euclaise/mathqa_programs huggingface dataset:
Problem: a box contains 2 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 7 / 5 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 5 black balls be bbbbb and 2 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 5 ! x 2 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 6 slots and 4 black ( bbbb ) and 2 red ( rrr ) they can be arranged in ( 7 ! ) / ( 4 ! x 2 ! ) hence required probability = [ ( 7 ! ) / ( 5 ! x 2 ! ) ] / [ ( 6 ! ) / ( 4 ! x 2 ! ) ] = 7 / 5 b"
Answer: b
Python program:
a = 2 + 5 
b = a / 5
Problem: sachin is younger than rahul by 4 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ?
Options: a ) 24.9 , b ) 24.6 , c ) 24.2 , d ) 24.8 , e ) 24.5
Rationale: "let rahul ' s age be x years . then , sachin ' s age = ( x - 7 ) years . ( x - 7 ) / x = 7 / 9 2 x = 63 = > x = 31.5 hence , sachin ' s age = ( x - 7 ) = 24.5 years . answer : e"
Answer: e
Python program:
a = 9 - 7
b = 4 / a
c = b * 7
Problem: if a ( a + 5 ) = 6 and b ( b + 5 ) = 6 , where a ≠ b , then a + b =
Options: a ) − 5 , b ) − 9 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 1 then b = - 6 or if a = - 6 then b = 1 but in each case a + b = - 6 + 1 = - 5 answer : option a"
Answer: a
Python program:
a = 6 / 10
b = 6 / 10
c = 6 / b
d = a + c
Problem: the l . c . m . of two numbers is 36 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 53 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 36 or x = 6 . the numbers are 12 and 18 . hence , required sum = ( 12 + 18 ) = 30 . answer : option b"
Answer: b
Python program:
a = 2 * 3
b = 36 / a
c = b * 3
d = 2 * 3
e = 36 / d
f = e * 2
g = c + f
Problem: a man can do a piece of work in 6 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 3 ) - ( 1 / 6 ) = 1 / 6 the son alone can do the work in 6 days answer is c"
Answer: c
Python program:
a = 6 * 3
b = 6 - 3
c = a / b
Problem: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 70 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 240 , c ) 385 , d ) 440 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 70 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 70 = 315 . total area = 70 + 315 = 385 answer : c ."
Answer: c
Python program:
a = 70 * 3
b = a / 2
c = b * 3
d = 70 + c
Problem: the sum of the present ages of a , b , c is 57 years . 3 years ago their ages were in the ratio 1 : 2 : 3 . what is the present age of a ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: three years ago : a : b : c = 1 : 2 : 3 let a = 1 x , b = 2 x , and c = 3 x . today : ( x + 3 ) + ( 2 x + 3 ) + ( 3 x + 3 ) = 57 x = 8 so the present age of a is x + 3 = 11 the answer is d .
Answer: d
Python program:
a = 3 * 3
b = 57 - a
c = 1 + 2 
d = c + 3 
e = b / d
f = e + 3
Problem: a parking garage rents parking spaces for $ 12 per week or $ 30 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 264
Rationale: "12 $ per week ! an year has 52 weeks . annual charges per year = 52 * 12 = 624 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 30 = 360 $ 624 - 360 = 264 ans e"
Answer: e
Python program:
a = 3 + 2 
b = 12 * a
c = b + 2 
d = c * 12
e = 30 * 12
f = d - e
Problem: the profit earned by selling an article for rs . 753 is equal to the loss incurred when the same article is sold for rs . 455 . what should be the sale price for making 50 % profit ?
Options: a ) 706 , b ) 786 , c ) 906 , d ) 896 , e ) 696
Rationale: "let c . p = rs . x then as given , ( 753 - x ) = ( x - 455 ) 2 x = 1208 x = 604 there fore s . p = 150 % of 604 = > rs . = rs . 906 answer : c"
Answer: c
Python program:
a = 753 - 455
b = a / 2
c = 753 - b
d = 50 / 100
e = 1 + d 
f = c * e
Problem: the sum of a number and its square is 1406 . what is the number ?
Options: a ) 1409
b ) 1402
c ) 1221
d ) 1406
e ) 8828
Rationale: explanation : by option verification 37 + 37 × 37 = 1406 answer : d
Answer: d
Python program:
a = 4 * 100
b = 1000 + a 
c = 2 * 3
d = b + c 
e = 1 - 2
f = d * e
g = f * 4
h = 1 - g
i = math.sqrt(h)
j = 1 - 2
k = i + j 
l = k / 2
Problem: 1 , 1 , 2 , 1 , 2 , 3 , 1 , 2 , 3 , 4 , 1 , 2 , __ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "1,1 , 2,1 , 2,3 , 1,2 , 3,4 , 1,2 , __ ? looking at the series 1 12 123 1234 12 ( 3 ) 45 so the answer is 3 . answer : c"
Answer: c
Python program:
a = 3 * 0
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 756 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1806 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 756 × 100 ) / ( 6 × 12 ) = rs . 1050 bg = bd – td = > 756 = bd - 1050 = > bd = 1050 + 756 = 1806 answer : option d"
Answer: d
Python program:
a = 756 * 100
b = 12 * 6
c = a / b
d = 756 + c
Problem: one fourth of one third of two fifth of a number is 35 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 420 , c ) c ) 180 , d ) d ) 200 , e ) e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 35 then x = 35 * 30 = 1050 40 % of 1050 = 420 answer : option b"
Answer: b
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 35 / f
h = g * 40
i = h / 100
Problem: a flagstaff 17.5 m high casts a shadow of length 40.25 m . what will be the height of a building , which casts a shadow of length 28.75 m under similar conditions ?  
Options: a ) 12.5 m , b ) 10.5 m , c ) 14 , d ) 12 , e ) 10
Rationale: explanation : let the required height of the building be x meter more shadow length , more height ( direct proportion ) hence we can write as ( shadow length ) 40.25 : 28.75 : : 17.5 : x ⇒ 40.25 × x = 28.75 × 17.5 ⇒ x = 28.75 × 17.5 / 40.25 = 2875 × 175 / 40250 = 2875 × 7 / 1610 = 2875 / 230 = 575 / 46 = 12.5 answer : option a
Answer: a
Python program:
a = 17 / 5
b = 28 * 75
Problem: in a party every person shakes hands with every other person . if there were a total of 153 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 153 n ( n - 1 ) / 2 = 153 â ˆ ´ n = 18 answer : option d"
Answer: d
Python program:
a = 153 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 1 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 1 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 4 - - - > 5 = 2 k + 4 - - - > k = 1 / 2 . the answer is , therefore , ( a ) ."
Answer: a
Python program:
a = 5 + 1 
b = a - 5
c = b / 2
Problem: if a lends rs . 25000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 1125 , b ) 1225 , c ) 1325 , d ) 1145 , e ) 2125
Rationale: "( 25000 * 1.5 * 3 ) / 100 = > 1125 answer : a"
Answer: a
Python program:
a = 25000 * 11
b = a * 3
c = b / 100
d = 25000 * 10
e = d * 3
f = e / 100
g = c - f
Problem: 50 is what percent of 125 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 50 / 125 × 100 = 50 % answer : b
Answer: b
Python program:
a = 50 / 125
b = a * 100
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 10 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 5 , b ) 5 / 15 , c ) 6 / 15 , d ) 3 / 10 , e ) 4 / 15
Rationale: p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.1 * 300 / 450 = 30 / 450 = 1 / 15 the sum of the probabilities is 6 / 15 = 2 / 5 the answer is c .
Answer: c
Python program:
a = 10 * 10
b = 40 / a
c = 1 - b
d = c * 150
e = d / 450
f = 10 * 10
g = 10 / f
h = g * 300
i = 10 * 10
j = 40 / i
k = j * 150
l = h + k 
m = l / 450
n = e + m
Problem: the least number by which 72 must be multiplied in order to produce a multiple of 112 , is
Options: a ) 6 , b ) 12 , c ) 14 , d ) 18 , e ) 20
Rationale: "solution required numbers is divisible by 72 as well as by 112 , if it is divisible by their lcm , which is 1008 . now , 1008 when divided by 72 , gives quotient = 14 . required number = 14 . answer c"
Answer: c
Python program:
a = math.gcd(72, 112)
b = 112 / a
Problem: find the number , difference between number and its 3 / 5 is 58 .
Options: a ) 140 , b ) 143 , c ) 144 , d ) 145 , e ) 146
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 58 , = > ( 2 / 5 ) x = 58 = > 2 x = 58 * 5 , = > x = 145 answer : option d"
Answer: d
Python program:
a = 58 / 2
b = a * 5
Problem: the unit digit in the product ( 891 * 781 * 912 * 463 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 1 * 1 * 2 * 3 ) = 6 answer : c"
Answer: c
Python program:
a = 891 * 781
b = a * 912
c = b * 463
d = 891 * 781
e = d * 912
f = e * 463
g = 4 + 4 
h = f - g
i = c - h
Problem: find the value of 3 + 2 . ( 8 - 3 )
Options: a ) 25 , b ) 13 , c ) 17 , d ) 24 , e ) 19
Rationale: "3 + 2 . ( 8 - 3 ) = 3 + 2 ( 5 ) , = 3 + 2 * 5 , = 3 + 10 , = 13 , correct answer : ( d )"
Answer: d
Python program:
a = 2 / 3
b = a + 3 
c = b * 8
Problem: two numbers a and b are such that the sum of 5 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 3 , b ) 1 : 1 , c ) 3 : 4 , d ) 4 : 3 , e ) 5 : 5
Rationale: "5 / 100 a + 4 / 100 b = 2 / 3 ( 6 / 100 a + 8 / 100 b ) = > 1 / 20 a + 1 / 25 b = 1 / 25 a + 4 / 75 b = > ( 1 / 20 - 1 / 25 ) b = 1 / 25 a + 4 / 75 b ( 1 / 20 - 1 / 25 ) a = ( 4 / 75 - 1 / 25 ) b 1 / 100 a = 1 / 75 b a / b = 100 / 75 = 4 / 3 req ratio = 4 : 3 answer d"
Answer: d
Python program:
a = 8 / 100
b = a * 4
c = b / 3
d = 4 / 100
e = c - d
f = 5 / 100
g = 6 / 100
h = g * 2
i = h / 3
j = f - i
k = e / j
Problem: when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 5 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 360 , c ) 400 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 5 of 300 = 60 total amount in her account = 360 answer b"
Answer: b
Python program:
a = 3 / 5
b = 1 - a
c = 200 / b
d = c - 200
e = 1 / 5
f = 1 + e 
g = d * f
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 32 . in the company , what is the maximum number of non - managers in a department that has 9 managers ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "9 / 7 * 32 = 41.1 the answer is c ."
Answer: c
Python program:
a = 32 * 9
b = a / 7
c = math.floor(b)
Problem: a man ' s speed with the current is 22 km / hr and the speed of the current is 5 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "man ' s rate in still water = ( 22 - 5 ) km / hr = 17 km / hr . man ' s rate against the current = ( 17 - 5 ) km / hr = 12 km / hr . answer : d"
Answer: d
Python program:
a = 22 - 5
b = a - 5
Problem: machine z takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine z to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of z is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and a reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of z . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Python program:
a = 40 / 20
b = 2 * 3
c = a * b
Problem: a certain pair of used shoes can be repaired for $ 13.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 17.69 , b ) 14.85 , c ) 21.3 , d ) 16.5 , e ) 18.51
Rationale: "1 ) cost of repairing = 13.5 ( for one year ) , therefore for 2 years it would be $ 27 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 32 - 27 ) / ( 27 ) * 100 = 18.51 % . ans is e"
Answer: e
Python program:
a = 13 * 50
b = 32 - 0
c = 13 * 50
d = b / c
e = 100 * d
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 31 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 31 kg joins the group , total weight of boys = 20 x + 31 so 20 x + 31 = 21 ( x + 1 ) = > x = 10 . answer : e"
Answer: e
Python program:
a = 20 + 1 
b = 31 - a
c = b + 1
Problem: if x = 55 + 2 q and y = 4 q + 41 , then for what value of q , x is equal to y ?
Options: a ) - 14 , b ) 14 , c ) - 7 , d ) 7 , e ) 0
Rationale: explanation : x = y < = > 55 + 2 q = 4 q + 41 < = > 2 q = 14 < = > q = 7 . answer : d
Answer: d
Python program:
a = 4 + 3 
b = 2 * a
c = b / 2
Problem: a man can swim in still water at 4 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.9 , c ) 1.1 , d ) 1.5 , e ) 0.75
Rationale: "m = 4 s = x ds = 4 + x us = 4 + x 4 + x = ( 4 - x ) 2 4 + x = 8 - 2 x 3 x = 4 x = 0.75 answer : e"
Answer: e
Python program:
a = 4 / 3
Problem: there are 10 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 90
Rationale: "every team plays with 9 teams . . . so total no of matches = 10 x 9 = 90 . now , each match is played twice = > 90 x 2 but 2 teams play a match = > 90 x 2 / 2 = 90 . answer : e"
Answer: e
Python program:
a = 10 - 1
b = 10 * a
c = b / 2
Problem: a sum fetched a total simple interest of rs . 100 at the rate of 5 p . c . p . a . in 4 years . what is the sum ?
Options: a ) 800 , b ) 600 , c ) 500 , d ) 1000 , e ) 300
Rationale: "sol . principal = rs . [ 100 * 100 / 5 * 4 ] = rs . [ 10000 / 20 ] = rs . 500 . answer c"
Answer: c
Python program:
a = 100 * 100
b = a / 5
c = b / 4
Problem: an auction house charges a commission of 18 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 200,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.18 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 200,000 ( 18 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c ."
Answer: c
Python program:
a = 18 * 10
b = a + 10
Problem: if one person completes a journey in 10 hrs . he travels 1 st half of the journey at the rate of 21 km / hr and 2 nd half at therate of 24 km / hr . find the total journey in km .
Options: a ) 200 km , b ) 212 km , c ) 224 km , d ) 230 km , e ) 256 km
Rationale: distance = speed x time let time taken to travel the first half = x hr then time taken to travel the second half = ( 10 - x ) hr distance covered in the the first half = 21 x distance covered in the the second half = 24 ( 10 - x ) but distance covered in the the first half = distance covered in the the second half = > 21 x = 24 ( 10 - x ) = > 21 x = 240 - 24 x = > 45 x = 240 = > 9 x = 48 = > 3 x = 16 ⇒ x = 163 hence distance covered in the the first half = 21 x = 21 × 163 = 7 × 16 = 112 kmtotal distance = 2 × 112 = 224 km c
Answer: c
Python program:
a = 10 / 2
b = 21 * a
c = 10 / 2
d = 24 * c
e = b + d
Problem: m = { - 6 , - 5 , - 4 , - 3 , - 2 , - 1 } t = { - 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 1 / 4 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: we will have a negative product only if 1 or 2 are selected from set t . p ( negative product ) = 2 / 8 = 1 / 4 the answer is b .
Answer: b
Python program:
a = 4 * 2
b = 2 / a
Problem: the radius of a cylinder is 6 m , height 21 m . the total surface area of the cylinder is ?
Options: a ) 525 , b ) 528 , c ) 522 , d ) 529 , e ) 521
Rationale: "total surface area of the cylinder is = 2 π r ( r + h ) = 2 × 22 / 7 × 6 ( 6 + 8 ) = 2 × 22 / 7 × 6 ( 14 ) = 44 × 12 = 528 m ( power 2 ) answer is b ."
Answer: b
Python program:
a = circumface * (
Problem: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 2,160 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( x + 5 ) * 150 + x * 85 = 2160 = > x = 6 total lens = 6 + ( 6 + 5 ) = 17 answer d"
Answer: d
Python program:
a = 4 * 100
b = 5 * 10
c = a + b 
d = c + 5 
e = d + 1000 
f = 150 * 5
g = e - f
h = 150 + 85 
i = g / h
j = i * 2
k = j + 5
Problem: what is the tenth digit of ( 5 ! * 5 ! - 5 ! * 3 ! ) / 5 ?
Options: a ) 1 , b ) 2 , c ) 0 , d ) 6 , e ) 7
Rationale: ( 5 ! * 5 ! + 5 ! * 3 ! ) / 5 = 5 ! ( 5 ! + 3 ! ) / 5 = 120 ( 120 + 6 ) / 5 = 3024 units digit of the above product will be equal to 2 answer b
Answer: b
Python program:
a = math.factorial(5)
b = math.factorial(5)
c = a * b
d = math.factorial(5)
e = math.factorial(3)
f = d * e
g = c - f
h = g / 5
i = 100 * 10
j = h / i
k = math.floor(j)
Problem: 30 pens and 75 pencils were purchased for 570 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 570 – 150 ) = 360 ∴ average price of a pen = 420 ⁄ 60 = 14 answer e"
Answer: e
Python program:
a = 75 * 2
b = 570 - a
c = b / 30
Problem: if 20 typists can type 42 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 189 , b ) 72 , c ) 144 , d ) 216 , e ) 400
Rationale: "20 typists can type 42 letters , so 30 typists can type = 42 * 30 / 20 42 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 42 * 30 * 60 / 20 * 20 = 189 a is the answer"
Answer: a
Python program:
a = 42 * 3
b = a / 20
c = b * 30
Problem: a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates q apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates q / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Python program:
a = 24 / 2
b = 2 + 3 
c = a * b
d = 24 * 2
e = c + d 
f = 3 + 4 
g = 24 * f
h = e / g
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 18 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 18 + 11 - - > { bike } = 53 - - > # those who have bike only is { bike } - { both } = 53 - 18 = 35 . answer : b ."
Answer: b
Python program:
a = 90 - 11
b = a + 18 
c = b - 44
d = c - 18
Problem: two trains of equal are running on parallel lines in the same direction at 42 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 30 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 42 - 36 = 6 km / hr . = 6 * 5 / 18 = 5 / 3 m / sec . 2 x / 36 = 5 / 3 = > x = 30 . answer : a"
Answer: a
Python program:
a = 42 - 36
b = a * 1000
c = b / 3600
d = 36 * c
e = d / 2
Problem: a customer pays 70 dollars for a coffee maker after a discount of 20 dollars what is the original price of the coffe maker ?
Options: a ) 50 , b ) 40 , c ) 90 , d ) 60 , e ) 20
Rationale: let x be the original price . x - 20 = 70 x - 20 + 20 = 70 + 20 x + 0 = 90 x = 90 answer is c
Answer: c
Python program:
a = 70 + 20
Problem: if 40 % of a certain number is 160 , then what is 50 % of that number ?
Options: a ) 270 , b ) 380 , c ) 200 , d ) 360 , e ) 290
Rationale: "explanation : 40 % = 40 * 4 = 160 50 % = 50 * 4 = 200 answer : option c"
Answer: c
Python program:
a = 40 / 100
b = 160 / a
c = 50 / 100
d = b * c
Problem: a man can row his boat with the stream at 12 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 4 kmph , c ) 98 kmph , d ) 6 kmph , e ) 4 kmph
Rationale: "ds = 12 s = ? s = ( 12 - 4 ) / 2 = 4 kmph answer : e"
Answer: e
Python program:
a = 12 - 4
b = a / 2