euclaise/mathqa_programs huggingface dataset:
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 2000 then loss of pyarelal ?
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 2000 , loss of pyarelal = 2000 * 9 x / 10 x = 1800 answer : c"
Answer: c
Python program:
a = 9 * 2000
b = 1 + 9 
c = a / b
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1200 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1500 , c ) rs . 2000 , d ) rs . 2400 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1200 x = 1200 . b ' s share = rs . 2 x = rs . ( 2 x 1200 ) = rs . 2400 . answer = d"
Answer: d
Python program:
a = 4 - 3
b = a * 1200
c = b * 3
Problem: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 60 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 105 / 2 , b ) 45 , c ) 44 , d ) 52 , e ) 50
Rationale: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 60 or 1 / 7 t + 1 t = 60 therefore t = 60 * 7 / 8 = 105 / 2 a"
Answer: a
Python program:
a = 60 * 2
b = 60 / 100
c = 60 * b
d = a - c
e = 60 / 100
f = e + 1 
g = d / f
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 60 % . in order to keep your gold in the vault , you must pay 10 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 45 % , b ) 46 % , c ) 50 % , d ) 55 % , e ) 44 %
Rationale: "( 100 % + 60 % ) * ( 100 % - 10 % ) = 160 * 0.90 = 144 % an increase of 44 % your gold holdings have increased in value by 44 % . the answer is e"
Answer: e
Python program:
a = 60 / 10
b = 60 - a
Problem: there is a square of side 6 cm . a circle is inscribed inside the square . find the ratio of the area of circle to square .
Options: a ) 11 / 14
b ) 1 / 14
c ) 13 / 14
d ) 12 / 14
e ) 5 / 14
Rationale: let the side of square = a unit so area of square = a ^ 2 diameter of inscribed circle = side of square = a radius of circle = a / 2 area of circle = ( 22 / 7 ) ( a / 2 ) ^ 2 ratio of area of circle to square = { ( 22 / 7 ) ( a / 2 ) ^ 2 } / a ^ 2 = 11 / 14 answer : a
Answer: a
Python program:
a = 6 / 2
b = circle_area / (
Problem: if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 9 have ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is d . 5 * 10 = 50"
Answer: d
Python program:
a = 4 + 1 
b = 9 + 1 
c = a * b
Problem: 30 is subtracted from 40 % of a number , the result is 50 . find the number ?
Options: a ) 200 , b ) 997 , c ) 266 , d ) 288 , e ) 271
Rationale: "( 40 / 100 ) * x – 30 = 50 4 x = 800 x = 200 answer : a"
Answer: a
Python program:
a = 30 + 50 
b = 40 / 100
c = a / b
Problem: calculate how many days it will take for 5 boys to paint a 65 m long wall if 2 boys can paint a 40 m long wall in 4 days ,
Options: a ) 2.6 days , b ) 3.6 days , c ) 5.6 days , d ) 6 days , e ) 2 days
Rationale: "the length of wall painted by one boy in one day = 40 / 2 * 1 / 4 = 5 m no . of days required to paint 50 m cloth by 8 boys = 65 / 5 * 1 / 5 = 2.6 days . a"
Answer: a
Python program:
a = 2 * 4
b = a * 65
c = 40 * 5
d = b / c
Problem: if a - b = 3 and a 2 + b 2 = 29 , find the value of ab ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 17 , e ) 18
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 a )"
Answer: a
Python program:
a = 3 ** 2
b = 29 - a
c = b / 2
Problem: mary invested a certain sum of money in a bank that paid simple interest . the amount grew to $ 260 at the end of 2 years . she waited for another 4 years and got a final amount of $ 380 . what was the principal amount that she invested at the beginning ?
Options: a ) $ 200 , b ) $ 220 , c ) $ 230 , d ) $ 240 , e ) $ 250
Rationale: "what shall be the rate of interest . ? does that is not required for the calculation ? not really ! keep in mind that the interest earned each year will be the same in simple interest . at the end of 2 years , amount = $ 260 at the end of 6 years , amount = $ 380 this means she earned an interest of $ 120 in 4 years . or $ 30 in each year . we know that the interest earned each year will be the same . therefore she must have earned $ 60 in 2 years . hence principal amount = $ 260 - $ 60 = $ 200 option a"
Answer: a
Python program:
a = 380 - 260
b = a / 4
c = b * 2
d = 260 - c
Problem: pipe a can fill a tank in 32 minutes . pipe b can fill the same tank 5 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 2 / 7 minutes , c ) 32 / 7 minutes , d ) 224 / 7 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 32 minutes - - > the rate of a = 1 / 32 tank / minute ; pipe b can fill the same tank 5 times fasterthan pipe a - - > the rate of b = 1 / 32 + 5 / 32 = 6 / 32 tank / minute . their combined rate = 1 / 32 + 6 / 32 = 7 / 32 tank / minute ; therefore , a and b can fill the tank in 32 / 7 minutes . answer : c"
Answer: c
Python program:
a = 1 / 32
b = 1 / 32
c = 5 / 32
d = b + c 
e = a + d 
f = 1/(e)
Problem: a taxi company charges $ 1.85 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 3 miles , e ) 6 1 / 4 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.85 for the first quarter - mile , we will have $ 3.05 left to spend on quarter - mile intervals . since $ 3.05 / $ 0.15 = 20.33 , we can buy 20.33 more quarter - miles , and will travel 21.33 quarter miles in all : 21.33 × 1 / 4 = 5 1 / 3 miles . the correct answer is choice ( d ) ."
Answer: d
Python program:
a = 4 - 90
b = a * 100
c = b / 3
d = c / 4
Problem: the speed of a train is 64 kmph . what is the distance covered by it in 9 minutes ?
Options: a ) 10 kmph , b ) 11 kmph , c ) 88 kmph , d ) 18 kmph , e ) 12 kmph
Rationale: "64 * 9 / 60 = 9.6 kmph answer : a"
Answer: a
Python program:
a = 9 / const_60
b = a * 64
Problem: if it is a 3 x 3 matrix , for which elements in first row are ( v , 50 , w ) , second row ( 196 , x , y ) and in third row are ( 269 , z , 123 ) . it is given that the sum of the numbers in each row , column , diagonal are same . then find the value of ( y + z ) .
Options: a ) 1012 , b ) 1011 , c ) 1212 , d ) 1122 , e ) 1021
Rationale: v 50 w 196 x y 269 z 123 in 1 st row and 1 st column v + 196 + 269 = v + 50 + w w = 415 again , in 2 nd column and 3 rd row 50 + x + z = 269 + z + 123 x = 342 as sum of each row column and diagonal are same . so , 269 + 342 + 415 = 1026 415 + y + 123 = 1026 y = 488 269 + z + 123 = 1026 z = 634 y + z = 488 + 634 = 1122 answer : d
Answer: d
Python program:
a = 269 + 123 
b = a - 50
c = 269 + b 
d = c - 123
e = 269 + 123 
f = e - 50
g = 196 + 269 
h = g - 50
i = f + h 
j = i - 123
k = d + j
Problem: in an examination 35 % of the students passed and 455 failed . how many students appeared for the examination ?
Options: a ) 540 , b ) 400 , c ) 700 , d ) 650 , e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 455 65 x / 100 = 455 x = 455 * 100 / 65 = 700 answer is c"
Answer: c
Python program:
a = 455 * 100
b = 100 - 35
c = a / b
Problem: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 140 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 80 coins , e ) none of these
Rationale: let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 140 ⇒ 1.75 x = 140 ⇒ x = 80 coins answer d
Answer: d
Python program:
a = 1/(4)
b = 1/(2)
c = a + b 
d = c + 1 
e = 140 / d
Problem: a 80 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 20 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 8.0 assume x gallons of water are added . 8.0 / 80 + x = 8 / 100 800 = 8 x + 640 8 x = 160 x = 20 correct option : a"
Answer: a
Python program:
a = 10 - 8
b = 80 * a
c = b / 8
Problem: what least value should be replaced by * in 223431 * so the number become divisible by 5
Options: a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : trick : number is divisible by 5 , if last digit is 0 or 5 so that least number is 0 . answer : option a
Answer: a
Python program:
a = 5 - 5
b = 5 - a
Problem: the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 182.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm + 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b"
Answer: b
Python program:
a = 35 * 184
b = a - 166
c = b + 106 
d = c / 35
e = math.floor(d)
Problem: a certain country had a total annual expenditure of $ 2.4 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 2,4 x 10 ^ 11 ) / 240 000 000 = ( 2,4 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 1 x 10 ^ ( 11 - 8 ) = 1 x 10 ^ 3 = 1000 . answer is b ."
Answer: b
Python program:
a = 10 ** 11
b = 2 * 4
c = 4 + 2 
d = 10 ** c
e = 240 * d
f = b / e
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 336 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 744 , c ) 788 , d ) 868 , e ) 177
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 336 62 % - - - - - - - - ? = > 868 answer : d"
Answer: d
Python program:
a = 100 - 62
b = 62 - a
c = b / 100
d = 336 / c
e = d * 62
f = e / 100
Problem: a train running at the speed of 60 km / hr crosses a pole in 3 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 50 metres , e ) 180 metres
Rationale: "speed = ( 60 x 5 / 18 ) / m / sec = 50 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 50 x 3 / 3 m = 50 m . answer : option d"
Answer: d
Python program:
a = 60 * 1000
b = a / 3600
c = b * 3
Problem: two positive integers differ by 4 , and sum of their reciprocals is 5 then one of the numbers is
Options: a ) a ) 3 , b ) b ) 1 , c ) c ) 5 , d ) d ) 21 , e ) 4
Rationale: "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 5 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 6 or ( n ^ 2 + 4 n ) * 5 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 4 . hence , e"
Answer: e
Python program:
a = 5 + 5
Problem: jennifer had $ 90 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 12 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0
Rationale: "1 / 5 x $ 90 = $ 15 for sandwich 1 / 6 x $ 90 = $ 45 for museum 1 / 2 x $ 90 = $ 78 for book $ 15 + $ 45 + $ 18 = $ 78 spent $ 90 - $ 78 = $ 12 left over correct answer a"
Answer: a
Python program:
a = 1 / 5
b = 90 * a
c = 1 / 6
d = 90 * c
e = b + d 
f = 1 / 2
g = 90 * f
h = e + g 
i = 90 - h
Problem: in one hour , a boat goes 11 km along the stream and 5 km against it . find the speed of the boat in still water
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "explanation : we know we can calculate it by 1 / 2 ( a + b ) = > 1 / 2 ( 11 + 5 ) = 1 / 2 ( 16 ) = 8 km / hr answer is c"
Answer: c
Python program:
a = 11 + 5 
b = a / 2
Problem: how long does a train 145 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 52.66 , b ) 53.66 , c ) 54.66 , d ) 58.66 , e ) 59.66
Rationale: "t = ( 660 + 145 ) / 54 * 18 / 5 t = 53.66 answer : b"
Answer: b
Python program:
a = 145 + 660 
b = 54 * const_0_2778
c = a / b
Problem: in a group of ducks and cows , the total number of legs are 36 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 36 = > 2 x = 36 = > x = 18 e"
Answer: e
Python program:
a = 36 / 2
Problem: in town x , 60 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 20 % , c ) 31 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 60 % , out of which 48 are employed males , hence 12 % are employed females . ( employed females ) / ( total employed people ) = 12 / 60 = 1 / 5 = 20 % answer : b ."
Answer: b
Python program:
a = 60 - 48
b = a / 60
c = b * 100
Problem: find large number from below question the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1254 , b ) 1376 , c ) 1456 , d ) 1599 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1335 ) . x + 1335 = 6 x + 15 5 x = 1320 x = 264 large number = 264 + 1335 = 1599 d"
Answer: d
Python program:
a = 1335 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: in a sample of college students , 20 percent are third year students and 80 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 1 / 4 , b ) 2 / 3 , c ) 4 / 7 , d ) 1 / 2 , e ) 3 / 7
Rationale: "= 20 / 80 . = 1 / 4 my answer is a too"
Answer: a
Python program:
a = 100 - 20
b = 3 * 10
c = a - b
d = 3 * 10
e = c / d
Problem: what is the product of all the possible values of x if x ^ 2 - 9 x + 20 ?
Options: a ) – 29 , b ) – 12 , c ) 12 , d ) 20 , e ) 168
Rationale: "explanation : = > y = x ^ 2 - 9 x + 20 = > y = ( x - 4 ) ( x - 5 ) = > x = 4 , y = 5 product y = ( 4 ) ( 5 ) = 20 answer option 20 answer : d"
Answer: d
Python program:
a = 20 / 1
Problem: in a group of ducks and cows , the total number of legs are 28 more than twice the number of heads . find the total number of cows .
Options: a ) 14 , b ) 12 , c ) 16 , d ) 8 , e ) 6
Rationale: "explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 28 + 2 ( c + d ) = > d + 2 c = 14 + c + d = > 2 c = 14 + c = > c = 14 i . e . , total number of cows = 14 answer : a"
Answer: a
Python program:
a = 28 / 2
Problem: a dog takes 3 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 8 , b ) 9 : 9 , c ) 9 : 6 , d ) 9 : 1 , e ) 9 : 2
Rationale: "explanation : dog : hare = ( 3 * 3 ) leaps of hare : 8 leaps of hare = 9 : 5 . answer : a ) 9 : 8"
Answer: a
Python program:
a = 3 * 3
b = a / 8
Problem: a certain no . when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) c"
Answer: c
Python program:
a = 50 - 25
b = a - 4
c = b - 2
Problem: a retailer bought a coat at wholesale and marked it up 90 % to its initial price of $ 76 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.9 x = 76 and x = 76 / 1.9 = 40 . to achieve a 100 % markup , the price needs to be $ 80 . the retailer needs to increase the price by $ 4 more . the answer is b .
Answer: b
Python program:
a = 90 / 100
b = a + 1 
c = 76 / b
d = c * 2
e = d - 76
Problem: if bat = 58 hat = 52 cat = 57 then whats rat = ?
Options: a ) 42 , b ) 45 , c ) 34 , d ) 76 , e ) 25
Rationale: a 42
Answer: a
Python program:
a = 57 + 3 
b = 3 * 3
c = b * 2
d = a - c
Problem: ( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ?
Options: a ) 24500 , b ) 21600 , c ) 36600 , d ) 22400 , e ) 12500
Rationale: "( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ? or , ? = 900 ã — 4 ã — 6 = 21600 answer b"
Answer: b
Python program:
a = 700 + 200 
b = a / 4
Problem: there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 16 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120
Rationale: "each person is one participant of 4 games . so there are in all 16 * 5 = 80 instances of one participant games . but each game has 2 participants so total number of games = 80 / 2 = 40 c"
Answer: c
Python program:
a = 5 * 16
b = a / 2
Problem: find the highest common factor of 36 and 84 .
Options: a ) 12 , b ) 10 , c ) 16 , d ) 19 , e ) 18
Rationale: "36 = 2 ^ 2 x 3 ^ 2 84 = 2 ^ 2 x 3 x 7 h . c . f . = 2 ^ 2 x 3 = 12 . answer : option a"
Answer: a
Python program:
a = math.gcd(36, 84)
Problem: a basket contains 7 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 5 , e ) 4 / 11
Rationale: "the total number of ways to choose 2 apples is 7 c 2 = 21 the number of ways that include the spoiled apple is 6 c 1 = 6 p ( the spoiled apple is included ) = 6 / 21 = 2 / 7 the answer is b ."
Answer: b
Python program:
a = 7 - 1
b = math.comb(a, 1)
c = math.comb(7, 2)
d = b / c
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1275 , find the loss % ?
Options: a ) 15 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 225 100 - - - - ? = > 15 % answer : a"
Answer: a
Python program:
a = 1500 - 1275
b = a / 1500
c = b * 100
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 54 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) none of these
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 54 km time taken = distance / speed = 54 / 27 = 2 hours . answer : option d"
Answer: d
Python program:
a = 22 + 5 
b = 54 / a
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 60 year . what is the age of the eldest child ?
Options: a ) 4 year , b ) 18 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 â ‡ ” 5 x = 30 â ‡ ” x = 6 . â ˆ ´ age of the eldest child = x + 12 = 6 + 12 = 18 years . answer b"
Answer: b
Python program:
a = 5 / 3
b = 60 / a
c = 5 - 1
d = c * 3
e = b - d
f = e / 3
Problem: the average age of 15 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 37 , c ) 99 , d ) 38 , e ) 27
Rationale: "total age increased = ( 15 * 2 ) years = 30 years . sum of ages of two new men = ( 21 + 23 + 30 ) years = 74 years average age of two new men = ( 74 / 2 ) years = 37 years . answer : b"
Answer: b
Python program:
a = 21 + 23 
b = a / 2
c = 1 * 15
d = b + c
Problem: how long does a train 110 m long running at the speed of 90 km / hr takes to cross a bridge 132 m length ?
Options: a ) 12.9 sec , b ) 9.68 sec , c ) 17.9 sec , d ) 16.8 sec , e ) 14.9 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 25 = 9.68 sec . answer : b"
Answer: b
Python program:
a = 110 + 132 
b = 90 * const_0_2778
c = a / b
Problem: 20 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 75 %
Rationale: initially 80 % and 20 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 80 so , the required % is [ ( 3 / 4 ) ∗ 80 / 100 ] ∗ 100 = 60 % answer : d
Answer: d
Python program:
a = 20 - 5
b = 200 * a
c = b / 100
d = 20 - 5
e = 200 * d
f = e / 100
g = c + f
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 12 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "explanation : l = r l = 3 c r = c + 12 we can substitute r for l in the second equation : r = 3 c . if r is equal to both 3 c and c + 12 , we can say 3 c = c + 12 , and solve for c . 3 c = c + 12 2 c = 12 c = 6 answer : ( a )"
Answer: a
Python program:
a = 3 - 1
b = 12 / a
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 72 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 17 , d ) 37 , e ) 57
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 72 - x now , 50 * x + 500 * ( 72 - x ) = 10350 50 x + 36000 - 500 x = 10350 - 450 x = - 25650 x = 57 . no . of 50 rupees note = 57 . answer : option e"
Answer: e
Python program:
a = 500 * 72
b = a - 10350
c = 500 - 50
d = b / c
Problem: mike earns $ 17.5 per hour and phil earns $ 10.5 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 17.5 is 10.5 let it be x % less , then = 17.5 ( 1 - x / 100 ) = 10.5 1 - x / 100 = 10.5 / 17.5 x = 200 / 5 x = 40 % ans e"
Answer: e
Python program:
a = 10 / 5
b = a * 100