euclaise/mathqa_programs huggingface dataset:
Problem: a birthday child reaches into a bag filled with toys ( 1 yo - yo , 1 ball , 1 whistle , and 1 box crayons ) . if the child randomly picks 3 toys , what is the probability the child will pick the yo - yo and a ball as two of the 3 toys ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 2 / 5
Rationale: combination formula : ncr = n ! / ( r ! ( n - r ) ! ) , where n is the population / set , and r is the sample / subset . total number possible = 4 c 3 - 4 ! / ( 3 ! ( 4 - 3 ) ! ) = 4 number yo - yo possible = 1 c 1 = 1 number ball possible = 1 c 1 = 1 number other possible = 2 c 1 = 2 probability formula : p ( a ) = ( number favorable outcomes ) / ( total number possible outcomes ) p ( yb ) = ( 1 c 1 ) ( 1 c 1 ) ( 2 c 1 ) / 4 c 3 = 2 / 4 = 1 / 2 answer : b
Answer: b
Python program:
a = 1 / 2
Problem: 3 investors , a , b , and c , divide the profits from a business enterprise in the ratio of 5 : 7 : 8 , respectively . if investor a earned $ 2500 , how much money did investors b and c earn in total ?
Options: a ) $ 4,000 , b ) $ 4,900 , c ) $ 7,500 , d ) $ 9,500 , e ) $ 10,500
Rationale: let profit for a = 5 x profit for b = 7 x profit for c = 8 x investor a earned = 2500 5 x = 2500 = > x = 500 total profit for b and c = 7 x + 8 x = 15 x therefore , 15 x = 15 * 500 = 7,500 answer c
Answer: c
Python program:
a = 5 + 7 
b = a + 8 
c = 7 / b
d = 5 + 7 
e = d + 8 
f = 5 / e
g = 2500 / f
h = c * g
i = 5 + 7 
j = i + 8 
k = 8 / j
l = 5 + 7 
m = l + 8 
n = 5 / m
o = 2500 / n
p = k * o
q = h + p 
r = q / 1000
s = r / 2
t = s + const_0_25
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 580 ( before payroll deductions ) ?
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 580 x = 80 / 0.16 = 500 the answer is b ."
Answer: b
Python program:
a = 12 * 50
b = 580 - a
c = b / 0
Problem: find the least number of complete years in which a sum of money put out at 15 % compound interest will be more than double of itself ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "5 years answer : a"
Answer: a
Python program:
a = math.log(2)
b = 15 / 100
c = 1 + b 
d = math.log(c)
e = a / d
f = e + 1 
g = math.floor(f)
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.3 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.95 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: let the fixed charge of jim â € ™ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 3 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 3 = 2.25 + 9 * . 3 = 4.95 $ answer b
Answer: b
Python program:
a = 2 / 5
b = 3 / 6
c = b * 0
d = c + 2
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 15 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 10 % . if ron imported a $ 15,000 imported car and ended up paying $ 1800 in taxes , what is the first tier ' s price level ?
Options: a ) $ 7000 , b ) $ 6500 , c ) $ 6050 , d ) $ 6000 , e ) $ 6100
Rationale: "let t be the tier price , p be total price = 15000 per the given conditions : 0.15 t + 0.10 ( p - t ) = 1800 0.15 t + 0.10 * 15000 - 0.10 t = 1800 0.05 t + 1500 = 1800 0.05 t = 1800 - 1500 = 300 t = 300 / 0.05 = 6000 answer d"
Answer: d
Python program:
a = 2 * 3
b = 3 * a
c = b * 1000
d = 10 / 100
e = c * d
f = 1800 - e
g = 15 / 100
h = 10 / 100
i = g - h
j = f / i
Problem: in what time will a train 90 meters long cross an electric pole , if its speed is 124 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2.6 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 124 * ( 5 / 18 ) = 34 m / sec time = distance / speed = 90 / 34 = 2.6 seconds option d"
Answer: d
Python program:
a = 124 * const_0_2778
b = 90 / a
Problem: what is the rate percent when the simple interest on rs . 600 amount to rs . 160 in 4 years ?
Options: a ) 6.66 % , b ) 7.66 % , c ) 6.06 % , d ) 6.16 % , e ) 8.66 %
Rationale: "160 = ( 600 * 4 * r ) / 100 r = 6.66 % answer : a"
Answer: a
Python program:
a = 100 * 160
b = 600 * 4
c = a / b
Problem: find two integers , neither of which ends in a zero , and whose product is exactly 10 , 000,000
Options: a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 128 and 78,125
Rationale: "10 , 000,000 = 10 ^ 7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 7 ) x ( 5 ^ 7 ) = 128 x 78125 so the numbers are 128 and 78,125 answer : e"
Answer: e
Python program:
a = 100 * 100
b = a * 100
c = 100 * 100
d = c * 100
e = 3 * 12
f = e - 4
g = d / f
h = b / g
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 3000 as profit , what is their total profit ?
Options: a ) 21000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 3000 = > total profit = 3000 * 7 = 21000 . answer : option a"
Answer: a
Python program:
a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c 
e = a / d
f = 3000 / e
Problem: a person crosses a 1080 m long street in 10 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 6.4 , c ) 4.8 , d ) 5.4 , e ) 5.5
Rationale: "speed = 1080 / ( 10 x 60 ) m / sec = 1.8 m / sec . converting m / sec to km / hr = 1.8 x ( 18 / 5 ) km / hr = 6.4 km / hr . answer : b"
Answer: b
Python program:
a = 1080 / 1000
b = 10 * const_60
c = b / 3600
d = a / c
Problem: exactly 12 % of the reporters for a certain wire service cover local politics in country x . if 40 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 80 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 12 reporters cover local politics . now , as 40 % of the reporters who cover all politics do not cover local politics then the rest 60 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 60 % of them equal to 12 ( # of reporters who cover local politics ) : 0.6 x = 12 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."
Answer: d
Python program:
a = 100 - 40
b = 12 / a
c = 1 - b
d = c * 100
Problem: a man can row his boat with the stream at 6 km / h and against the stream in 3 km / h . the man ' s rate is ?
Options: a ) 1.5 kmph , b ) 3 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 6 us = 3 s = ? s = ( 6 - 3 ) / 2 = 1.5 kmph answer : a"
Answer: a
Python program:
a = 6 - 3
b = a / 2
Problem: ronald and elan are working on an assignment . ronald takes 6 hours to type 32 pages on a computer , while elan takes 5 hours to type 40 pages . how much time will they take , working together on two different computers to type an assignment of 110 pages ?
Options: a ) 3 hours , b ) 6 hours , c ) 4 hours , d ) 8 hours , e ) 10 hours
Rationale: number of pages typed by ronald in one hour = 32 / 6 = 16 / 3 number of pages typed by elan in one hour = 40 / 5 = 8 number of pages typed by both in one hour = ( ( 16 / 3 ) + 8 ) = 40 / 3 therefore , time taken by both to type 110 pages = 110 x 3 / 40 = 8 hours . answer : d
Answer: d
Python program:
a = 32 / 6
b = 40 / 5
c = a + b 
d = 110 / c
Problem: the difference between a number and its two - fifth is 510 . what is 50 % of that number ?
Options: a ) 426 , b ) 425 , c ) 427 , d ) 428 , e ) 429
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 50 % of 850 = 425 . answer : b"
Answer: b
Python program:
a = 4 + 1 
b = 510 * a
c = 1 + 2 
d = b / c
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 46 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 54 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 45 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.46 m = = > revenue = price x quantity = 0.54 ( m + w ) = = > profit = 0.54 ( m + w ) - 0.46 m = 0.2 * ( 0.46 m ) [ 20 % of cost ] = = > 0.54 m + 0.54 w - 0.46 m = 0.092 m = = > 0.012 m = 0.54 w = = > m / w = 0.54 / 0.012 = 45 - - or - - w / m = 1 / 45 d is correct ."
Answer: d
Python program:
a = 20 / 2
b = 1 / a
Problem: a train 441 m long can cross an electric pole in 21 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 76 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: length = speed * time speed = l / t s = 441 / 21 s = 21 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 76 kmph answer : c
Answer: c
Python program:
a = 441 / 1000
b = 21 / 3600
c = a / b
Problem: a can run 4 times as fast as b and gives b a start of 75 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 100 m , d ) 65 m , e ) 75 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 75 m he gains 75 * ( 4 / 3 ) i . e 100 m answer : c"
Answer: c
Python program:
a = 75 / 4
b = 4 - 1
c = a / b
d = 4 * c
e = d + 75
Problem: when the price of an article was reduced by 15 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 44 % increase , b ) 44 % decrease , c ) 53 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: if n items are sold for $ p each , revenue is $ np . if we reduce the price by 15 % , the new price is 0.85 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.85 p ) ( 1.8 n ) = 1.53 np , which is 1.53 times the old revenue , so is 53 % greater . answer : c
Answer: c
Python program:
a = 80 + 100 
b = 100 - 15
c = a * b
d = c / 100
e = d - 100
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 64 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 82 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 64 % is one st . dev , then on either side of m we have 64 / 2 = 32 % . so , 32 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 32 = 82 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 82 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it d"
Answer: d
Python program:
a = 100 - 64
b = a / 2
c = 100 - b
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 27 sec . the length of each train is ?
Options: a ) 50 , b ) 37.5 , c ) 27 , d ) 28 , e ) 21
Rationale: let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 27 = 25 / 9 = > x = 37.5 . answer : b
Answer: b
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = 27 * c
e = d / 2
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 7 more than 1 / 4 of the fine and peter paid $ 7 less than 1 / 3 of the fine , leaving pay $ 12 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 65 , b ) $ 55 , c ) $ 50 , d ) $ 60 , e ) $ 45
Rationale: call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 7 ] + [ ( 1 / 3 ) f – 7 ] + [ ( 1 / 2 ) f – 12 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 12 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 144 12 f = 13 f – 144 – f = – 144 f = 144 well , if the fine cost $ 144 , then sam paid the part not covered by joe or peter . half the fine is $ 72 , and sam paid $ 12 less than this : $ 60 . answer = d
Answer: d
Python program:
a = 1 / 2
b = 1 / 4
c = 1 / 3
d = b + c 
e = a + d 
f = e * 12
g = f + 12 
h = g * 2
i = h + 10
Problem: if two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "the projectiles travel a total of 999 km per hour . the time to meet is 1998 / 999 = 2 hours = 120 minutes the answer is d ."
Answer: d
Python program:
a = 444 + 555 
b = 1998 / a
c = b * const_60
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5650 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5650 = 21150 exp in % = 100 - 10 = 90 % , 21150 = 90 % saving = 10 % = 21150 x 10 / 90 = rs . 2350 answer : b
Answer: b
Python program:
a = 5000 + 1500 
b = a + 4500 
c = b + 2500 
d = c + 2000 
e = d + 5650 
f = e * 100
g = 100 - 10
h = f / g
i = 5000 + 1500 
j = i + 4500 
k = j + 2500 
l = k + 2000 
m = l + 5650 
n = h - m
Problem: a large box contains 15 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 375 , d ) d ) 450 , e ) e ) 690
Rationale: "the only thing you have to do is a simple multiply we have : 15 * 25 = 375 correct answer is : c ) 375"
Answer: c
Python program:
a = 15 * 25
Problem: an assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72
Rationale: "the time to produce the first 60 cogs is 60 / 90 = 2 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 5 / 3 ) hours = 72 cogs per hour . the answer is e ."
Answer: e
Python program:
a = 60 * 2
b = 60 / 90
c = b + 1 
d = a / c
Problem: there has been successive increases of 25 % and then 15 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 30 % , b ) 50 % , c ) 66.66 % , d ) 15 % , e ) 75 %
Rationale: let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.15 * 1.25 * p = x * p y = x / ( 1.15 * 1.25 ) which is about 0.7 x which is a decrease of about 30 % . the answer is a .
Answer: a
Python program:
a = 100 + 25 
b = 100 + 25 
c = b * 15
d = c / 100
e = a + d 
f = 100 / e
g = 1 - f
h = g * 100
Problem: a train covers a distance of 12 km in 5 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 220 m , e ) 280 m
Rationale: "speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the train = 40 * 6 = 240 m . answer : c"
Answer: c
Python program:
a = 12 / 5
b = a - 6
c = 12 / b
Problem: ab + ba ___ 202 in the addition problem above , a and b represent digits in two different two - digit numbers . what is the sum of a and b ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 20 , e ) 14
Rationale: two ways to do it . . 1 ) straight logic . . only 20 fits in . . d
Answer: d
Python program:
a = 10 + 1 
b = 202 / a
c = b + 2 
d = math.floor(c)
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 29 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 227 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 29 : x = > x = { \ color { blue } \ frac { 29 \ times 1 } { 0.128 } } = > x = 226.56 so time will be approx 227 seconds answer : d"
Answer: d
Python program:
a = 29 / 0
Problem: the sum of three consecutive even numbers is 36 , find the first number ?
Options: a ) 21 , b ) 18 , c ) 12 , d ) 16 , e ) 10
Rationale: "let the first number be n let the second number be n + 2 let the third number be n + 4 n + n + 2 + n + 4 = 36 combine like terms : 3 n + 6 = 36 3 n = 36 - 6 3 n = 30 3 n = 30 n = 10 n + 2 = 12 n + 4 = 16 the first number is 10 answer : e"
Answer: e
Python program:
a = 36 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 36 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 36 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 36 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: 30 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 3 : 4 ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let x be the amount of liquid q to be added . ( 2 / 5 ) * 30 + x = ( 4 / 7 ) * ( 30 + x ) 420 + 35 x = 600 + 20 x 15 x = 180 x = 12 the answer is c ."
Answer: c
Python program:
a = 3 + 4 
b = 30 * 3
c = 3 + 2 
d = b / c
e = a * d
f = e / 3
g = f * 4
h = 3 + 4 
i = g / h
j = 30 * 2
k = 3 + 2 
l = j / k
m = i - l
Problem: . for the fifa world cup , paul the octopus has been predicting the winner of each match with amazing success . it is rumored that in a match between 2 teams a and b , paul picks a with the same probability as a ’ s chances of winning . let ’ s assume such rumors to be true and that in a match between ghana and bolivia ; ghana the stronger team has a probability of 2 / 3 of winning the game . what is the probability that paul will correctly pick the winner of the ghana - bolivia game ?
Options: a ) 59 , b ) 88 , c ) 77 , d ) 26 , e ) 18
Rationale: the probability that paul correctly picks the winner = ( a ' s chances of winning ) x ( pauls picking the winner corectly ) + ( a ' s chances of loosing ) x ( paul picks wrongly ) = 23 × 23 + 13 × 13 = 59 answer : a
Answer: a
Python program:
a = 3 + 2 
b = 10 * a
c = b + 3 
d = c + 3 
e = d + 3
Problem: john has 10 pairs of matched socks . if he loses 5 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 4 , e ) 3
Rationale: because we have to maximize the pair of matched socks , we will remove 2 pairs ( 4 socks ) out of 10 pairs 1 sock from the 3 th pair . thus the no of matching socks pair remaining = 10 - 3 = 7 answer b
Answer: b
Python program:
a = 10 - 3
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 18 } + { 16 } ?
Options: a ) 23 , b ) 20 , c ) 11 , d ) 19 , e ) 2
Rationale: soln : { 18 } + { 16 } = 18 * { 16 } + { 16 } = 19 * { 16 } answer : d
Answer: d
Python program:
a = 18 + 16 
b = a / 2
c = 1 * 2
d = b + c
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 125 billion gallons to 150 billion gallons . if the storm increased the amount of water in the reservoirs to 80 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 9 , b ) 14 , c ) 25 , d ) 30 , e ) 44
Rationale: after the reservoir is filled to 150 gallons the amount of water is at 80 % - which means that 20 % of the reservoir is empty . to figure out what that 20 % is approximate : 150 gallons / 80 percent = x gallons / 20 percent , therefore , x = 37.5 gallons , answer choices a , b , c , d are below 37.5 . we know that the reservoir must be short more than 37.5 gallons , therefore , the only possible choice is e .
Answer: e
Python program:
a = 150 * 100
b = a / 80
c = b / 2
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 50 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 ) 0.5 , 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 + 0.5 * 52 = ~ 45 , so percent of people who are less than 25 years old is 100 - 45 = 55 . answer : b ."
Answer: b
Python program:
a = 40 / 100
b = 100 - 50
c = b / 100
d = a * c
e = 1 - d
Problem: if ( a – b ) is 7 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 7 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 7 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 7 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 7 = ( c – a ) – 3 = > 2 ( a – c ) = 4 = > ( a – c ) = 2 answer : b"
Answer: b
Python program:
a = 7 / 3
Problem: a man is 27 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 25 , c ) 27 , d ) 22 , e ) 91
Rationale: let the son ' s present age be x years . then , man ' s present age = ( x + 27 ) years . ( x + 27 ) + 2 = 2 ( x + 2 ) x + 29 = 2 x + 4 = > x = 25 . answer : b
Answer: b
Python program:
a = 2 * 2
b = a - 2
c = 27 - b
d = 2 - 1
e = c / d
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 65 , b ) 68 , c ) 70 , d ) 77 , e ) 80
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 2 x 60 ) = 30 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 30 x + 20 x + 15 x + 12 x ) = 77 x . for minimum number of pencils x = 1 . the person should have atleast 77 pencils . d )"
Answer: d
Python program:
a = math.lcm(2, 1)
b = math.lcm(a, 1)
c = math.lcm(b, 3)
d = c / 2
e = math.lcm(2, 1)
f = math.lcm(e, 1)
g = math.lcm(f, 3)
h = g / 1
i = d + h 
j = math.lcm(2, 1)
k = math.lcm(j, 1)
l = math.lcm(k, 3)
m = l / 1
n = i + m 
o = math.lcm(2, 1)
p = math.lcm(o, 1)
q = math.lcm(p, 3)
r = q / 3
s = n + r