euclaise/mathqa_programs huggingface dataset:
Problem: what will be the difference between simple and compound interest at 10 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) rs . 31 , b ) rs . 32.10 , c ) rs . 40.40 , d ) rs . 64.10 , e ) rs . 74.10
Rationale: "s . i . = ( 1000 * 10 * 4 ) / 100 = rs . 400 c . i . = [ 1000 * ( 1 + 10 / 100 ) 4 - 1000 ] = rs . 464.10 difference = ( 464.10 - 400 ) = rs . 64.10 answer : d"
Answer: d
Python program:
a = 10 / 100
b = a + 1 
c = b ** 4
d = 1000 * c
e = d - 1000
f = 10 / 100
g = 1000 * f
h = g * 4
i = e - h
Problem: 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 50 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 100 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 12 ( 44 - 12 ) must be those with four screens or more a is the answer
Answer: a
Python program:
a = 20 / 100
b = 20 / 100
c = b * 300
d = a * c
Problem: a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 28 , b ) 50 , c ) 77 , d ) 22 , e ) 12
Rationale: "speed of the train relative to man = ( 200 / 10 ) m / sec = ( 20 ) m / sec . [ ( 20 ) * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 72 = = > x = 77 km / hr . answer : c"
Answer: c
Python program:
a = 5 * const_0_2778
b = a * 5
c = 200 - b
d = c / 5
e = d / const_0_2778
Problem: if there are 156 laborers in a crew , and on a certain day , 70 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 45.9 % , b ) 43.9 % , c ) 42.9 % , d ) 41.9 % , e ) 44.9 %
Rationale: "70 / 156 * 100 = 44.87 44.9 % correct answer e"
Answer: e
Python program:
a = 70 * 100
b = a / 156
Problem: a work can be finished in 16 days by 30 women . the same work can be finished in 10 days by sixteen men . the ratio between the capacity of a man and a woman is
Options: a ) 3 : 1 , b ) 4 : 3 , c ) 2 : 3 , d ) 2 : 1 , e ) 2 : 4
Rationale: "work done by 30 women in 1 day = 1 / 16 work done by 1 woman in 1 day = 1 / ( 16 × 30 ) work done by 16 men in 1 day = 1 / 10 work done by 1 man in 1 day = 1 / ( 10 × 16 ) ratio of the capacity of a man and woman = 1 / ( 10 × 16 ) : 1 / ( 16 × 30 ) = 1 / 10 : 1 / 30 = 1 / 1 : 1 / 3 = 3 : 1 option a"
Answer: a
Python program:
a = 16 + 2 
b = a * 10
c = 1 / b
d = 16 * 10
e = 1 / d
f = c / e
Problem: the ratio of numbers is 4 : 5 and their h . c . f is 4 . their l . c . m is :
Options: a ) 80 , b ) 16 , c ) 24 , d ) 48 , e ) 98
Rationale: "let the numbers be 4 x and 5 x . then their h . c . f = x . so , x = 4 . so , the numbers are 16 and 20 . l . c . m of 16 and 20 = 80 . answer : a"
Answer: a
Python program:
a = 4 * 4
b = 5 * 4
c = math.lcm(a, b)
Problem: length of a rectangular plot is 12 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 56 m
b ) 60 m
c ) 80 m
d ) 82 m
e ) 84 m
Rationale: let breadth = x metres . then , length = ( x + 12 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 12 ) + x ] = 200 2 x + 12 = 100 2 x = 88 x = 44 hence , length = x + 12 = 56 m a
Answer: a
Python program:
a = 5300 / 26
b = 2 * 12
c = a + b 
d = c / 4
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 65 km more than the other . what is the distance between the two stations ?
Options: a ) 585 km , b ) 767 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 65 km more than the other , 25 x â € “ 20 x = 65 5 x = 65 x = 13 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 13 = 585 km . answer : a"
Answer: a
Python program:
a = 20 + 25 
b = 25 - 20
c = 65 / b
d = a * c
Problem: what is the length of a bridge ( in meters ) , which a train 140 meters long and travelling at 45 km / h can cross in 30 seconds ?
Options: a ) 205 , b ) 220 , c ) 235 , d ) 250 , e ) 265
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 140 = 235 meters the answer is c ."
Answer: c
Python program:
a = 45 * const_0_2778
b = a * 30
c = b - 140
Problem: a train crosses a platform of 140 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 190 , b ) 88 , c ) 77 , d ) 62 , e ) 52
Rationale: length of the train be â € ˜ x â € ™ x + 140 / 15 = x + 250 / 20 4 x + 560 = 3 x + 750 x = 190 m answer : a
Answer: a
Python program:
a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 140 * e
g = c - f
Problem: what is the sum of the integers from - 170 to 171 , inclusive ?
Options: a ) 181 , b ) 171 , c ) 191 , d ) 201 , e ) 202
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 171 , a = - 170 , d = 1 hence , 171 = - 170 + ( n - 1 ) or n = 342 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 342 * ( - 170 + 171 ) / 2 sn = 342 * 1 / 2 sn = 171 answer : b"
Answer: b
Python program:
a = 170 * 171
b = a / 4
Problem: if 7 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 21 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 7 * 6 / 2 = 21 answer : a"
Answer: a
Python program:
a = math.factorial(7)
b = 7 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: a sum was put a simple interest at a certain rate for 3 years . had it been put at 3 % higher rate , it would have fetched rs . 90 more . the sum is :
Options: a ) s . 750 , b ) s . 900 , c ) s . 1000 , d ) s . 1200 , e ) s . 1500
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 3 ) ã — 3 / 100 â ˆ ’ x ã — r ã — 3 / 100 = 90 â ‡ ’ x ã — 3 ã — 3 / 100 = 90 â ‡ ’ x ã — 3 / 100 = 30 â ‡ ’ 3 x = 3000 â ‡ ’ x = 1000 answer : option c"
Answer: c
Python program:
a = 90 / 3
b = a / 3
c = b * 100
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 8.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be a .
Answer: a
Python program:
a = 5 - 1
b = 0 * 25
c = b + 0
Problem: find the ratio in which rice at rs . 7.00 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 6 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 70 = 6 : 7 answer : a"
Answer: a
Python program:
a = 6 - 30
b = 7 - 0
c = a / b
Problem: if the lcm and hcf of 4 and another number is 36 and 2 respectively . find the other number ?
Options: a ) 18 , b ) 16 , c ) 14 , d ) 13 , e ) 15
Rationale: hcf x lcm = product of numbers 2 x 36 = 4 x the other number other number = ( 2 x 36 ) / 4 other number = 18 answer : a
Answer: a
Python program:
a = 36 * 2
b = a / 4
Problem: a certain car uses one gallon of gasoline every 40 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 50 %
Rationale: "4 miles on the highway = 4 / 40 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 40 + 4 / 20 = 3 / 10 gallons . 8 miles on the highway = 8 / 40 gallons . the % change = ( 3 / 10 - 8 / 40 ) / ( 8 / 40 ) = 1 / 2 = 0.50 . answer : e ."
Answer: e
Python program:
a = 1 / 20
b = a * 4
c = 1 / 40
d = 4 * c
e = b + d 
f = 1 / 40
g = 8 * f
h = e - g
i = 1 / 40
j = 8 * i
k = h / j
l = k * 100
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 864 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 668 , d ) s . 700 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 864 - 815 ) = rs . 49 . s . i . for 3 years = rs . ( 49 x 3 ) = rs . 147 . principal = rs . ( 815 - 147 ) = rs . 668 . answer : option c"
Answer: c
Python program:
a = 864 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: the breadth of a rectangular hall is two - thirds of its length . if the area of the hall is 2400 sq metres , what is the length in metres ?
Options: a ) 120
b ) 80
c ) 60
d ) 40
e ) none of these
Rationale: let the length of the rectangular hall be ‘ x ’ m , then the breadth of the rectangular hall = 2 x ⁄ 3 m . area of hall = 2 x ⁄ 3 × x = 2 x 2 ⁄ 3 or , 2 x 2 ⁄ 3 = 2400 or x = 60 m answer c
Answer: c
Python program:
a = 2 / 3
b = 2400 / a
c = math.sqrt(b)
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.50 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,650 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5.5 $ then total value is 300 * 5.5 = 1650 . imo option c is correct answer . ."
Answer: c
Python program:
a = 3 * 100
b = 8 * 10
c = a + b 
d = c + 4 
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 5
j = i / 1000
Problem: find √ ? / 18 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 5184 , e ) none
Rationale: "answer let √ n / 18 = 4 then √ n = 18 x 4 = 72 ∴ n = 72 x 72 = 5184 . correct option : d"
Answer: d
Python program:
a = 4 * 18
b = a ** 2
Problem: the population of a city increases by 6 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 15.76 % , e ) none of these
Rationale: actual increase in population = 5 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 5 / 100 ) ^ 3 = 115.7625 ∴ required percentage = 15.7625 % answer : d
Answer: d
Python program:
a = 6 - 1
b = 100 + a 
c = 6 - 1
d = b * c
e = d / 100
f = 6 - 1
g = e + f 
h = 100 + g 
i = 6 - 1
j = h * i
k = j / 100
l = 6 - 1
m = 100 + l 
n = 6 - 1
o = m * n
p = o / 100
q = 6 - 1
r = p + q 
s = k + r
Problem: find the average of all the numbers between 6 and 34 which are divisible by 6 .
Options: a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 21
Rationale: "solution average = ( ( 12 + 18 + 24 + 30 ) / 5 ) = 84 / 4 = 21 . answer e"
Answer: e
Python program:
a = 6 + 4 
b = 34 - 4
c = a + b 
d = c / 2
Problem: a can do a piece of work in 3 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 6 hours , b ) 3 hours , c ) 2 hours , d ) 5 hours , e ) 4 hours
Rationale: "a ' s 1 hour work = 1 / 3 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 3 + 1 / 2 ) = 5 / 6 b ' s 1 hour work = ( 5 / 6 - 1 / 2 ) = 1 / 3 b alone will take 3 hours to do the work . answer : b"
Answer: b
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 3
d = b - c
e = a - d
f = 1 / e
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is ?
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) 5 : 2
Rationale: "answer : option b let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 16 : â ˆ š 9 = 4 : 3"
Answer: b
Python program:
a = math.sqrt(16)
b = math.sqrt(9)
c = a / b
Problem: at what rate percent on simple interest will rs . 650 amount to rs . 950 in 5 years ?
Options: a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 9.23 %
Rationale: "300 = ( 650 * 5 * r ) / 100 r = 9.23 % answer : e"
Answer: e
Python program:
a = 950 - 650
b = a / 650
c = b / 5
d = c * 100
Problem: a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and the other digits are correct , then the correct answer would be :
Options: a ) 288889 , b ) 556677 , c ) 555681 , d ) 267788 , e ) 268811
Rationale: "explanation : 987 = 3 * 7 * 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 = > ( sum of digits = 28 , not divisible by 3 ) 555181 = > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by each one of 3 , 7 , 47 . answer : c ) 555681"
Answer: c
Python program:
a = 559981 / 987
b = a - 4
c = b - const_0_33
d = c * 987
Problem: when leo imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that leo paid was $ 87.50 , what was the total value of the item ?
Options: a ) $ 1600 , b ) $ 1850 , c ) $ 2250 , d ) $ 2400 , e ) $ 2750
Rationale: let the value of the item be $ x , then 0.07 ( x − 1000 ) = 87.5 - - > x − 1000 = 1250 x − 1000 = 1250 - - > x = 2250 . answer : c .
Answer: c
Python program:
a = 7 / 100
b = 87 / 5
c = b + 1000
Problem: the annual interest rate earned by an investment increased by 6 percent from last year to this year . if the annual interest rate earned by the investment this year was 15.90 percent , what was the annual interest rate last year ?
Options: a ) 20 % , b ) 18 % , c ) 16 % , d ) 25 % , e ) 15 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.06 i ( last year ) = 1.06 i ( last year ) 15.90 = 1.06 x i ( last year ) i ( last year ) = 15.90 / 1.06 = 1590 / 106 = 15 % answer : e"
Answer: e
Python program:
a = 15 * 90
b = 15 + 90 
c = a / b
Problem: john and steve are speed walkers in a race . john is 12 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 28 seconds
Rationale: let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 12 + 2 - - - > 0.5 t = 14 - - - > t = 28 seconds . e is the correct answer .
Answer: e
Python program:
a = 12 + 2 
b = 3 * 7
c = 4 - 2
d = b / c
e = 12 + 2 
f = d + e 
g = f / 4
Problem: i chose a number and divide it by 6 . then i subtracted 189 from the result and got 3 . what was the number i chose ?
Options: a ) 1200 , b ) 1152 , c ) 1189 , d ) 1190 , e ) 100
Rationale: "let x be the number i chose , then x / 6 − 189 = 3 x / 6 = 192 x = 1152 answer is b ."
Answer: b
Python program:
a = 189 + 3 
b = a * 6
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 400 more . what was the sum ?
Options: a ) s . 1200 , b ) s . 800 , c ) s . 1400 , d ) s . 1000 , e ) s . 920
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 400 ( given ) so , at 5 % more rate , the increase in si for 1 year = 400 / 10 = rs . 40 / - i . e . rs . 40 is 5 % of the invested sum so , 1 % of the invested sum = 40 / 5 therefore , the invested sum = 40 × 100 / 5 = rs . 800 answer : b"
Answer: b
Python program:
a = 5 / 100
b = a * 10
c = 400 / b
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m ?
Options: a ) 29798 , b ) 27908 , c ) 78902 , d ) 26000 , e ) 27991
Rationale: "26 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 26 = 1 / 1000 * x = > x = 26000 answer : d"
Answer: d
Python program:
a = 26 * 100
b = 2 * 100
c = a * b
d = 0 * 75
e = c * d
f = e / 20
g = f / 10
h = g / 7
Problem: the product of two successive numbers is 462 . which is the smaller of the two numbers ?
Options: a ) 21 , b ) 23 , c ) 26 , d ) 27 , e ) 29
Rationale: a 21 from the given alternatives , 21 × 22 = 462 ∴ smaller number = 21
Answer: a
Python program:
a = math.sqrt(462)
Problem: in a group of ducks and cows , the total number of legs are 30 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "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 ) = 30 + 2 ( c + d ) = > d + 2 c = 15 + c + d = > 2 c = 15 + c = > c = 15 i . e . , total number of cows = 15 answer is b ."
Answer: b
Python program:
a = 30 / 2
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is ?
Options: a ) 40 meter , b ) 45 meter , c ) 50 meter , d ) 55 meter , e ) none of these
Rationale: "explanation : let the length of each train is x meter distance will be x + x = 2 x relative speed = 46 - 36 = 10 km / hr = 10 * ( 5 / 18 ) = 25 / 9 m / sec distance = speed * time 2 x = 25 / 9 ∗ 36 2 x = 100 = > x = 50 so length of both the trains are 50 meters option c"
Answer: c
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 36
e = d / 2
Problem: if a ' s height is 25 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 33.33 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 25 / ( 100 - 25 ) ] x 100 % = 33.33 % answer : d )"
Answer: d
Python program:
a = 100 - 25
b = 25 / a
c = b * 100
Problem: the tax on a commodity is diminished by 24 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 76 * 112 = 8512 10000 - - - - - - - 1488 100 - - - - - - - ? = 15 % answer : c"
Answer: c
Python program:
a = 100 + 12 
b = 100 - 24
c = a * b
d = c / 100
e = 100 - d
Problem: a and b can do a piece of work in 6 2 / 3 days and 5 days respectively . they work together for 2 days and then a leaves . in how many days after that b will complete the work alone .
Options: a ) 6 â ½ days , b ) 1 â ½ days , c ) 8 â ½ days , d ) 5 â ½ days , e ) 2 â ½ days
Rationale: "explanation : 3 / 20 * 2 + ( 2 + x ) / 5 = 1 x = 1 â ½ days answer : b"
Answer: b
Python program:
a = 1/(5)
b = 2 / 3
c = 6 + b 
d = 1/(c)
e = a + d 
f = 2 - e
g = 5 * f
Problem: convert the 13 / 48 m / s into kilometers per hour ?
Options: a ) 1.5 kmph . , b ) 0.91 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 0.98 kmph .
Rationale: "13 / 48 m / s = 13 / 48 * 18 / 5 = 49 / 50 = 0.98 kmph . answer : e"
Answer: e
Python program:
a = 13 / 48
b = const_3_6 * a
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?
Options: a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 50 cm
Rationale: "let bresdth x cm length = 2 x cm new l = ( 2 x - 5 ) cm new breadth = ( x + 5 ) new area = ( 2 x - 5 ) sq cm = ( 2 x - 5 ) ( x + 5 ) = 2 x 2 + 75 x = 20 cm l = 2 x - 2 = 2 * 20 = 40 cm answer c"
Answer: c
Python program:
a = 100 / 3
Problem: there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 6 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?
Options: a ) 3 / 5 , b ) 7 / 15 , c ) 11 / 15 , d ) 19 / 30 , e ) 23 / 30
Rationale: "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 30 / 30 - 5 / 30 - 6 / 30 = 19 / 30 the answer is d ."
Answer: d
Python program:
a = 1 / 6
b = 1 / 5
c = a + b 
d = 1 - c
Problem: what is the average of first 21 multiples of 7 ?
Options: a ) 67 , b ) 69 , c ) 77 , d ) 79 , e ) 81
Rationale: "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 7 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 77 c"
Answer: c
Python program:
a = 21 + 1 
b = 21 * a
c = b / 2
d = c / 21
e = d * 7
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 14 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 5 , e ) 9
Rationale: "answer is d . x / x + 36 = 1 / 5 x = 9 14 - 9 = 5"
Answer: d
Python program:
a = 20 / 100
b = a * 20
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 25 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 55 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 25 / 5 = 5 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 5 = 55 secs . answer : b"
Answer: b
Python program:
a = 6 - 1
b = 25 / a
c = 12 - 1
d = b * c
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "q 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b
Problem: two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 2 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 3 1 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 2 ½ h . d = 5 / 4 * 5 / 2 = 25 / 8 = 3 1 / 8 km answer : c"
Answer: c
Python program:
a = 1 / 2
b = 2 + a 
c = 3 / 4
d = 5 + c 
e = 1 / 2
f = 4 + e 
g = d - f
h = b * g
i = h + 2
Problem: if an object travels at 85 feet per second , how many feet does it travel in 30 minutes ?
Options: a ) 3000 , b ) 1500 , c ) 1800 , d ) 9000 , e ) 2500
Rationale: "if an object travels at 85 feet per second it covers 85 x 60 feet in one minute , and 5 x 60 x 30 feet in 30 minutes . answer = 9000 answer : d"
Answer: d
Python program:
a = 3 * const_60
b = a * const_60
Problem: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a"
Answer: a
Python program:
a = 14 - 10
b = 20 / a
c = 10 * b