euclaise/mathqa_programs huggingface dataset:
Problem: two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer e between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) e = 18 , e ) 20
Rationale: "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Python program:
a = 3 * 2
b = a * 3
Problem: a merchant purchased a jacket for $ 60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "markup = x x = 0.25 ( 60 + x ) = > 3 x / 4 = 15 = > x = 20 so sp = 80 but actual sp = 0.8 * 80 = 64 so profit = $ 4 answer - c"
Answer: c
Python program:
a = 25 / 100
b = 1 - a
c = 60 / b
d = 20 / 100
e = 1 - d
f = c * e
g = f - 60
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 7 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 455 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 7 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 = 7 × 65 = 455 miles correct answer is c ) 455 miles"
Answer: c
Python program:
a = 65 * 7
Problem: the percentage profit earned by selling an article for rs . 1720 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 1875 , d ) 5600 , e ) 3400
Rationale: "then , ( 1720 - x ) / x * 100 = ( x - 1280 ) / x * 100 1720 - x = x - 1280 2 x = 3000 = > x = 1500 required s . p . = 125 % of rs . 1500 = 125 / 100 * 1500 = rs . 1875 . answer c"
Answer: c
Python program:
a = 100 + 25 
b = a / 100
c = 1720 + 1280 
d = c / 2
e = b * d
Problem: a motorcyclist goes from bombay to pune , a distance of 192 kms at an average of 32 kmph speed . another man starts from bombay by car 2 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 10 : 27 , d ) 5 : 4 , e ) 10 : 40
Rationale: "explanation : t = 192 / 32 = 6 h t = 6 - 3 = 3 time ratio = 6 : 3 = 2 : 1 speed ratio = 1 : 2 answer is a"
Answer: a
Python program:
a = 192 / 32
b = 192 / a
c = 192 / 32
d = c - 3
e = 192 / d
f = b / e
Problem: a certain country is divided into 4 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 4 p / 12 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Python program:
a = 4 / 12
b = 4 / 12
c = b + 1 
d = a / c
e = 1 - d
Problem: 12.5 * 3.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 224 , d ) 646 , e ) 742
Rationale: "a 352 ? = 12.5 * 3.2 * 8.8 = 352"
Answer: a
Python program:
a = 12 * 5
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6069 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2100 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6069 = x = 6069 / 2.89 = 2100 therefore , amount invested by raghu is rs . 2100 . answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 10 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 - f
h = e + g 
i = h + 1 
j = 6069 / i
Problem: a train 125 m long passes a man , running at 7 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 50 , c ) 52 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 7 ) km / hr . x - 7 = 45 = = > x = 52 km / hr . answer : c"
Answer: c
Python program:
a = 7 * const_0_2778
b = a * 7
c = 125 - b
d = c / 7
e = d / const_0_2778
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 25,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 60000 , c ) 50000 , d ) 75000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 125000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 125000 - x ) = x / 3 + x / 2 = 62500 = 5 x / 6 = 62500 = x = 62500 x 6 / 5 = 75000 savings in public provident fund = rs . ( 125000 - 75000 ) = rs . 50000 answer is c ."
Answer: c
Python program:
a = 100 * 10
b = a * 100
c = 100 * 10
d = c * 100
e = 2 * 100
f = e * 100
g = d - f
h = b + g 
i = 3 / 2
j = i + 1 
k = 1 / j
l = h * k
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 25 metres of cloth ?
Options: a ) 488 , b ) 204 , c ) 195 , d ) 178 , e ) 133
Rationale: let the required time be x seconds . more metres , more time ( direct proportion ) 0.128 : 25 : : 1 : x 0.128 x = 25 x 1 x = 25 / 0.128 = ( 25 x 1000 ) / 128 x = 195.31 . required time = 195 sec ( approximately ) . answer is c .
Answer: c
Python program:
a = 25 / 0
Problem: the sum of two numbers is 45 . the sum of their quotient and is reciprocal is 2.05 , the product of the numbers is ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: a + b = 45 a / b + b / a = 2.05 = > ( a ^ 2 + b ^ 2 ) / ab = 2.05 = > ( ( a + b ) ^ 2 − 2 ab ) / ab = 2.05 = > ( a + b ) ^ 2 = 2.05 ab + 2 ab = 4.05 ab = > ab = 45 ^ 2 / 4.05 = 500 answer : c
Answer: c
Python program:
a = 2 + 3 
b = 45 * 100
c = b / 10
d = c + 45 
e = a + d
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 15 % of the money for taxi fare and buys 15 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 17.5 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 15 % of 200 = 30 for taxi fare , so he is left with 170 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 70 ( 170 - 100 ) no of oranges he can buy = 70 / 4 = > 17,5 so , george can buy 15 oranges . b"
Answer: b
Python program:
a = 15 / 100
b = 1 - a
c = 15 / 50
d = b - c
e = d * 50
Problem: daal is now being sold at rate rs . 20 a kg . during last month its rate was rs 16 per kg . by how reduce percent should a family its consumption so as to keep the expenditure fixed ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: last month rate = 16 per kg this month rate = 20 per kg if 20 = 100 % then 16 = ? therefore % = ( 16 * 100 ) / 20 = 80 % to reduce consumption 100 - 80 = 20 % answer : b
Answer: b
Python program:
a = 20 / 16
b = 1/(a)
c = b * 100
d = 100 - c
Problem: a certain maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight . a certain green paint contains 10 percent blue pigment and 90 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 1.5 , b ) 2 , c ) 2.5 , d ) 3 , e ) 3.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 3 = 1.5 grams of red pigment
Answer: a
Python program:
a = 100 + 100 
b = 70 / a
c = b * 10
Problem: before 4 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 52 , d ) 60 , e ) 64
Rationale: "a - 4 = 4 ( b - 4 ) - - > a - 4 b = - 12 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 20 - - > a = 3 ( 24 ) = 72 a - b = 72 - 20 = 52 answer : c"
Answer: c
Python program:
a = 4 * 4
b = a - 4
c = 4 * 4
d = c - 4
e = b + d 
f = 4 * e
g = 4 * 4
h = g - 4
i = f - h
j = 4 * 4
k = j - 4
l = 4 * 4
m = l - 4
n = k + m 
o = i - n
Problem: a cricket bat is sold for $ 850 , making a profit of $ 225 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "225 / ( 850 - 225 ) = 225 / 625 = 9 / 25 bit more than 33 % . answer : d"
Answer: d
Python program:
a = 850 - 225
b = 225 / a
c = b * 100
Problem: what is the least number to be added to 661 to make it a perfect square ?
Options: a ) 13 , b ) 15 , c ) 20 , d ) 16 , e ) 45
Rationale: "the numbers greater than 661 and are square of number is 676 . the least number that should be added 661 to make it perfect square = 676 - 661 = 15 . answer : b"
Answer: b
Python program:
a = 12 + 4 
b = a + 2 
c = b / 100
d = 12 + 4 
e = d + 2 
f = e / 100
g = c * f
h = g - 661
Problem: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 40 . he was allowed to drop his lowest score . after doing so , his average test score improved to 45 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 40 . so what we can assume is that we have 4 test scores , each 40 . he dropped his lowest score and the avg went to 45 . this means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 40 . so the lowest score = 40 - 15 = 25 answer ( b )"
Answer: b
Python program:
a = 40 * 4
b = 45 * 3
c = a - b
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 49 , e ) 52
Rationale: "let their ages are 9 x , 15 x and 25 x respectively . difference between the ages of patrick and monica = 25 x - 9 x = 16 x where 49 x = 147 or x = 3 so diff in ages = 16 x = 16 * 3 = 48 yrs answer : a"
Answer: a
Python program:
a = 5 * 5
b = 3 * 3
c = 3 * 5
d = b + c 
e = 5 * 5
f = d + e 
g = 147 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k 
m = 5 * 5
n = l + m 
o = 147 / n
p = i * o
q = h - p
Problem: if the price of a certain bond on may 1 st was 2 / 3 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 2 / 3 * 12 = 8 ; the price on july 1 st = 8 * 1.50 = 12 . the average price of the bond on may 1 st and july 1 st = ( 8 + 12 ) / 2 = 10 . the price of the bond on june 1 st ( 12 ) is 6 / 5 times ( 120 % ) the average price of the bond on may 1 st and july 1 st . answer : c ."
Answer: c
Python program:
a = 50 * const_0_33
b = 100 + const_0_33 
c = a + b
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 252 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 5.5 , e ) 8
Rationale: "required run rate = 252 - ( 3.2 x 10 ) = 220 = 5.5 40 40 d"
Answer: d
Python program:
a = 3 * 2
b = 252 - a
c = b / 40
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 48 = 21 $ ( 21 / 69 ) * 100 = 30.434 % answer : b"
Answer: b
Python program:
a = 69 - 0
b = a / 69
c = b * 100
Problem: a and b started a business investing rs . 90,000 and rs 30,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 1 , c ) 18 : 20 , d ) 18 : 4 , e ) 17 : 4
Rationale: "a : b = 90000 : 30000 = 9 : 3 = 3 : 1 answer : b"
Answer: b
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 2 
f = 3 * 3
g = f + 1 
h = 2 * g
i = e / h
Problem: what is the time required for a bike to cover a distance of 450 km with a speed of 90 kmh ?
Options: a ) 5 hours , b ) 3 hours , c ) 8 hours , d ) 6 hours , e ) 4 hours
Rationale: time = distance / speed time = 450 / 90 = 5 answer : a
Answer: a
Python program:
a = 450 / 90
Problem: how many even multiples of 25 are there between 249 and 501 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "250 = 10 * 25 500 = 20 * 25 the even multiples are 25 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Python program:
a = 501 - 249
b = 25 * 2
c = a / b
d = c + 1
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 8 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 64 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 8 = 128 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 128 pi / 200 pi = 0.64 a"
Answer: a
Python program:
a = 8 / 10
b = a ** 2
c = 8 / 8
d = b * c
e = d * 100
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors c ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have c = 2 * 3 * 5 * 7 = 840 thus , answer b"
Answer: b
Python program:
a = 1 + 4 
b = 60 / 2
c = b / 2
d = c / 3
e = a / d
f = e + 2
Problem: if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 150 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) − 80 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 150 = = = > b + c = 300 ( a + b ) - ( b + c ) = 220 - 300 = = = > a + b - b - c = - 80 = = = > a - c = - 80 answer : d"
Answer: d
Python program:
a = 150 * 2
b = 110 * 2
c = a - b
Problem: the average of marks obtained by 120 boys was 40 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 125 , d ) 130 , e ) 145
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 40 24 x = 4800 - 1800 = > x = 3000 / 24 x = 125 hence , the number of boys passed = 125 . answer : c"
Answer: c
Python program:
a = 40 * 120
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
Problem: in a group of 27 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 6
Rationale: "a 7 add 7 + 10 + 4 to get 21 . then subtract 21 from the total students ⇒ 27 – 21 = 6 . answer is e"
Answer: e
Python program:
a = 7 + 10 
b = 27 - a
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 4,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 11,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 4,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 4,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 320 = 0.10 x combine terms and subtract 0.08 x from both sides : 230 = 0.02 x divide both sides by 0.02 : 11,500 = x your answer is a ."
Answer: a
Python program:
a = 8 / 100
b = 4 * 0
c = 550 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 4
i = math.floor(h)
Problem: the points a ( 0 , 0 ) , b ( 0 , 4 a - 4 ) and c ( 2 a + 1 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 88 , b ) 98 , c ) 108 , d ) 78 , e ) 90
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 6 ) now 4 a - 4 = 2 a + 6 2 a = 10 , a = 5 therefore , a ( 0,0 ) ; b ( 0,16 ) ; c ( 11,16 ) 1 / 2 * 11 * 16 = 88 answer : a"
Answer: a
Python program:
a = 6 + 4 
b = a / 4
c = b * 4
d = c - 4
e = 6 + 4 
f = e / 4
g = 4 - 4
h = f * g
i = h + 1 
j = d * i
k = j / 4
Problem: machine a takes 100 hours to complete a certain job and starts that job at 7 am . after two hour of working alone , machine a is joined by machine b and together they complete the job at 6 pm . how long would it have taken machine b to complete the jobif it had worked alone for the entire job ?
Options: a ) 10.11 , b ) 9.99 , c ) 11.1 , d ) 44.11 , e ) 1.01
Rationale: "let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 2 hr ( so 2 units done ) then a and b finish total work in 15 hours . hence a and b finish 98 units in 9 hours . of these 1 x 9 = 9 units were done by a . hence b did 89 units in 9 hours . hence b ( working rate ) = 89 / 9 units / hr hence b takes 100 x 9 / 89 = 10.11 hours to complete the job . answer a ."
Answer: a
Python program:
a = 1/(100)
b = a * 2
c = 1 - b
d = 6 * 2
e = d - 7
f = e - 2
g = c / f
h = 1/(100)
i = g - h
j = 1/(i)
Problem: average age of students of an adult school is 46 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 120 , c ) 360 , d ) 168 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 46 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 48 so , required no . of students after joining the new students = x + 120 = 168 . answer : d"
Answer: d
Python program:
a = 32 + 4 
b = a * 120
c = 120 * 32
d = b - c
e = 32 + 4 
f = 46 - e
g = d / f
h = g * 4
Problem: on a map , 3.5 inches represent 35 miles . how many miles approximately is the distance if you measured 127 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 515 , b ) 500 , c ) 525 , d ) 530 , e ) 535
Rationale: "1 inch = 2.54 cm 3.5 inch = 2.54 * 3.5 cm 8.89 cm = 35 miles 127 cms = 35 / 8.89 * 127 = 500 miles answer : b"
Answer: b
Python program:
a = 127 / 2
b = 35 / 3
c = a * b
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length ?
Options: a ) 16.5 , b ) 16.0 , c ) 15 , d ) 16.8 , e ) 16.1
Rationale: "d = 110 + 140 = 250 m s = 60 * 5 / 18 = 50 / 3 t = 250 * 3 / 50 = 15 sec answer : c"
Answer: c
Python program:
a = 110 + 140 
b = 60 * const_0_2778
c = a / b
Problem: if the product of two numbers is 51216 and their h . c . f . is 33 , find their l . c . m .
Options: a ) 600 , b ) 680 , c ) 582 , d ) 560 , e ) none of these
Rationale: "explanation : hcf * lcm = 51216 , because we know product of two numbers = product of hcf and lcm lcm = 51216 / 88 = 582 option c"
Answer: c
Python program:
a = 51216 / 33
Problem: at an elementary school , 70 % of the faculty members are women and 40 % of the faculty members are married . if 1 ⁄ 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 2 / 7 , d ) 7 ⁄ 30 , e ) 5 ⁄ 70
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 20 - - - - - 20 - - - - - - - - - 40 not married - - - - - 10 - - - - - 50 - - - - - - - - - 60 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married woman / total woman , so 20 / 70 = 2 / 7 c"
Answer: c
Python program:
a = 1 / 3
b = 1 - a
Problem: a train which has 300 m long , is running 80 kmph . in what time will it cross a person moving at 16 kmph in same direction ?
Options: a ) 25 sec , b ) 35 sec , c ) 15 sec , d ) 45 sec , e ) 20 sec
Rationale: time taken to cross a moving person = length of train / relative speed time taken = 300 / ( ( 80 - 16 ) ( 5 / 18 ) = 300 / 64 * ( 5 / 18 ) = 300 / 20 = 15 sec answer : c
Answer: c
Python program:
a = 80 / const_3_6
b = 16 / 2
c = b / const_3_6
d = a - c
e = 300 / d
Problem: what is the number of integers from 1 to 500 ( inclusive ) that are divisible by neither 10 nor by 15 ?
Options: a ) 170 , b ) 250 , c ) 300 , d ) 560 , e ) 420
Rationale: in 500 consecutive numbers , number of multiples of 10 = 500 / 10 = 50 ( ignore decimals ) in 500 consecutive numbers , number of multiples of 15 = 500 / 15 = 33 number of multiples of 10 * 15 i . e . 150 = 500 / 150 = 3 number of integers from 1 to 500 that are divisible by neither 10 nor by 15 = 500 - ( 50 + 33 - 3 ) { using the concept of sets here ) = 420 answer is e
Answer: e
Python program:
a = 500 / 10
b = 500 / 15
c = a + b 
d = 10 * 15
e = 500 / d
f = c - e
g = 500 - f