100 - 30
c = b / 100
d = a * c
e = 1 - d
Problem: an alloy weighing 26 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 34 , e ) 48
Rationale: in 24 ounces , gold is 26 * ( 70 / 100 ) = 18.2 ounces . now we add x ounces of pure gold to make it 90 % gold . so 18.2 + x = ( 24 + x ) * 90 / 100 = > x = 34 . answer is d .
Answer: d
Python program:
a = 90 / 100
b = a * 26
c = 70 / 100
d = b / c
Problem: an inspector rejects 10 % of the meters as defective . how many will he examine to reject 15 ?
Options: a ) a ) 100 , b ) b ) 150 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 15 ( 10 / 100 ) x = 15 x = ( 15 * 100 * ) / 10 = 150 answer is b"
Answer: b
Python program:
a = 15 * 100
b = a / 10
Problem: the sale price sarees listed for rs . 400 after successive discount is 25 % and 20 % is ?
Options: a ) 297 , b ) 879 , c ) 342 , d ) 240 , e ) 269
Rationale: "400 * ( 75 / 100 ) * ( 80 / 100 ) = 240 answer : d"
Answer: d
Python program:
a = 400 * 25
b = a / 100
c = 400 - b
d = 400 * 25
e = d / 100
f = 400 - e
g = f * 20
h = g / 100
i = c - h
Problem: two trains of length 120 m and 210 m are 80 m apart . they start moving towards each other on parallel tracks , at speeds 69 kmph and 82 kmph . after how much time will the trains meet ?
Options: a ) 15 / 10 , b ) 19 / 10 , c ) 20 / 19 , d ) 16 / 10 , e ) 27 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 69 + 82 ) * 5 / 18 = 41.9 mps . the time required = d / s = 80 / 41.9 = 19 / 10 sec . answer : b"
Answer: b
Python program:
a = 69 + 82 
b = a * const_0_2778
c = 80 / b
Problem: a shopkeeper sold 10 articles at the cost price of 8 articles . then find the profit % or lost % ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 30 % , e ) 20 %
Rationale: "here 10 articles selling price = 8 articles cost price so the difference = 10 - 8 = 2 % of profit = 2 * 100 / 10 = 20 % correct option is e"
Answer: e
Python program:
a = 8 - 10
b = a / 10
c = b * 100
Problem: a and b can finish a work in 16 days while a alone can do the same work in 24 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 16 – 1 / 24 = 1 / 48 = > 48 days answer : b"
Answer: b
Python program:
a = 1/(16)
b = 1/(24)
c = a - b
d = 1/(c)
Problem: . 009 / ? = . 01
Options: a ) . 9 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them
Rationale: "let . 009 / x = . 01 ; then x = . 009 / . 01 = . 9 / 1 = . 9 answer is a"
Answer: a
Python program:
a = 9 / 1000
b = 1 / 100
c = a / b
Problem: a can run a kilometer race in 4 1 / 2 min while b can run same race in 5 min . how many meters start can a give b in a kilometer race , so that the race mat end in a dead heat ?
Options: a ) 200 m , b ) 700 m , c ) 800 m , d ) 100 metre , e ) 1004 m
Rationale: explanation : a can give b ( 5 min - 4 1 / 2 min ) = 30 sec start . the distance covered by b in 5 min = 1000 m . distance covered in 30 sec = ( 1000 * 30 ) / 300 = 100 m . a can give b 100 m start . answer : d
Answer: d
Python program:
a = 1 / 2
b = 4 + a 
c = b / 5
d = 1 - c
e = d * 1000