euclaise/mathqa_programs huggingface dataset:
Problem: in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 3 ohms and y is 5 ohms ?
Options: a ) 15 / 8 , b ) 3 / 8 , c ) 5 / 8 , d ) 7 / 15 , e ) 8 / 15
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 3 + 1 / 5 = 8 / 15 r = 15 / 8 the answer is a ."
Answer: a
Python program:
a = 5 * 3
b = 3 + 5 
c = a / b
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.12510168 ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 9 digits after decimal total no . of decimals = 11 req . no . of digits = ( n - 1 ) = ( 11 - 1 ) = 10 answer : c"
Answer: c
Python program:
a = 52 / 416
Problem: a person want to give his money of $ 4500 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 2000 , b ) $ 1500 , c ) $ 2500 , d ) $ 1800 , e ) $ 1600
Rationale: b ' s share = 4500 * 3 / 9 = $ 1500 answer is b
Answer: b
Python program:
a = 2 + 3 
b = a + 4 
c = 3 / b
d = c * 4500
Problem: how many integers between 100 and 180 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 39 , b ) 41 , c ) 43 , d ) 45 , e ) 47
Rationale: "the total numbers between 100 and 180 , inclusive , is 81 . 3 * 34 = 102 and 3 * 60 = 180 so the number of multiples of 3 is 27 . 5 * 20 = 100 and 5 * 36 = 180 so the number of multiples of 5 is 17 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 12 = 180 so the number of multiples of 15 is 6 . thus the total number is 81 - 27 - 17 + 6 = 43 . the answer is c ."
Answer: c
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 180 - e
Problem: what is the least number of squares tiles required to pave the floor of a room 2 m 42 cm long and 1 m 76 cm broad ?
Options: a ) 88 , b ) 82 , c ) 84 , d ) 44 , e ) 54
Rationale: "length of largest tile = h . c . f . of 242 cm and 176 cm = 22 cm . area of each tile = ( 22 x 22 ) cm 2 . required number of tiles = 242 x 176 / ( 22 ^ 2 ) = 88 . answer : a"
Answer: a
Python program:
a = 2 * 100
b = 42 * 100
c = rectangle_area / (
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 105 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 42 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 105 * 2 / 5 = $ 42 answer is b"
Answer: b
Python program:
a = 3 + 2 
b = 2 / a
c = b * 105
Problem: a number , x is chosen at random from the set of positive integers less than 12 . what is the probability that ( 9 / x ) > x ?
Options: a ) 1 / 11 , b ) 2 / 9 , c ) 2 / 11 , d ) 2 / 3 , e ) 7 / 9
Rationale: "number x has to be chosen from numbers 1 - 11 ( 9 / x ) > x = > 9 > x ^ 2 = > x ^ 2 - 9 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 11 answer c"
Answer: c
Python program:
a = 12 - 9
b = a / 9
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 600 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 7799 , c ) 2500 , d ) 7500 , e ) 2912
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 600 b capital = 45000 * 1 / 6 = 7500 . answer : d"
Answer: d
Python program:
a = 600 * 100
b = a / 2
Problem: what least number must be subtracted from 427398 so that remaining number is divisible by 15
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) none of these
Rationale: "explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a"
Answer: a
Python program:
a = 427398 / 15
b = math.floor(a)
c = b * 15
d = 427398 - c
Problem: what is the value of 4 ^ 5 + 4 ^ 7 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 )
Rationale: "4 ^ 5 + 4 ^ 7 = 4 ^ 5 ( 1 + 4 ^ 2 ) = 4 ^ 5 * 17 answer c"
Answer: c
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: if 3 eighth of a number is 141 . what will be the approximately value of 32.08 % of this number ?
Options: a ) 119 , b ) 187 , c ) 181 , d ) 120 , e ) 891
Rationale: explanation : x * 3 / 8 = 141 = > x = 376 376 * 32.08 / 100 = 120 answer : d
Answer: d
Python program:
a = 4 + 4 
b = 141 * a
c = b / 3
d = c * 32
e = d / 100
Problem: the number of positive integers valued pairs ( x , y ) ssatisfying 4 x - 17 y = 1 and x < = 1000 ( x is less than or equal to 1000 ) is
Options: a ) fifty nine , b ) 57 , c ) 55 , d ) 58 , e ) 60
Rationale: 4 x - 17 y = 1 y = ( 4 x - 1 ) / 17 x has to be a positive integer such that 1 < = x < = 1000 ( 4 x - 1 ) is a factor of 17 so that y is also a positive integer so we need to know how many numbers in the set { 37 , 1115 , . . . . , 3999 } are divisible by 17 lets try to observe the pattern 1 . 3 mod 17 = 3 2 . 7 mod 17 = 7 3 . 11 mod 17 = 11 4 . 15 mod 17 = 15 5 . 19 mod 17 = 2 6 . 23 mod 17 = 6 7 . 27 mod 17 = 10 8 . 31 mod 17 = 14 9 . 35 mod 17 = 1 10 . 39 mod 17 = 5 11 . 43 mod 17 = 9 12 . 47 mod 17 = 13 13.51 mod 17 = 0 14 . 55 mod 17 = 4 15 . 59 mod 17 = 8 16 . 63 mod 17 = 12 17 . 67 mod 17 = 16 . . . and after this the remainders will repeat ( this is no co - incidence that the cyclicity is also 17 ) so the right choices are x = 1313 + 1713 + 17 + 17 , . . . . . the number of such numbers is 59 ( highest one being 999 ) a
Answer: a
Python program:
a = 4 * 1000
b = a - 1
c = b / 17
d = math.floor(c)
e = d + 1 
f = e / 2
g = f / 2
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 2 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 4
Rationale: "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 2 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 2 ) = 3 / 4 . b ' s 1 hour ' s work = ( 3 / 4 - 1 / 2 ) = 1 / 4 . therefore a alone will take 4 hours to do the work . e"
Answer: e
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 4
d = b - c
e = a - d
f = 1 / e
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 40 % ?
Options: a ) 700 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 40 % of 500 = rs . 200 selling price = cost price + profit = 500 + 200 = 700 answer : a"
Answer: a
Python program:
a = 40 / 100
b = 500 * a
c = 500 + b
Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?
Options: a ) 25 , b ) 75 , c ) 125 , d ) 150 , e ) 175
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) has two appearances of 3 ( in 12 ^ 2 ) and no appearances of 5 . thus n must include at least 3 * 5 ^ 2 = 75 the answer is b ."
Answer: b
Python program:
a = 5 * 2
b = a * 2
c = 5 * 2
d = c * 2
e = b + d 
f = 5 * 2
g = f * 2
h = e + g 
i = h + 2 
j = i + 4 
k = j + 4
Problem: find the compound interest on $ 56,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532 , b ) 2552 , c ) 6524 , d ) 8827 , e ) 9512
Rationale: "principal = $ 56000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 56000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 64827 . ci . = $ ( 64827 - 56000 ) = $ 8827 . answer d ."
Answer: d
Python program:
a = 9 / 100
b = 1 + a 
c = b ** 20
d = 56 * 0
e = d - 56
Problem: the radius of the two circular fields is in the ratio 5 : 4 the area of the first field is what percent greater than the area of the second ?
Options: a ) 22 % , b ) 32 % , c ) 34 % , d ) 64 % , e ) 36 %
Rationale: "r = 5 ï € r 2 = 25 r = 4 ï € r 2 = 16 25 ï € â € “ 9 ï € 100 - - - - ? = > 36 % . answer : d"
Answer: d
Python program:
a = 4 ** 2
b = 5 ** 2
c = a - b
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 250 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 250 * 2 / 5 = $ 100 answer is d
Answer: d
Python program:
a = 3 + 2 
b = 2 / a
c = b * 250
Problem: if n is a natural number , then ( 6 n 2 + 6 n ) is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 both , c ) 12 only , d ) 6 or 12 only , e ) none
Rationale: "( 6 n 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . b )"
Answer: b
Python program:
a = 6 * 100
b = 2 * 6
c = a + b
Problem: how many numbers from 10 to 46 are exactly divisible by 3 ?
Options: a ) 13 , b ) 12 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 . 12 numbers . 10 / 3 = 3 and 46 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits b )"
Answer: b
Python program:
a = 46 / 3
b = math.floor(a)
c = b * 3
d = 10 / 3
e = math.floor(d)
f = e + 1 
g = f * 3
h = c - g
i = h / 3
j = i + 1
Problem: the total number of digits used in numbering the pages of a book having 366 pages is
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 1305 , e ) 1605
Rationale: "explanation : total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 267 ) = ( 9 + 180 + 801 ) = 990 . answer : b"
Answer: b
Python program:
a = 366 * 3
b = 100 - 1
c = a - b
d = 10 - 1
e = c - d
Problem: the sum of three consecutive numbers is 252 . the greatest among these three number is :
Options: a ) 45 , b ) 80 , c ) 85 , d ) 55 , e ) 40
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 252 3 x = 252 x = 83 greatest number , ( x + 2 ) = 85 answer : c"
Answer: c
Python program:
a = 252 + 1 
b = a / 2
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 15 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 45 , e ) 96
Rationale: "d 45 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 45 miles"
Answer: d
Python program:
a = 36 / 2
b = a / 6
c = 15 * b
Problem: how many 3 - digit even numbers are possible such that if one of the digits is 4 , the next / succeeding digit to it should be 7 ?
Options: a ) 305 , b ) 5 , c ) 365 , d ) 405 , e ) 495
Rationale: 470 , 472 , 474 , 476 , and 478 , so total 5 . hence option b .
Answer: b
Python program:
a = 3 + 7 
b = a + 7
Problem: in a public show 45 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 330 , b ) 110 , c ) 120 , d ) 140 , e ) 150
Rationale: 75 % of 600 = 45 / 100 × 600 = 270 therefore , the number of vacant seats = 600 - 270 = 330 . answer : a
Answer: a
Python program:
a = 100 - 45
b = 600 * a
c = b / 100
Problem: if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 2 = 1 / ( ( 10 ) ^ 4 ) , then m =
Options: a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 2
Rationale: 1 / 5 ^ m * 1 / 4 ^ 2 = 1 / 2 ^ 4 * 5 ^ 4 2 ^ 4 * 5 ^ 4 / 2 ^ 4 = 5 ^ m or 5 ^ 4 = 5 ^ m therefore m = 4 a
Answer: a
Python program:
a = 1 / 4
b = a * 10
c = 1 / 5
d = c * 10
e = b + d 
f = 5 / 10
g = e - f
Problem: two workers completed the painting of a building in 10 days . if they were to paint the building separately , how many days will it take each worker , if one of them can complete it in approximately 2 days earlier than the other .
Options: a ) 9 and 11 , b ) 19 and 21 , c ) 8 and 10 , d ) 10 and 15 , e ) 10 and 12
Rationale: work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two workers would complete a job in 10 days . this means that ( individually ) each of them would take more than 10 days to do the job . answers e , a and c are illogical , since the individual times must both be greater than 10 days . so we can test the values for answers b and d . using the values for answers b and d . . . answer b : ( 19 ) ( 21 ) / ( 19 + 21 ) = 399 / 40 = 9.97 this is a match ( complete it in approximately 2 days earlier than the other ) this is a match final answer : b
Answer: b
Python program:
a = 10 * 4
b = a - 2
c = b / 2
d = c * 100
e = 10 * 4
f = e - 2
g = f / 2
h = g + 2 
i = d + h
Problem: frank is 15 years younger then john . in 3 years john will be twice as old as frank . how old will frank be in 4 years ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: frank is 15 years younger then john - - > f + 15 = j ; in 5 years john will be twice as old as frank ( in 3 year john will be j + 3 years old and frank will be f + 3 years old ) - - > j + 3 = 2 * ( f + 3 ) - - > ( f + 15 ) + 3 = 2 * ( f + 3 ) - - > f = 12 ; in 4 years frank will be 12 + 4 = 16 years old . answer : e .
Answer: e
Python program:
a = 2 * 15
b = 15 + 3 
c = a - b
d = c + 4
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 50 vehicles were involved in accidents . if 5 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 800 , b ) 850 , c ) 900 , d ) 500 , e ) 1000
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 50 accidents as 5 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 5,000 million rather than 5 billion . creating a proportion we have : 100 / 50 = 5,000 / x cross multiplying gives us : 100 x = 2,000 * 50 x = 20 * 50 = 1000 answer : e"
Answer: e
Python program:
a = 5 * 10
b = 50 * a
Problem: a man sitting in a train which is traveling at 30 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 82 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 30 ) kmph = 82 kmph . answer : b ."
Answer: b
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 30
Problem: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 72 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 120 , d ) 40 , e ) 150
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 72 + 2 / 3 of 72 80 / 100 x = 120 x = 150 . answer : option e"
Answer: e
Python program:
a = 2 / 3
b = 72 * a
c = 72 + b 
d = 20 / 100
e = 1 - d
f = c / e
Problem: if 4 x + 3 y = 8 and y - 3 x = 8 , then what is the value of x + 4 y ?
Options: a ) 1 / 7 , b ) 16 , c ) 15 , d ) 52 / 7 , e ) 60 / 7
Rationale: "4 x + 3 y = 8 . . . equation 1 - 3 x + y = 8 . . . equation 2 adding both the equations x + 4 y = 16 correct answer option b"
Answer: b
Python program:
a = const_60 + 0 
b = 3 + 4 
c = a / b
d = 8 + 4 
e = 3 + 4 
f = d / e
g = 3 * f
h = g - 4
i = h / 3
j = c * i
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 28 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 677 , c ) 800 , d ) 867 , e ) 932
Rationale: "if mike had scored 28 marks more , he could have scored 30 % therefore , mike required 212 + 28 = 240 marks let the maximum marks be m . then 30 % of m = 240 ( 30 / 100 ) × m = 240 m = ( 240 × 100 ) / 30 m = 24000 / 30 m = 800 answer : c"
Answer: c
Python program:
a = 212 + 28 
b = 30 / 100
c = a / b
Problem: a man can ride on motorcycle at 50 kmph upward road and 100 kmph downward road . he takes 12 hours to ride motorcycle uphill from lower point a to upper point b and back to a . what is the total distance traveled by him in 12 hours ? he must return back to base point a in remaining time .
Options: a ) 1000 , b ) 900 , c ) 800 , d ) 400 , e ) 1200
Rationale: upward distance traveled per hour - 50 km , distance traveled after 8 hours = 400 km . he remained with 4 hours travel downward , i . e . distance traveled in remaining 4 hours downward = 400 km so total distance traveled from a to b and back to point a = 400 km upward + 400 km downhill = 800 km ( answer : c )
Answer: c
Python program:
a = 50 * 100
b = a * 2
c = 50 + 100 
d = b / c
e = d * 12
Problem: 7 machines at a certain factory operate at the same constant rate . if 6 of these machines , operating simultaneously , take 42 hours to fill a certain production order , how many fewer hours does it take all 7 machines , operating simultaneously , to fill the same production order ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the total work is 6 * 42 = 252 machine hours the time required for seven machines is 252 / 7 = 36 hours , thus 6 fewer hours . the answer is d .
Answer: d
Python program:
a = 6 * 42
b = a / 7
c = 42 - b
Problem: what number is obtained by adding the units digits of 734 ^ 99 and 347 ^ 83 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: the units digit of 734 ^ 99 is 4 because 4 raised to the power of an odd integer ends in 4 . the units digit of 347 ^ 83 is 3 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 83 is in the form 4 n + 3 , the units digit is 3 . then 4 + 3 = 7 . the answer is a .
Answer: a
Python program:
a = 99 - 83
b = 1 + 10 
c = 99 / b
d = a - c
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 1 year is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 8400 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) = rs 8400 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 1
d = 8000 * c
Problem: the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 150 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
Options: a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 600
Rationale: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 150 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 150 n = 600 answer = ( e )"
Answer: e
Python program:
a = 3 / 4
b = 1 - a
c = 150 / b
Problem: if x = 4 ^ 16 and x ^ x = 4 ^ k , what is k ?
Options: a ) 4 ^ 14 , b ) 4 ^ 16 , c ) 4 ^ 18 , d ) 4 ^ 20 , e ) 4 ^ 22
Rationale: "solution : we know that x = 4 ^ 16 which implies x ^ x = ( 4 ^ 16 ) ^ ( 4 ^ 16 ) = 4 ^ ( 16 * 4 ^ 16 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 4 ^ ( 4 ^ 2 * 4 ^ 16 ) = 4 ^ ( 4 ^ ( 2 + 16 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 4 ^ ( 4 ^ 18 ) given that x ^ x = 4 ^ k so 4 ^ ( 4 ^ 18 ) = 4 ^ k since the base is same the exponent will also be same therefore k = 4 ^ 18 answer : c"
Answer: c
Python program:
a = 4 ** 16
b = a * 16
Problem: a man can row 5 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 2.25 , b ) 2.35 , c ) 2.45 , d ) 2.55 , e ) 2.65
Rationale: "m = 5 s = 1.2 ds = 5 + 1.2 = 6.2 us = 5 - 1.2 = 3.8 x / 6.2 + x / 3.8 = 1 x = 2.35 . answer : b"
Answer: b
Python program:
a = 5 + 1 
b = 5 - 1
c = a * b
d = 5 + 1 
e = 5 - 1
f = d + e 
g = c / f
h = g * 2
Problem: a taxi company charges $ 1.15 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 / 2 miles , e ) 6 1 / 2 miles
Rationale: if we start out with $ 4.90 and have to spend $ 1.15 for the first quarter - mile , we will have $ 3.75 left to spend on quarter - mile intervals . since $ 3.75 / $ 0.15 = 25 , we can buy 25 more quarter - miles , and will travel 26 quarter miles in all : 26 × 1 / 4 = 6 1 / 2 miles . the correct answer is choice ( e ) .
Answer: e
Python program:
a = 4 - 9
b = a * 100
c = b / 3
d = c / 4
Problem: in a race where 10 cars are running , the chance that car x will win is 1 / 7 , that y will win is 1 / 3 and that z will win is 1 / 5 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 71 / 105 , d ) 21 / 113 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 7 + 1 / 3 + 1 / 5 = 71 / 105 answer : c"
Answer: c
Python program:
a = 1 / 7
b = 1 / 3
c = a + b 
d = 1 / 5
e = c + d
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 20 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50
Rationale: "200 men do the rest of the work in 100 - 20 = 80 days 100 men can do the rest of the work in 80 * 200 / 100 = 160 days required number of days = 160 - 80 = 80 days answer is b"
Answer: b
Python program:
a = 100 - 20
Problem: find the cost of fencing around a circular field of diameter 32 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 132 , c ) 150.9 , d ) 158 , e ) 267
Rationale: "2 * 22 / 7 * 16 = 100.6 100.6 * 1 1 / 2 = rs . 150.9 answer : c"
Answer: c
Python program:
a = 32 / 2
b = circumface * (
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 5 minutes 20 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 50 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 640 secs . his sis ' time = 320 secs . percent increase needed = ( 640 - 320 / 640 ) * 100 = 320 / 640 * 100 = 50 % . ans ( b ) ."
Answer: b
Python program:
a = 10 * 10
b = 5 * const_60
c = b + 20 
d = 10 * const_60
e = d + 40 
f = c / e
g = 1 - f
h = a * g
Problem: how much time does a train 100 metres long running at 72 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 5 s , d ) 7.6 s , e ) 7.4 s
Rationale: explanation : 72 km / hr = 72 * 5 / 18 = 20 m / s speed = distance / time ; v = d / t 20 = 100 / t t = 5 s answer : c
Answer: c
Python program:
a = 100 / 1000
b = a / 72
c = b * 3600
Problem: sahil purchased a machine at rs 12000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24000 , c ) rs . 26000 , d ) rs . 27000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 12000 + 5000 + 1000 = 18000 150 % of 18000 = 150 / 100 * 18000 = 27000 option d"
Answer: d
Python program:
a = 12000 + 5000 
b = a + 1000 
c = 12000 + 5000 
d = c + 1000 
e = d / 100
f = e * 50
g = b + f