euclaise/mathqa_programs huggingface dataset:
Problem: pr is tangent to a circle at point p . q is another point on circle such that pq is diameter of circle and rq cuts circle at m . if radius of circle is 4 units and pr = 6 units . find ratio of triangle pmr to pqr .
Options: a ) 11 / 20
b ) 3 / 5
c ) 13 / 20
d ) 18 / 25
e ) 18 / 26
Rationale: let pm = y qm = x mr = 10 - x in triangle pqm , pm ^ 2 + qm ^ 2 = pq ^ 2 = > x ^ 2 + y ^ 2 = 64 . . . . . ( 1 ) in triangle pmr , pm ^ 2 + mr ^ 2 = pr ^ 2 y ^ 2 + ( 10 - x ) ^ 2 = 36 . . . . . . ( 2 ) solving for x and y x = 6.4 y = 4.8 taking permineter of triangle pqr = 24 perimeter of triangle pmr = 14.4 take ratio 14.4 / 24 = 0.6 answer : c
Answer: c
Python program:
a = 4 * 2
b = a * 6
c = 4 * 2
d = c ** 2
e = 6 ** 2
f = d + e 
g = math.sqrt(f)
h = b / g
i = 6 * 6
j = 4 * 2
k = i / j
l = triangle_perimeter / (
Problem: if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by :
Options: a ) 6 , b ) 12 , c ) 24 , d ) 6 only , e ) 6 and 12 both
Rationale: explanation : ( 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 . e
Answer: e
Python program:
a = 6 * 100
b = 2 * 6
c = a + b
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 17 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 391 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 17 ) . larger number = ( 23 x 17 ) = 391 . answer : option c"
Answer: c
Python program:
a = 23 * 17
Problem: a rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet . if the surface of the rug does not extend beyond the area of the floor , what fraction of the area of the floor is not covered by the rug ?
Options: a ) a . 3 / 16
b ) 1 / 4
c ) c . 1 / 2
d ) 25 / 32
e ) 7 / 8
Rationale: area of the rectangular rug = 2 * 7 = 14 fraction not covered by the rug = ( total area - rug area ) / total area = ( 64 - 14 ) / 64 = 25 / 32 = d
Answer: d
Python program:
a = 2 * 7
b = 64 - a
c = b / 64
Problem: find the value of ( 55 + 113 / 78 ) × 78
Options: a ) 4423 , b ) 4403 , c ) 4413 , d ) 2403 , e ) 4375
Rationale: "= ( 55 + 113 / 78 ) × 78 = ( 4290 + 113 ) / 78 × 78 = 4403 / 78 × 78 = 4403 answer is b ."
Answer: b
Python program:
a = 113 / 78
b = a + 55 
c = b * 78
Problem: if two typists can type two pages in two minutes , how many typists will it take to type 25 pages in 5 minutes ?
Options: a ) 3 , b ) 4 , c ) 10 , d ) 12 , e ) 36
Rationale: in 2 minutes 2 typists type 2 pages which means that in 5 minutes they will type 5 pages but to type 25 pages ( 5 times ) we need 5 times more typists i . e . 2 x 5 = 10 typists . c
Answer: c
Python program:
a = 1 / 2
b = 25 / a
c = b / 5
Problem: the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 11 years
Rationale: "given that a + b = 11 + b + c = > a â € “ c = 11 + b â € “ b = 11 = > c is younger than a by 11 years answer : e"
Answer: e
Python program:
a = 11 * 1
Problem: n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 12 ?
Options: a ) 12 , b ) 6 , c ) 14 , d ) 16 , e ) 10
Rationale: n ^ ( n / 2 ) = 12 apply log n / 2 logn = log 12 nlogn = 2 log 12 = log 12 ^ 2 = log 144 logn = log 144 now apply antilog n = 144 / n now n = 12 answer : a
Answer: a
Python program:
a = 12 ** 2
b = a / 12
Problem: a sum of money at simple interest amounts to rs . 800 in 3 years and to rs . 850 in 4 years . the sum is :
Options: a ) rs . 670 , b ) rs . 690 , c ) rs . 600 , d ) rs . 625 , e ) rs . 654
Rationale: "explanation : s . i . for 1 year = rs . ( 850 - 800 ) = rs . 50 . s . i . for 3 years = rs . ( 50 x 3 ) = rs . 150 . principal = rs . ( 800 - 150 ) = rs . 600 . answer : option c"
Answer: c
Python program:
a = 850 - 800
b = a * 3
c = b / 4
d = 800 - c
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? e"
Answer: e
Python program:
a = 3 * 10
b = 150 + a
Problem: if y is the smallest positive integer such that 4410 multiplied by y is the square of an integer , then y must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 10
Rationale: 4410 = 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 2 * 5 = 10 . the answer is e .
Answer: e
Python program:
a = 2 + 3 
b = a * 2
Problem: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 20 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 35 , b ) 42 , c ) 44 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 20 / 17 - - > the least positive value of p + 1 is 20 , so the least value of p is 19 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 19 + 16 = 35 . answer : a"
Answer: a
Python program:
a = 20 + 17 
b = a - 2
Problem: a portion of the 80 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 50 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.8 ( 1 - x ) + 0.2 * x = 0.5 - - > x = 1 / 2 . answer : b ."
Answer: b
Python program:
a = 80 - 50
b = 80 - 20
c = a / b
Problem: the maximum number of students among them 1008 pens and 928 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 16 , b ) 18 , c ) 36 , d ) 19 , e ) 32
Rationale: "number of pens = 1008 number of pencils = 928 required number of students = h . c . f . of 1008 and 928 = 16 answer is a"
Answer: a
Python program:
a = math.gcd(1008, 928)
Problem: lilly has 10 fish and rosy has 12 fish . in total , how many fish do they have in all ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: 10 + 12 = 22 the answer is c .
Answer: c
Python program:
a = 10 + 12
Problem: what is the least common multiple of 6 , 18 , and 24 ?
Options: a ) 72 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 6 = 2 * 3 18 = 2 * 3 ^ 2 24 = 2 ^ 3 * 3 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 72 option a"
Answer: a
Python program:
a = 10 + 2 
b = 3 * 10
c = b - 3
d = math.lcm(a, c)
e = math.lcm(d, 18)
Problem: the ratio of number of boys and girls in a school is 2 : 5 . if there are 420 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 420 number of girls in the school = 5 * 420 / 7 = 300 answer is c"
Answer: c
Python program:
a = 420 / 3
b = a * 2
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 20 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 15 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: speed = 100 / 1 = 100 km / hr new speed = 100 - 20 = 80 km / hr time taken = 100 / 80 = 1 hr 15 min answer is b
Answer: b
Python program:
a = 100 / 1
b = a - 20
c = 100 / b
Problem: a bag contains 3 red , 4 black and 2 white balls . what is the probability of drawing a red and a white ball in two successive draws , each ball being put back after it is drawn ?
Options: a ) 2 / 27 , b ) 1 / 9 , c ) 1 / 3 , d ) 4 / 27 , e ) 2 / 9
Rationale: p = 2 ∗ 39 ∗ 29 = 427 p = 2 ∗ 39 ∗ 29 = 427 we are multiplying by 2 as there are two possible wining scenarios rw and wr . answer : d .
Answer: d
Python program:
a = 3 + 4 
b = a + 2 
c = 3 / b
d = 3 + 4 
e = d + 2 
f = 2 / e
g = c * f
h = g * 2
Problem: last year sandy saved 10 % of her annual salary . this year , she made 10 % more money than last year , and she saved 15 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 142 % , b ) 150 % , c ) 165 % , d ) 176 % , e ) 188 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.1 x this year , sandy saved 0.15 * 1.1 x = 0.165 x 0.165 x / 0.1 x = 1.65 = 165 % the answer is c ."
Answer: c
Python program:
a = 15 / 100
b = 100 + 10 
c = a * b
d = 10 * 100
e = d / 100
f = c / e
g = f * 100
Problem: the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate t , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate
Rationale: "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e"
Answer: e
Python program:
a = 840 / 0
Problem: the difference between the place values of 7 and 3 in the number 527435 is
Options: a ) 4 , b ) 5 , c ) 45 , d ) 6970 , e ) none
Rationale: "sol . = ( place value of 7 ) – ( place value of 3 ) = ( 700 - 30 ) = 6970 answer d"
Answer: d
Python program:
a = 10 * 7
b = a - 7
Problem: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container m ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Python program:
a = 9 + 16 
b = 9 / a
c = math.sqrt(b)
d = 1 - c
e = 15 / d
Problem: a and b together can do a work in 2 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 2.4 days , b ) 8 days , c ) 1.2 days , d ) 1.0 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 2 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 2 ) - ( 1 / 12 ) = 2.4 days answer : option a"
Answer: a
Python program:
a = 1 / 2
b = 1 / 12
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: list k consists of 12 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: "answer = c = 7 if least = - 3 , then largest = 8 range = 8 - 1 = 7"
Answer: c
Python program:
a = 12 - 3
b = a - 1
c = b - 1
Problem: a train running at the speed of 60 km / hr crosses a pole in 21 seconds . find the length of the train .
Options: a ) 350 m , b ) 145 m , c ) 240 m , d ) 135 m , e ) 255 m
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 350 meter answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 21
Problem: instead of multiplying a number by 7 , the number is divided by 7 . what is the percentage of error obtained ?
Options: a ) 97.959 % , b ) 98.959 % , c ) 99.959 % , d ) 96.959 % , e ) 95.959 %
Rationale: "let the number be x the right number is 7 x the wrong number is x / 7 error is ( 7 x - x / 7 ) = 48 x / 7 percentage of error is ( ( 48 x / 7 ) / 7 x ) * 100 = 97.959 % answer : a"
Answer: a
Python program:
a = 7 / 7
b = 7 * 7
c = a / b
d = c * 100
e = 100 - d
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 3 times , what is the probability that it will land tails up on the first flip and not on the last 2 flips ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 3 / 4
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 8 answer : a
Answer: a
Python program:
a = 2 ** 3
b = 1/(a)
Problem: a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 43 , c ) 50 , d ) 53 , e ) 62
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 360 / 9 = 40 , so the median is also 40 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 43 . option b"
Answer: b
Python program:
a = 360 / 9
b = a + 3
Problem: a factory produces 4340 toys per week . if the workers at this factory work 2 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1375 toys , b ) 2170 toys , c ) 2375 toys , d ) 2175 toys , e ) 5375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 2 days ) by 2 . 4340 / 2 = 2170 toys correct answer b"
Answer: b
Python program:
a = 4340 / 2
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 9 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 65.25 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 91 / 100 ) = 59.375 mp = 65.25 answer : a"
Answer: a
Python program:
a = 47 * 50
b = a / 100
c = 47 + 50 
d = c * 100
e = 100 - 9
f = d / e
Problem: the mean of 50 observations was 36 . it was found later that an observation 34 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.0 , b ) 36.5 , c ) 36.24 , d ) 36.12 , e ) 36.22
Rationale: "explanation : correct sum = ( 36 * 50 + 434 - 23 ) = 1825 . correct mean = = 1811 / 50 = 36.5 answer : e ) 36.22"
Answer: e
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: in the coordinate plane , line a has a slope of - 1 and an x - intercept of 1 . line b has a slope of 3 and a y - intercept of - 3 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - x + 1 the equation of line b is y = 3 x - 3 3 x - 3 = - x + 1 x = 1 y = 0 the point of intersection is ( 1,0 ) and then a + b = 1 . the answer is b ."
Answer: b
Python program:
a = 3 - 3
b = a - 1
c = b / 1
Problem: if - 11 and - 8 are negative integers , then - 11 * - 8 + 5 is
Options: a ) - 14 , b ) 14 , c ) 33 , d ) 83 , e ) 93
Rationale: answer : e
Answer: e
Python program:
a = negate * (
b = a + negate
Problem: if there are 20 apples and the apples have to be shared equally among 3 babies . what number of apples are to be added ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: given there are 20 apples . if 1 extra apple is added , then it becomes 21 which can be divided equally that is 7 apples to each baby . option a is correct .
Answer: a
Python program:
a = 4 + 3 
b = a * 3
c = b - 20
Problem: 8 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire rest of the car , then the share of each of the remaining persons increased by ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 7 , d ) 7 / 8 , e ) 8 / 7
Rationale: when there are eight people , the share of each person is 1 / 8 th the total cost answer : b
Answer: b
Python program:
a = 1 / 8
Problem: a box contains 3 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 7 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: my complicated version of your simple approach let the 5 black balls be bbbbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 4 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 3 red ( rrr ) they can be arranged in ( 6 ! ) / ( 3 ! x 3 ! ) hence required probability = [ ( 7 ! ) / ( 4 ! x 3 ! ) ] / [ ( 6 ! ) / ( 3 ! x 3 ! ) ] ans = 7 / 4 a
Answer: a
Python program:
a = 3 + 4 
b = a / 4
Problem: in kaya ' s teacher ' s desk there are 4 pink highlighters , 2 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 4 + 2 + 5 = 11 . answer is a ."
Answer: a
Python program:
a = 4 + 2 
b = a + 5
Problem: the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 85 kg , d ) 90 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 10 ã — 2.5 = 25 if x is the weight of the new person , total increase in weight = x â ˆ ’ 65 = > 25 = x - 65 = > x = 25 + 65 = 90 answer : option d"
Answer: d
Python program:
a = 10 * 2
b = a + 65
Problem: on a map , 1 inch represents 28 miles . how many z inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "z inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Python program:
a = 383 / 6
Problem: a train 150 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 8
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 150 * 3 / 55 = 8 sec . answer : e"
Answer: e
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 150 / b
Problem: the h . c . f . of two numbers is 40 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 600 , c ) 699 , d ) 722 , e ) 745
Rationale: "the numbers are ( 40 x 11 ) and ( 40 x 15 ) . larger number = ( 40 x 15 ) = 600 . answer : b"
Answer: b
Python program:
a = 40 * 15
Problem: excluding stoppages , the speed of a train is 54 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 13.55 , b ) b ) 14.55 , c ) c ) 15.55 , d ) d ) 16.55 , e ) e ) 17.55
Rationale: "explanation : t = 14 / 54 * 60 = 15.55 answer : option c"
Answer: c
Python program:
a = 40 / 54
b = const_60 * a
c = const_60 - b
Problem: a train 385 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 21 , c ) 7 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 385 * 3 / 55 ] sec = 21 sec answer : option b"
Answer: b
Python program:
a = 385 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 15 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 61 % , b ) 70 % , c ) 75 % , d ) 85 % , e ) 95 %
Rationale: "find the product of the two increases : ( 1.4 ) * ( . 15 ) , which is 1.61 and a 61 % increase . a"
Answer: a
Python program:
a = 40 / 100
b = 1 + a 
c = 100 * b
d = 15 / 100
e = 1 + d 
f = c * e
g = f / 100
h = g - 1
i = h * 100
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 9 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 22 litres , e ) 18 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 9 ) = 4 / 5 20 x = 4 ( 3 x + 9 ) 8 x = 36 x = 4.5 quantity of alcohol = ( 4 x 4.5 ) litres = 18 litres . answer is e"
Answer: e
Python program:
a = 9 * 1
Problem: if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 39 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 39 women = 15 women + 39 women = 54 women 20 women can do the work in 54 days . so , 54 women can do it in ( 20 * 54 ) / 54 = 20 days .
Answer: c
Python program:
a = 12 * 54
b = 9 / a
c = 20 * 54
d = 39 / c
e = b + d 
f = 1/(e)
Problem: in an election , candidate a got 79 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate .
Options: a ) 357003 , b ) 357090 , c ) 37667 , d ) 379888 , e ) 287761
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357090 answer : b"
Answer: b
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 79 / 100
e = c * d