euclaise/mathqa_programs huggingface dataset:
Problem: two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 70 km more than the other . what is the distance between the two stations ?
Options: a ) 630 km , b ) 540 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 70 km more than the other , 25 x â € “ 20 x = 70 5 x = 70 x = 14 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 14 = 630 km . answer : a"
Answer: a
Python program:
a = 20 + 25 
b = 25 - 20
c = 70 / b
d = a * c
Problem: the average age of 10 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years . find the average age of the women ?
Options: a ) 21 , b ) 32 , c ) 30 , d ) 41 , e ) 37
Rationale: "10 + 12 + 10 * 2 = 42 / 2 = 21 answer : a"
Answer: a
Python program:
a = 10 + 12 
b = 10 * 2
c = a + b 
d = c / 2
Problem: a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 , c receives :
Options: a ) 8400 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 * 12 / 50 ) = rs . 8,400 . answer : a )
Answer: a
Python program:
a = 4000 + 5000 
b = a + 5000 
c = 50000 - b
d = c / 3
e = d / 50000
f = 35000 * e
Problem: due to construction , the speed limit along an 6 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 4 , b ) 8 , c ) 10 , d ) 15 , e ) 24
Rationale: 6 / 35 - 6 / 55 = 6 / 5 * ( 11 - 7 ) / 77 = 6 / 5 * 4 / 77 * 60 min = 6 * 12 * 4 / 77 = 288 / 77 ~ 3.7 answer - a
Answer: a
Python program:
a = 55 + 6 
b = a - 1
c = 6 / 35
d = 6 / 55
e = c - d
f = b * e
g = max(f)
Problem: a , b and c invested rs . 600 , rs . 800 and rs . 1200 respectively , in a partnership business . find the share of b in profit of rs . 900 after a year ?
Options: a ) 276.92 , b ) 267.92 , c ) 266.27 , d ) 900 , e ) 237.8
Rationale: "explanation : 600 : 800 : 1200 3 : 4 : 6 4 / 13 * 900 = 276.92 answer : a"
Answer: a
Python program:
a = 600 + 800 
b = a + 1200 
c = 600 / b
d = c * 900
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 21 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 36 , b ) 42 , c ) 45 , d ) 48 , e ) 51
Rationale: "let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 21 r / 2 = 21 r = 42 the answer is b ."
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = b * 21
d = 1 / 3
e = 1 - d
f = 1 - e
g = c / f
Problem: p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 135 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 92.4 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 385 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 135 days - - > 135 / 250 work done = > 54 % 24 % work left . . . r alone will take 24 % * 385 = 92.4 days answer is ( b )"
Answer: b
Python program:
a = 4 * 50
b = 135 / 100
c = b * 60
d = a - c
Problem: find a number such that when 15 is subtracted from 7 times the number , the result is 10 more than twice the number .
Options: a ) 1 , b ) 4 , c ) 5 , d ) 0 , e ) 3
Rationale: let the number be x . then , 7 x - 15 = 2 x + 10 = > 5 x = 25 = > x = 5 . hence , the required number is 5 . answer is c .
Answer: c
Python program:
a = 15 + 10 
b = 7 - 2
c = a / b
Problem: harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1000 , b ) b ) 1055 , c ) c ) 965 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 45 × 9 = 405 . total cost he has to pay = 560 + 405 = 965 . c )"
Answer: c
Python program:
a = 8 * 70
b = 9 * 45
c = a + b
Problem: the average monthly income of a and b is rs . 4050 . the average monthly income of b and c is rs . 5250 and the average monthly income of a and c is rs . 4200 . what is the monthly income of a ?
Options: a ) 2000 , b ) 2500 , c ) 3000 , d ) 3500 , e ) 4000
Rationale: let monthly income of a = x monthly income of b = y monthly income of c = z x + y = 2 × 4050 . . . . ( equation 1 ) y + z = 2 × 5250 . . . . ( equation 2 ) z + x = 2 × 4200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > x + y + x + z - ( y + z ) = ( 2 × 4050 ) + ( 2 × 4200 ) - ( 2 × 5250 ) = > 2 x = 2 ( 4050 + 4200 - 5250 ) = > x = 3000 i . e . , monthly income of a = 3000 answer : c
Answer: c
Python program:
a = 2 * 4050
b = 2 * 4050
c = 2 * 5250
d = 2 * 4200
e = c - d
f = b + e 
g = f / 2
h = a - g
Problem: a merchant marks his goods up by 40 % and then offers a discount of 15 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 21 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %
Rationale: let the original price be 100 . after 40 % markup , price = 140 after 15 % discount on this marked - up price , price = 140 - ( 15 % of 140 ) = 140 - 21 = 119 final profit = ( ( 119 - 100 ) / 100 ) * 100 = 19 % option e
Answer: e
Python program:
a = 40 + 100 
b = 40 + 100 
c = b * 15
d = c / 100
e = a - d
f = e - 100
Problem: a rectangular grassy plot 100 m . by 70 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 90 paise per sq . metre .
Options: a ) rs . 700 , b ) rs . 708.50 , c ) rs . 732.50 , d ) rs . 742.50 , e ) none of these
Rationale: "explanation : area of the plot = ( 100 x 70 ) m 2 = 7000 m 2 area of the plot excluding the path = [ ( 100 - 5 ) * ( 70 - 5 ) ] m 2 = 6175 m 2 . area of the path = ( 7000 - 6175 ) m 2 = 825 m 2 . cost of gravelling the path = rs . 825 * ( 90 / 100 ) = rs . 742.50 answer : option d"
Answer: d
Python program:
a = 100 * 70
b = 2 * 5
c = 100 - b
d = 2 * 5
e = 70 - d
f = c * e
g = a - f
h = g * 90
i = h / 100
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 4 : 3 and b : c = 4 : 5 . if the total runs scored by all of them are 75 , the runs scored by b are ?
Options: a ) 20.23 , b ) 20.13 , c ) 30.93 , d ) 20.93 , e ) 10.93
Rationale: "a : b = 4 : 3 b : c = 4 : 5 a : b : c = 16 : 12 : 15 12 / 43 * 75 = 20.93 answer : d"
Answer: d
Python program:
a = 4 / 3
b = 5 / 4
c = a + b 
d = c + 1 
e = 75 / d
f = e * 5
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) rs . 15500 , b ) rs . 16500 , c ) rs . 17500 , d ) rs . 18500 , e ) rs . 19500
Rationale: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : b"
Answer: b
Python program:
a = 5 * 5
b = 800 * a
Problem: the ages of 2 persons differ by 38 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 30.5 , b ) 48.5 , c ) 50.4 , d ) 62.6 , e ) 57.6
Rationale: "age of the younger person = x age of the elder person = x + 38 6 ( x - 12 ) = x + 38 - 12 x = 19.6 age of elder person = 19.6 + 38 = 57.6 answer is e"
Answer: e
Python program:
a = 2 * 38
b = 38 - 1
c = a / b
d = c + 38 
e = d - 2
Problem: the product x of two prime numbers is between 15 and 70 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 69
Rationale: option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 69 = 3 * 23 > > answer answer = e
Answer: e
Python program:
a = 2 + 1 
b = 25 - 2
c = a * b
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value r of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "r - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Python program:
a = 2020 / 2020
b = 2020 / 2020
c = 2020 / 2020
d = b + c 
e = a / d
Problem: a candidate got 40 % of the votes polled and he lost to his rival by 5000 votes . how many votes were cast ?
Options: a ) 25000 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 6851
Rationale: "40 % - - - - - - - - - - - l 60 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - 5000 100 % - - - - - - - - - ? = > 25000 answer : a"
Answer: a
Python program:
a = 40 / 100
b = 1 - a
c = 40 / 100
d = b - c
e = 5000 / d
Problem: two employees a and b are paid a total of rs . 560 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 224 , e ) s . 280
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 560 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 560 ⇒ y [ 15 / 10 + 1 ] = 560 ⇒ 25 y / 10 = 560 ⇒ 25 y = 5600 ⇒ y = 5600 / 25 = rs . 224 d )"
Answer: d
Python program:
a = 150 / 100
b = a + 1 
c = 560 / b
Problem: what is the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "cyclicity of 7 is 4 - - > 7 , 9 , 3 , 1 cyclicity of 3 is 4 - - > 3 , 9 , 7 , 1 11 raised to any positive power has a units digit 1 17 ^ 83 × 13 ^ 82 × 11 ^ 87 = units digit of 3 * 9 * 1 = 7 answer : d"
Answer: d
Python program:
a = math.factorial(17)
b = math.factorial(83)
c = a * b
d = math.factorial(17)
e = math.factorial(82)
f = d * e
g = c + f 
h = g / 17
Problem: find the lowest common multiple of 10 , 14 and 20 .
Options: a ) 360 , b ) 420 , c ) 510 , d ) 320 , e ) 140
Rationale: "lcm = 2 * 2 * 5 * 7 = 140 . answer is e"
Answer: e
Python program:
a = math.lcm(10, 14)
b = math.lcm(a, 20)
Problem: 3034 - ( 1002 / 200.4 ) = ?
Options: a ) 2984 , b ) 3029 , c ) 2982 , d ) 2981 , e ) none of these
Rationale: "3034 - 5 = 3029 answer : b"
Answer: b
Python program:
a = 1002 / 200
b = 3034 - a
Problem: if 2 x = 3 y = 10 , then 6 xy = ?
Options: a ) 100 , b ) 200 , c ) 120 , d ) 40 , e ) 20
Rationale: "2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 6 xy = 6 * 5 * 10 / 3 = 100 answer : a ."
Answer: a
Python program:
a = 2 * 100
b = a / 2
c = b - 2
d = 2 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 6 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 160 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 160 - x ) = 8000 × 1000 = > ( 160 - x ) = 8000 × 1000 / 320 = 100 = > x = 60 cm = 6 dm . answer : b
Answer: b
Python program:
a = 3 * 3
b = a * 1
c = 8000 / 1000
d = b - c
Problem: the length of minute hand of a clock is 5.5 cm . what is the area covered by this in 10 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 19.27 , e ) 15.83
Rationale: "area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.5 ^ 2 ) * ( 60 / 360 ) = 15.83 cm ^ 2 answer : e"
Answer: e
Python program:
a = 2 * 10
b = a + 2 
c = 3 + 4 
d = b / c
e = 5 * 5
f = 1 * const_60
g = 100 * const_3_6
h = f / g
i = e * h
j = d * i
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 290 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 180 , b ) 184 , c ) 188 , d ) 192 , e ) 196
Rationale: "j + k = 290 and so k = 290 - j j - 8 = 2 k j - 8 = 2 ( 290 - j ) 3 j = 588 j = 196 the answer is e ."
Answer: e
Python program:
a = 290 - 8
b = a / 3
c = b * 2
d = c + 8
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 80 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 3 hours to travel 240 km , so c leaves 5 hours after a . the answer is d ."
Answer: d
Python program:
a = 40 - 30
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent x of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march x = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Python program:
a = 40 / 100
b = 25 / 100
c = 40 / 100
d = b * c
e = a - d
f = 25 / 100
g = 40 / 100
h = f * g
i = 1 - h
j = e / i
k = j * 100
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 16 th highest price and the 23 rd lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "there were 15 items sold at a higher price than the radio and 22 items sold at a lower price than the radio . including the radio , there were 15 + 22 + 1 = 38 items sold . the answer is d ."
Answer: d
Python program:
a = 23 + 16 
b = a - 1
Problem: one hour after yolanda started walking from x to y , a distance of 52 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 28 , b ) 23 , c ) 22 , d ) 21 , e ) 19.5
Rationale: "when b started walking y already has covered 3 miles out of 52 , hence the distance at that time between them was 52 - 3 = 49 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 49 / 7 = 7 hours . in 6 hours b walked 7 * 4 = 28 miles . answer : a ."
Answer: a
Python program:
a = 52 - 3
b = 3 + 4 
c = a / b
d = c * 4
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 13 of money ?
Options: a ) 1300 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 13 ( 100 / 10 ) 2 = > p = 1300 answer : a"
Answer: a
Python program:
a = 10 * 2
b = 13 / a
c = b * 100
d = 10 * 2
e = c * d
Problem: 30 men can do a work in 40 days . when should 10 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 10 days , c ) 55 days , d ) 44 days , e ) 20 days
Rationale: "total work to be done = 30 * 40 = 1200 let 10 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 10 * 40 ) = 1200 40 p = 800 = > p = 20 days answer : e"
Answer: e
Python program:
a = 30 * 40
b = 40 * 10
c = a - b
d = c / 40
Problem: two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 120 + 120 ) / 20 = 12 sec . answer : b"
Answer: b
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: jill ' s favorite number is even and has some repeating prime factors . john is guessing jills favorite number , and the only hint she gives is that 7 is a prime factor . what is johns best guess ?
Options: a ) 84 , b ) 105 , c ) 54 , d ) 42 , e ) 70
Rationale: a 84 = 2 * 2 * 2 * 7 b 105 is odd c 54 = 2 * 3 * 3 d 42 = 2 * 3 * 7 e 70 = 2 * 5 * 7 the answer must meet three criteria : odd , have repeating prime factors , and 7 is a prime factor . a is the only answer that meets all criteria
Answer: a
Python program:
a = 2 ** 2
b = 7 * 3
c = a * b
Problem: kamal obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 65 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 75 . answer d"
Answer: d
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 1 + 4 
f = d / e
Problem: find the number of factors of 180 that are in the form ( 4 * k + 2 ) , where k is a non - negative integer ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: make sure to follow posting guidelines ( link in my signatures ) . title of the thread must mention the first few words of the question itself . as for the question , the most straightforward way is to list out the factors ( this is fine for this question as 180 is a relatively small number ) . number of factors of 180 ( = 2 ^ 2 * 3 ^ 2 * 5 ) = 18 . so listing the factors gives us : 1 , 180 2 , 90 3 , 60 4 , 45 5 , 36 6 , 30 9 , 20 10 , 18 12 , 15 as the question asks us about the factors of the form 4 k + 2 - - - > eliminate all odd factors . you are now left with 24 , 610 , 1218 , 2030 , 3660 , 90180 for the form 4 k + 2 , the first few values are 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 . . . already giving you 5 factors ( = 2 , 610 , 1830 ) . you can stop here and mark 6 ( 6 th one = 90 ) as the correct answer as 5 is not given . for checking any particular factor whether they conform to the form 4 k + 2 - - - > do the following 4 k + 2 = 36 - - - > 4 k = 34 - - > this will not give you an integer value for k - - - > reject . proceed with others until you find all the values asked . e is thus the correct answer .
Answer: e
Python program:
a = 180 / 3
b = a / 2
c = 3 + 2 
d = b / c
Problem: every student of a certain school must play an instrument . in last year , 1 / 2 of the students picked a woodwind instrument , 2 / 5 of the students picked a brass instrument , and all of the other students took percussion . in this year , 1 / 2 of the students who play woodwind and 1 / 4 of the students who play brass instruments left school , other students did not leave , and no fresh student come in . what fraction of all students play either a woodwind or brass instrument ?
Options: a ) 7 / 13 , b ) 4 / 5 , c ) 9 / 13 , d ) 11 / 13 , e ) 7 / 10
Rationale: lets pick smart numbers . total number of students : 20 woodwind ( 1 / 2 ) : 10 brass ( 2 / 5 ) : 8 percussion ( 1 / 10 ) : 2 after leaving school woodwind : 5 brass : 6 percussion : 2 new total number of students : 13 woodwind and brass : 11 answer 11 / 13 or d
Answer: d
Python program:
a = 1 / 2
b = 1 - a
c = 1 / 2
d = c / 2
e = b - d
f = 2 / 5
g = 2 / 5
h = g / 4
i = f - h
j = e + i 
k = 1 / 2
l = 1 - k
m = 1 / 2
n = m / 2
o = l - n
p = 1 - o
q = 1 / 2
r = 1 - q
s = 2 / 5
t = r - s
u = p - t
v = j / u
Problem: a cylinder is being filled with sand weighing 200 kg per cubic foot . the cylinder has a diameter of 1 foot and is 5 feet tall . how much sand is being used ? ?
Options: a ) 250 pi kg
b ) 500 pi kg
c ) 500 pi ^ 2 kg
d ) 1000 pi kg
e ) 1000 pi ^ 2 kg
Rationale: answer is a . volume of cylinder = pi * r ^ 2 * h - - - - - - - - > pi * ( 1 / 2 ) ^ 2 * 5 - - - - - - - - > pi * ( 1 / 4 ) * 5 - - - - - - - - > ( 5 / 4 ) pi cubic feet . 1 cubic feet = 200 kg . so ( 5 / 4 ) pi cubic feet = ( ( 200 * 5 ) / 4 ) pi - - - - - - - - - > 250 pi regards , abhijit answer is a
Answer: a
Python program:
a = 1 / 2
b = 200 * volume_cylinder
Problem: a can complete the job in 4 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 7 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 7
Answer: a
Python program:
a = 4 - 1
b = a - 3
c = 4 * 3
d = b / c
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 16 days more ?
Options: a ) 122 , b ) 140 , c ) 199 , d ) 188 , e ) 190
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 16 x * 16 = 760 * 20 x = 950 760 - - - - - - - 190 answer : e"
Answer: e
Python program:
a = 22 - 2
b = 760 * a
c = b / 16
d = c - 760
Problem: if n = 8 ^ 8 – 8 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 8 , d ) 2 , e ) 4
Rationale: "8 ^ 8 - 8 = 8 ( 8 ^ 7 - 1 ) = = > 8 ( 2 ^ 21 - 1 ) last digit of 2 ^ 21 is 2 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit . now on multiply this with 8 , we get unit digit as 8 answer : c"
Answer: c
Python program:
a = math.log(8)
b = 8 ** 8
c = math.log(b)
d = a / c
Problem: if w is the set of all the integers between 19 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 54
Rationale: "multiples of 2 from 19 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 18 = [ 99 / 2 ] - [ 18 / 2 ] = 49 - 9 = 40 multiples of 3 from 19 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 18 = [ 99 / 3 ] - [ 18 / 3 ] = 33 - 6 = 27 multiples of 2 and 3 bothi . e . 6 from 19 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 18 = [ 99 / 6 ] - [ 18 / 6 ] = 16 - 3 = 13 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 40 + 27 - 13 = 54 answer option e"
Answer: e
Python program:
a = 99 - 19
b = a / 3
c = math.floor(b)
d = 99 - 19
e = d / 2
f = c + e 
g = 99 - 19
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
Problem: find the curved surface area , if the radius of a cone is 28 m and slant height is 30 m ?
Options: a ) 2550 , b ) 2640 , c ) 3960 , d ) 4280 , e ) 5490
Rationale: "cone curved surface area = ï € rl 22 / 7 ã — 28 ã — 30 = 88 ã — 30 = 2640 m ( power 2 ) answer is b ."
Answer: b
Python program:
a = 28 * 30
b = math.pi * a