euclaise/mathqa_programs huggingface dataset:
Problem: a car travels uphill at 30 km / hr and downhill at 50 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 50 = 5 / 5 ; avg speed = 150 / ( 10 / 3 + 5 / 5 ) = 35 kmph answer : d"
Answer: d
Python program:
a = 100 + 50 
b = 100 / 30
c = 50 / 50
d = b + c 
e = a / d
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 7 ] ] ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 67 , e ) 25
Rationale: "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 7 ] ] = 7 ^ 2 + 2 * 7 + 4 = 67 . option d"
Answer: d
Python program:
a = 2 ** 2
b = 2 * 2
c = a + b 
d = c + 4
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 540 oranges . how many oranges he had originally ?
Options: a ) 700 , b ) 900 , c ) 720 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 540 100 % of oranges = ( 540 × 100 ) / 6 = 900 total oranges = 900 answer : b"
Answer: b
Python program:
a = 40 / 100
b = 540 * a
c = 540 + b
Problem: if | 5 x - 15 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 6 , d ) - 3 , e ) 4
Rationale: "| 5 x - 15 | = 100 5 x - 15 = 100 or 5 x - 15 = - 100 5 x = 115 or 5 x = - 85 x = 23 or x = - 17 sum = 23 - 17 = 6 answer is c"
Answer: c
Python program:
a = 100 - 15
b = 100 + 15 
c = a - b
d = c - 15
Problem: the speed of a boat in still water is 25 kmph . if it can travel 10 km upstream in 1 hr , what time it would take to travel the same distance downstream ?
Options: a ) 26 minutes , b ) 23 minutes , c ) 15 minutes , d ) 19 minutes , e ) 28 minutes
Rationale: speed of boat in still water = 25 km / hr speed upstream = 10 ⁄ 1 = 10 km / hr speed of the stream = ( 25 - 10 ) = 15 km / hr speed downstream = ( 25 + 15 ) = 40 km / hr time taken to travel 10 km downstream = 10 / 40 hours = ( 10 × 60 ) / 40 = 15 minutes answer is c
Answer: c
Python program:
a = 25 - 10
Problem: a train 125 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 55 , d ) 26 , e ) 29
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 10 ) km / hr . x - 10 = 45 = = > x = 55 km / hr answer : c"
Answer: c
Python program:
a = 10 * const_0_2778
b = a * 10
c = 125 - b
d = c / 10
e = d / const_0_2778
Problem: on an order of 5 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 15 % , b ) 16 1 / 6 % , c ) 16 2 / 3 % , d ) 20 % , e ) 30 %
Rationale: "clearly , the retailer gets 1 dozen out of 6 dozens free . equivalent discount = 1 / 6 * 100 = 16 2 / 3 % . answer : c"
Answer: c
Python program:
a = 5 / 4
b = a * 100
c = 100 - b
Problem: seller selling an apple for rs . 17 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 18 , d ) 19 , e ) 20
Rationale: "sp = 17 loss = cp 18 loss = cp − sp = cp − 17 ⇒ cp 18 = cp − 17 ⇒ 17 cp 18 = 17 ⇒ cp 18 = 1 ⇒ cp = 18 c"
Answer: c
Python program:
a = 17 + 1
Problem: there are two positive numbers in the ratio 7 : 11 . if the larger number exceeds the smaller by 16 , then find the smaller number ?
Options: a ) 25 , b ) 26 , c ) 30 , d ) 24 , e ) 28
Rationale: let the two positive numbers be 7 x and 11 x respectively . 11 x - 7 x = 16 4 x = 16 = > x = 4 = > smaller number = 7 x = 28 . answer : e
Answer: e
Python program:
a = 16 * 7
b = a / 4
Problem: what is rate of interest if principal . amount be 400 , simple interest 120 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 12 , e ) 15
Rationale: "s . i = ( p * r * t ) / 100 120 = 800 r / 100 r = 120 / 8 = 15 % answer e"
Answer: e
Python program:
a = 400 * 2
b = 120 / a
c = b * 100
Problem: a fair coin is tossed 15 times . what is the probability of getting more heads than tails in 15 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Python program:
a = math.comb(15, 2)
b = math.comb(15, 3)
c = a + b 
d = math.comb(15, 4)
e = c + d 
f = math.comb(15, 15)
g = e + f 
h = 2 ** 15
i = g / h
Problem: a bowler can take max . 3 wickets in a over . if he bowls 6 overs in an innings , how many maximum wickets can he take ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 7 , e ) 10
Rationale: 10 because after 10 wickets , the innings is complete . answer : e
Answer: e
Python program:
a = 6 * 3
b = a - 6
c = b - 2
Problem: if the personal income tax rate is lowered from 42 % to 32 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 42400 ?
Options: a ) $ 3500 , b ) $ 5000 , c ) $ 4240 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 42 - 32 ) % of 42400 = 4240 . answer : c"
Answer: c
Python program:
a = 42400 / 100
b = 42 - 32
c = a * b
Problem: ( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( ? ) 1 / 2 ?
Options: a ) 256 , b ) 4 , c ) √ 2 , d ) 16 , e ) none
Rationale: answer ? ) 1 / 2 = ( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( 64 ) 1 / 3 + ( 144 ) 1 / 2 ∴ ? = ( 4 + 12 ) 2 = 256 correct option : a
Answer: a
Python program:
a = 5568 / 87
b = 1 / 3
c = a ** b
d = 72 * 2
e = 1 / 2
f = d ** e
g = c + f 
h = g ** 2
Problem: at the end of the first quarter , the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 50 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %
Rationale: say price at the beginning of year = 100 end of 1 st quarter = 100 + 20 = 120 end of 2 nd quarter = 100 + 50 = 150 percentage increase between 1 st & 2 nd quarter = 150 − 120 / 120 ∗ 100 = 25 answer = b
Answer: b
Python program:
a = 100 + 50 
b = 100 + 20 
c = a / b
d = c - 1
e = d * 100
Problem: find the 25 % of rs . 800 .
Options: a ) s . 50 , b ) s . 200 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 800 = > 25 / 100 * 800 = rs . 200 answer : b"
Answer: b
Python program:
a = 25 / 100
b = 800 * a
Problem: what is the 50 th digit to the right of the decimal point in the decimal form of 48 / 88 ?
Options: a ) 6 , b ) 7 , c ) 9 , d ) 11 , e ) 4
Rationale: "we have to use some long division . this long division allows us to get 48 / 88 in decimal form , which is 0.545454 … where “ 54 ” is repeating . we can see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 5 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 4 . in other words , each odd - positioned digit is a 5 , and each even - positioned digit is a 4 . then about the 50 digit to the right of the decimal point and we see that 50 is even , we know that the 50 th digit is a 4 . answer e ."
Answer: e
Python program:
a = 48 / 88
Problem: a crate measures 5 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 5 for the surface 8 * 12 face . volume = 125 pi answer c"
Answer: c
Python program:
a = 8 * 12
b = a * 5
c = b / 12
d = c / 8
Problem: a pharmaceutical company received $ 4 million in royalties on the first $ 50 million in sales of and then $ 12 million in royalties on the next $ 170 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 50 million in sales to the next $ 170 million in sales ?
Options: a ) 12 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "( 12 / 170 ) / ( 4 / 50 ) = 15 / 17 = 88 % it means that 12 / 170 represents only 88 % . therefore a decrease of 12 % . answer a"
Answer: a
Python program:
a = 4 / 50
b = a * 100
Problem: what is the minimum number of square tiles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm ?
Options: a ) 187 , b ) 180 , c ) 190 , d ) 195 , e ) 197
Rationale: length = width = = > square = 5 m 78 cm and 3 m 74 5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm hcf of 578 and 374 = 34 square is 34 = 578 * 374 / 34 * 34 = = 17 * 11 = 187 answer a
Answer: a
Python program:
a = 100 * 5
b = a + 78 
c = 4 * 4
d = c * 2
e = d + 2 
f = b / e
g = 100 * 3
h = g + 74 
i = 4 * 4
j = i * 2
k = j + 2 
l = h / k
m = f * l
Problem: three rugs have a combined area of 204 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 204 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 20 . answer : b ."
Answer: b
Python program:
a = 204 - 140
b = a - 24
c = b / 2
Problem: there is a train and car . the ratio between the speed of a train & a car is 24 : 19 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 2 / 3 rd of the speed of the train . how many kilometers will the car cover in 4 hours ?
Options: a ) 276 , b ) 290 , c ) 304 , d ) 318 , e ) 332
Rationale: "the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 3 ) / 2 = 96 km / hr the speed of the car is 96 / 24 * 19 = 76 km / hr the distance covered by the car in 4 hours is 76 × 4 = 304 km the answer is c ."
Answer: c
Python program:
a = 320 / 5
b = a * 5
c = b / 2
d = c * 19
e = d / 24
f = e * 4
Problem: in a group of 100 cars , 37 cars do not have air conditioning . if at least 41 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 45 , b ) 47 , c ) 59 , d ) 51 , e ) 53
Rationale: "lets assume ac = 63 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 41 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 41 . . we have to assign atleast 4 tocars with ac and racing stripes . hence ac = 63 - 4 = 59 . the answer is"
Answer: c
Python program:
a = 100 - 41
Problem: a man goes downstream at 12 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 2 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 12 - 8 ) kmph = 2 kmph . correct option a"
Answer: a
Python program:
a = 12 - 8
b = a / 2
Problem: micheal and adam can do together a piece of work in 20 days . after they have worked together for 18 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 25 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 18 = 9 / 10 left work = 1 - 9 / 10 = 1 / 10 adam completes 1 / 10 work in 10 day so he took 10 * 10 = 100 days to complete the left work alone . thus the rate of adam is 1 / 100 rate of micheal = 1 / 20 - 1 / 100 = 1 / 25 thus micheal takes 25 days to complete the whole work . ans . a ."
Answer: a
Python program:
a = 1/(20)
b = 1/(20)
c = b * 18
d = 1 - c
e = 1/(d)
f = e * 10
g = 1/(f)
h = a - g
i = 1/(h)
Problem: how many 7 in between 1 to 80 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78,79 18 7 ' s between 1 to 80 answer : a"
Answer: a
Python program:
a = 7 * 1
b = 80 / a
Problem: a batsman in his 12 th innings makes a score of 115 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 82 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 4 ) + 115 ∴ x = 82 answer d"
Answer: d
Python program:
a = 12 * 3
b = 115 - a
c = b + 3
Problem: the ratio 3 : 5 expressed as a percent equals
Options: a ) 60 % , b ) 40 % , c ) 80 % , d ) 125 % , e ) none
Rationale: "solution 3 : 5 = 3 / 5 = ( 3 / 5 x 100 ) % . = 60 % . answer a"
Answer: a
Python program:
a = 3 / 5
b = a * 100
Problem: when positive integer n is divided by positive integer j , the remainder is 28 . if n / j = 142.07 , what is value of j ?
Options: a ) 300 , b ) 375 , c ) 400 , d ) 460 , e ) 500
Rationale: when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 142.07 here 142 is the quotient . given that remainder = 28 so , 142.07 = 142 + 28 / j so , j = 400 answer - c
Answer: c
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 142 - 7
e = 28 / d
Problem: find the annual dividend received by nishita from 1200 preferred shares and 3000 common shares both of par value rs . 50 each if the dividend paid on preferred shares is 10 % and semi - annual dividend of 3 ½ % is declared on common shares .
Options: a ) 16000 , b ) 16500 , c ) 17000 , d ) 17500 , e ) 18000
Rationale: total number of preferred shares = 1200 face value = rs . 50 dividend paid on preferred shares is 10 % dividend per share = 50 × 10 / 100 = rs . 5 total dividend = 1200 × 5 = 6000 total number of common shares = 3000 face value = rs . 50 semi - annual dividend of 3 ½ % is declared on common shares . semi - annual dividend per share = 50 × 7 / 2 × 100 = rs . 74 total semi - annual dividend = 7 / 4 × 3000 = rs . 5250 annual dividend = rs . 5250 × 2 = rs . 10500 total dividend on all all shares ( preferred and common ) = 6000 + 10500 = rs . 16500 answer is b .
Answer: b
Python program:
a = 1200 * 50
b = a * 10
c = b / 100
d = 3000 * 50
e = 1 / 2
f = e + 3 
g = d * f
h = g / 100
i = c + h 
j = 3000 * 50
k = 1 / 2
l = k + 3 
m = j * l
n = m / 100
o = i + n
Problem: length of a rectangular plot is 32 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 56 m , b ) 66 m , c ) 76 m , d ) 86 m , e ) 96 m
Rationale: "let breadth = x metres . then , length = ( x + 32 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 32 ) + x ] = 200 2 x + 32 = 100 2 x = 68 x = 34 . hence , length = x + 32 = 66 m b"
Answer: b
Python program:
a = 5300 / 26
b = 2 * 32
c = a + b 
d = c / 4
Problem: the distance from city a to city b is 120 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: the time it takes bob to drive to city b is 120 / 40 = 3 hours . alice needs to take less than 2.5 hours for the trip . alice needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour . the answer is b .
Answer: b
Python program:
a = 120 / 40
b = 30 / const_60
c = a - b
d = 120 / c
Problem: solve : 12.05 * 5.4 + 0.6
Options: a ) 108.45 , b ) 110.45 , c ) 106.45 , d ) 109.45 , e ) none of them
Rationale: = 12.05 * ( 5.4 / 0.6 ) = ( 12.05 * 9 ) = 108.45 answer is a .
Answer: a
Python program:
a = 5 / 4
b = 12 * 5
Problem: an investment yields an interest payment of $ 225 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 30,000 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 35,100
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 225 = > p = ( 225 * 4 * 10 ^ 2 ) / 3 = 75 * 4 * 10 ^ 2 = 300 * 10 ^ 2 = 30000 answer a"
Answer: a
Python program:
a = 3 * 4
b = 9 / a
c = 225 / b
d = c * 100
Problem: list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median q of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals
Options: a ) 5 , b ) 7 , c ) 8 , d ) q = 9 , e ) 10
Rationale: mode of list ii = 3 median q of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d )
Answer: d
Python program:
a = 6 + 3
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 135 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 351 , c ) 452 , d ) 416 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 135 x = 27 total number of students = 13 x = 13 * 27 = 351 answer is b"
Answer: b
Python program:
a = 8 / 5
b = a * 135
c = b + 135
Problem: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 18 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 887 , d ) 720 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 18 < = > ( 25 / 10 * 1 / 100 * x ) = 18 < = > x = 720 . answer : d"
Answer: d
Python program:
a = 2 / 5
b = 18 / a
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 19 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 = > 45 - [ 28 - { 37 - 15 + * } ] = 58 45 - [ 28 - 37 + 15 - * ] = 58 = > 45 [ 43 - 37 - * ] = 58 45 - [ 6 - * ] = 58 = > 45 - 6 + * = 58 39 + * = 58 = > * = 58 - 39 = 19 answer : c"
Answer: c
Python program:
a = 28 - 37
b = a + 15 
c = 45 - b
d = 58 - c
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 17 , b ) 19 , c ) 17 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 14 * x = 1056 = > x = 12 answer : d"
Answer: d
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 1056 / g
Problem: a man walked a certain distance south and then the same distance plus 7 km due west . he is now 13 km from his starting point . what are the distances south and west that he walked ?
Options: a ) 512 , b ) 612 , c ) 712 , d ) 513 , e ) 613
Rationale: if a man walked distance ( in km ) ' x ' towards south & then ' x + 7 ' towards west . distance from starting point = hypotenuse of a right triangle with sides x & ( x + 7 ) so 13 ^ 2 = x ^ 2 + ( x + 7 ) ^ 2 x ^ 2 + 7 x - 60 = 0 or ( x + 12 ) ( x - 5 ) = 0 , so x = 5 distance towards west = x + 7 = 5 + 7 = 12 km . answer : a
Answer: a
Python program:
a = 13 * 7
b = a * 3
c = b * 2
d = 10 * 4
e = c - d
Problem: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many r applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) r = 20 - 15 = 5 answer : a"
Answer: a
Python program:
a = 10 + 15 
b = 40 - a
c = 20 - b
Problem: a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 12 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 150 , c ) 280 , d ) 300 , e ) 420
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 5 * 12 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( b )"
Answer: b
Python program:
a = 25 * 42
b = a * 60
c = 7 * 12
d = c * 5
e = b / d
Problem: if 25 % of x is 15 less than 15 % of 1600 , then x is ?
Options: a ) 872 , b ) 738 , c ) 900 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 15 % of 1600 = 15 / 100 * 1600 = 240 given that , x / 4 = 240 - 15 = > x / 4 = 225 = > x = 900 . answer : c"
Answer: c
Python program:
a = 15 / 100
b = 1600 * a
c = b - 15
d = 25 / 100
e = c / d
Problem: 30 ladies and 60 gentlemen are present at a party . there are 23 couples among them . if a lady and a gentleman is selected at random , what is the probability that they will be a couple ?
Options: a ) 1 / 200 , b ) 1 / 100 , c ) 1 / 50 , d ) 1 / 40 , e ) 23 / 1800
Rationale: in how many ways we can select a woman and a man from 30 women and 60 men ? in 30 * 60 = 1800 ways . we have a total of 23 couples so , the probability of selecting a couple is 23 / 1800 = 23 / 1800 . ans - e
Answer: e
Python program:
a = 30 * 60
b = 23 / a
Problem: in a class , 30 % of the students speaks truth , 20 % speaks lie and 10 % speaks both . if a student is selected at random , what is the probability that he has speak truth or lie ?
Options: a ) 1 / 4 , b ) 2 / 3 , c ) 3 / 5 , d ) 2 / 5 , e ) 2 / 7
Rationale: d ) 2 / 5
Answer: d
Python program:
a = 5 * 5
b = a * 4
c = 10 / b
d = 5 * 5
e = d * 4
f = 30 / e
g = 5 * 5
h = g * 4
i = 20 / h
j = f + i 
k = c + j 
l = 1 - k
Problem: the milk level in a rectangular box measuring 50 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 4687.5 , e ) 5635.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 50 * 25 * 1 / 2 = 625 feet ^ 3 of milk must be removed , which equals to 625 * 7.5 = 4687.5 gallons . answer : d ."
Answer: d
Python program:
a = 50 * 25
b = 1 / 2
c = a * b
d = c * 7
Problem: in the new budget , the price of kerosene oil rose by 25 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) none of them
Rationale: reduction in consumption = [ ( ( r / ( 100 + r ) ) * 100 ] % = [ ( 25 / 125 ) * 100 ] % = 20 % . answer is b .
Answer: b
Python program:
a = 25 - 4
b = a - 1