euclaise/mathqa_programs huggingface dataset:
Problem: john spends $ 320 buying his favorite dolls . if he buys only small monkey dolls , which are $ 4 cheaper than the large monkey dolls , he could buy 40 more dolls than if he were to buy only large monkey dolls . how much does a large monkey doll cost ?
Options: a ) $ 7.2 , b ) $ 7.5 , c ) $ 8 , d ) $ 9 , e ) $ 10
Rationale: a and b is not an integer . so we start with c if large doll costs $ 8 , then he can buy 320 / 8 = 40 large dolls and 320 / 4 = 80 small dolls . difference is 40 , which is we wanted . answer c .
Answer: c
Python program:
a = 4 * 40
b = 320 - a
c = b / 4
d = c + 40 
e = 320 / d
f = e + 4
Problem: the number 110 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ?
Options: a ) 10 , b ) 12 , c ) 18 , d ) 14 , e ) 17
Rationale: "sum of the squares of 3 different positive integers = 110 5 ^ 2 + 6 ^ 2 + 7 ^ 2 = 110 now , sum of these 3 different integers = 5 + 6 + 7 = 18 ans - c"
Answer: c
Python program:
a = 110 / 2
b = math.sqrt(a)
c = 2 * b
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 12 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 26 km / hr , b ) 40 km / hr , c ) 60 km / hr , d ) 77 km / hr , e ) 46 km / hr
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 12 = 3 x = > x = 50 / 9 . so , speed of the faster train = 100 / 9 = 100 / 9 * 18 / 5 = 40 km / hr . answer : b"
Answer: b
Python program:
a = 100 + 100 
b = 1 + 2 
c = 12 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
Problem: a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 200 , b ) s . 100 , c ) s . 300 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 600 and 400 . difference in profit share = 600 - 400 = 200 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 1 / 3
c = a + b 
d = 1000 / c
e = d / 2
f = 1 / 2
g = 1 / 3
h = f + g 
i = 1000 / h
j = i / 3
k = e - j
Problem: there is a total of 120 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 / 4 and the probability that it will be green is 1 / 3 . what is the probability that the marble will be either red or blue ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 2 / 7 , d ) 1 / 3 , e ) 5 / 12
Rationale: "total marbles in the box = 120 white marbles = 120 / 4 = 30 green marbles = 120 / 3 = 40 w + g = 70 red + blue = 50 p ( red or blue ) = 50 / 120 = 5 / 12 answer : e"
Answer: e
Python program:
a = 1 / 4
b = 1 / 3
c = a + b 
d = 1 - c
Problem: three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in ?
Options: a ) 08 hours , b ) 12 hours , c ) 03 hours , d ) 04 hours , e ) 21 hours
Rationale: "the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b"
Answer: b
Python program:
a = 2 / 3
b = 1 / 8
c = a * b
d = 1/(c)
Problem: if a 2 + b 2 + c 2 = 941 and ab + bc + ca = 10 , then a + b + c is
Options: a ) 44 , b ) 56 , c ) 16 , d ) 32 , e ) 31
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 941 and ab + bc + ca = 10 , ( a + b + c ) ^ 2 = 941 + 2 ( 10 ) = 961 = 31 ^ 2 therefore : a + b + c = 31 answer : e"
Answer: e
Python program:
a = 10 * 2
b = 941 + a 
c = math.sqrt(b)
Problem: what is the tens digit of 6 ^ 18 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 18 has the form 5 n + 3 , so the tens digit of 6 ^ 18 is 1 . the answer is a ."
Answer: a
Python program:
a = 4 + 1 
b = 6 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: if dev works alone he will take 20 more hours to complete a task than if he worked with tina to complete the task . if tina works alone , she will take 5 more hours to complete the complete the task , then if she worked with dev to complete the task ? what is the ratio of the time taken by dev to that taken by tina if each of them worked alone to complete the task ?
Options: a ) 4 : 1 , b ) 2 : 1 , c ) 10 : 1 , d ) 3 : 1 , e ) 1 : 2
Rationale: let time taken by dev to complete the work alone be x days and that by tina be y days work done by dev in 1 day = 1 / x work done by tina in 1 day = 1 / y work done by devtina in 1 day = 1 / x + 1 / y = ( x + y ) / xy thus working together they will complete the work in xy / ( x + y ) days acc . to the ques : 1 ) if dev works alone he will take 20 more hours to complete a task than if he worked with tina ' x - xy / ( x + y ) = 20 = > ( x ^ 2 ) / ( x + y ) = 20 . . . . . . . . . . . . . ( i ) 2 ) if tina works alone , she will take 5 more hours to complete the complete the task , then if she worked with dev y - xy / ( x + y ) = 5 = > ( y ^ 2 ) / ( x + y ) = 5 . . . . . . . . . . . . . . ( ii ) dividing ( i ) by ( ii ) x ^ 2 / y ^ 2 = 4 = > x / y = 2 ans : b hope it helps
Answer: b
Python program:
a = 20 * 5
b = math.sqrt(a)
c = 20 + b 
d = 20 * 5
e = math.sqrt(d)
f = 5 + e 
g = c / f
Problem: a train 140 m long is running with a speed of 50 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 8.1 , b ) 7.0 , c ) 9.33 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 50 + 4 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . time taken to pass the men = 140 * 1 / 15 = 9.33 sec . answer : option c"
Answer: c
Python program:
a = 50 + 4 
b = a * const_0_2778
c = 140 / b
Problem: a train 110 m long is running with a speed of 40 km / hr . in what time will it pass a man who is running at 5 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7.5 , d ) 8.8 , e ) 9
Rationale: "speed of train relative to man = 40 + 5 = 45 km / hr . = 45 * 5 / 18 = 25 / 2 m / sec . time taken to pass the men = 110 * 2 / 25 = 8.8 sec . answer : option d"
Answer: d
Python program:
a = 40 + 5 
b = a * const_0_2778
c = 110 / b
Problem: john and steve are speed walkers in a race . john is 15 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 3.8 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 ) 42.5 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.8 t + 15 + 2 - - - > 0.4 t = 17 - - - > t = 42.5 seconds . e is the correct answer ."
Answer: e
Python program:
a = 15 + 2 
b = 3 * 8
c = 4 - 2
d = b / c
e = 15 + 2 
f = d + e 
g = f / 4
Problem: the average of 10 consecutive integers is 20 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 14 , b ) 14.5 , c ) 15 , d ) 15.5 , e ) 16
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d ."
Answer: d
Python program:
a = 10 * 20
b = 4 + 1 
c = b * 9
d = a - c
e = d / 10
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 10 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 ) 90
Rationale: "200 men do the rest of the work in 100 - 10 = 90 days 100 men can do the rest of the work in 90 * 200 / 100 = 180 days required number of days = 180 - 90 = 90 days answer is e"
Answer: e
Python program:
a = 100 - 10
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 30 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 30 = 12 hours answer d"
Answer: d
Python program:
a = 9 / 15
b = 1 - a
c = b * 30
Problem: if a rectangular room measures 10 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000 , b ) 240,000 , c ) 2 , 400,000 , d ) 200 , 000,000 , e ) 240 , 000,000
Rationale: "d . 200 , 000,000 10 * 100 * 5 * 100 * 4 * 100 = 200 , 000,000"
Answer: d
Python program:
a = 4 * 100
b = 1 / 10
c = a * b
d = 5 * 100
e = c * d
f = 10 * 100
g = e * f
Problem: only a single rail track exists between stations a and b on a railway line . one hour after the north bound super fast train n leaves station a for station b , a south - bound passenger train s reaches station a from station b . the speed of the super fast train is twice that of a normal express train e , while the speed of a passenger train s is half that of e . on a particular day , n leaves for b from a , 20 min behind the normal schedule . in order to maintain the schedule , both n and s increased their speeds . if the super fast train doubles its speed , what should be the ratio ( approximately ) of the speeds of passenger train to that of the super fast train so that the passenger train s reaches exactly at the scheduled time at a on that day ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 1 : 6 , e ) 1 : 7
Rationale: explanation : if speed of n = 4 , speed of s = 1 . = > average speed = ( 2 x 4 x 1 ) / ( 4 + 1 ) = 1.6 . because time available is 2 / 3 , speed = 3 / 2 . now average speed = 2.4 now speed of n = 8 . speed of s = y . = > ( 2 x 8 x y ) / ( 8 + y ) = 2.4 = > y = 1.3 the required ratio is 1.3 : 8 i . e 1 : 6 . answer : d
Answer: d
Python program:
a = 12 / 2
b = 20 - a
c = b - 2
d = 2 / c
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 15 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 30
Rationale: a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 15 days , b can do 1 / 2 of the project . thus a and b must complete 1 / 2 of the project , which takes 6 days . the total number of days is 6 + 15 = 21 . the answer is b .
Answer: b
Python program:
a = 1 / 30
b = a * 15
c = 1 - b
d = 1 / 20
e = 1 / 30
f = d + e 
g = c / f
h = g + 15
Problem: how many positive integers less than 200 are there such that they are multiples of 13 or multiples of 14 ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "200 / 13 = 15 ( plus remainder ) so there are 15 multiples of 13 200 / 14 = 14 ( plus remainder ) so there are 14 multiples of 14 we need to subtract 1 because 13 * 14 is a multiple of both so it was counted twice . the total is 15 + 14 - 1 = 28 the answer is d ."
Answer: d
Python program:
a = 4 + 13 
b = a - 1
c = math.factorial(b)
d = math.factorial(13)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: there are 2 sections a and b in a class , consisting of 36 and 24 students respectively . if the average weight of section a is 30 kg and that of section b is 30 kg , find the average of the whole class ?
Options: a ) 30 kg , b ) 37 kg , c ) 42 kg , d ) 55.12 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 36 * 30 + 24 * 30 = 1800 average weight of the class is = 1800 / 60 = 30 kg answer is a"
Answer: a
Python program:
a = 36 * 30
b = 24 * 30
c = a + b 
d = 36 + 24 
e = c / d
Problem: sarah is driving to the airport . after driving at 25 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 50 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 100 , b ) 175 , c ) 210 , d ) 245 , e ) 280
Rationale: "after driving at 25 miles per hourfor one hour , this distance left to cover is d - 25 . say this distance is x miles . now , we know that the difference in time between covering this distance at 25 miles per hour and 50 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 25 - x / 50 = 3 / 2 - - > 2 x / 50 - x / 50 = 3 / 2 - - > x / 50 = 3 / 2 - - > x = 75 . total distance = x + 25 = 100 miles . answer : a"
Answer: a
Python program:
a = 25 - 30
b = 30 - a
Problem: two trains start from p and q respectively and travel towards each other at a speed of 50 km / hr and 40 km / hr respectively . by the time they meet , the first train has travelled 100 km more than the second . the distance between p and q is :
Options: a ) 500 km , b ) 630 km , c ) 900 km , d ) 660 km , e ) none
Rationale: "sol . at the time of meeting , let the distane travelled byb the second train be x km . then , distance covered by the first train is ( x + 100 ) km ∴ x / 40 = ( x + 100 ) / 50 ⇔ 50 x = 40 x 4000 ⇔ x = 400 . so , distance between p and q = ( x + x + 100 ) km = 900 km . answer c"
Answer: c
Python program:
a = 100 * 40
b = 50 - 40
c = a / b
d = c + 100 
e = 100 * 40
f = 50 - 40
g = e / f
h = d + g
Problem: a is thrice as good a workman as b and takes 10 days less to do a piece of work than b takes . b alone can do the whole work in
Options: a ) 15 days , b ) 10 days , c ) 9 days , d ) 8 days , e ) 7 days
Rationale: explanation : ratio of times taken by a and b = 1 : 3 means b will take 3 times which a will do in 1 time if difference of time is 2 days , b takes 3 days if difference of time is 10 days , b takes ( 3 / 2 ) * 10 = 15 days option a
Answer: a
Python program:
a = 3 * 10
b = a / 2
Problem: the difference between simple and compound interest on rs . 1500 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.0 , b ) 3.0 , c ) 9.5 , d ) 3.75 , e ) 2.15
Rationale: "s . i . = ( 1500 * 10 * 1 ) / 100 = rs . 150 c . i . = [ 1500 * ( 1 + 5 / 100 ) 2 - 1500 ] = rs . 153.75 difference = ( 153.75 - 150 ) = rs . 3.75 answer : d"
Answer: d
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = 10 / 100
f = e + 1 
g = d - f
h = g * 1500
Problem: in a class , 12 students like to play basketball and 8 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) 18 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 12 + 8 - 3 = 17 c )"
Answer: c
Python program:
a = 12 + 8 
b = a - 3
Problem: in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if one - sevenths of the male students are married , what fraction of the female students is single ?
Options: a ) 1 / 3 , b ) 1 / 7 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 1 / 7 of 70 = 10 males are married if 30 is the total number of students who are married and out of that 10 are males then the remaining 20 will be females who are married . total females = 30 married females = 20 then single females = 30 - 20 = 10 we need to find the fraction of female students who are single i . e single female students / total female student = 10 / 30 = 1 / 3 [ a ]
Answer: a
Python program:
a = 10 / 30
Problem: a train ride from two p to town q costs $ 6.35 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?
Options: a ) $ 1.75 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20
Rationale: "let x be the cost of a bus ride . x + ( x + 635 ) = 985 2 x = 350 x = $ 1.75 the answer is a ."
Answer: a
Python program:
a = 9 - 85
b = a / 2
Problem: a drink vendor has 10 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 261 , c ) 422 , d ) 430 , e ) 438
Rationale: "the number of liters in each can = hcf of 10 , 144 and 368 = 2 liters . number of cans of maaza = 10 / 2 = 5 number of cans of pepsi = 144 / 2 = 72 number of cans of sprite = 368 / 2 = 184 the total number of cans required = 5 + 72 + 184 = 261 cans . answer : b"
Answer: b
Python program:
a = math.gcd(10, 144)
b = math.gcd(a, 368)
c = 368 / b
d = math.gcd(10, 144)
e = math.gcd(d, 368)
f = 10 / e
g = math.gcd(10, 144)
h = math.gcd(g, 368)
i = 144 / h
j = f + i 
k = c + j
Problem: if 40 % of a certain number is 160 , then what is 30 % of that number ?
Options: a ) 270 , b ) 380 , c ) 120 , d ) 360 , e ) 180
Rationale: "explanation : 40 % = 40 * 4 = 160 30 % = 30 * 4 = 120 answer : option c"
Answer: c
Python program:
a = 40 / 100
b = 160 / a
c = 30 / 100
d = b * c
Problem: if the sum of two numbers is 45 and the l . c . m and sum of the reciprocal of the numbers are 120 and 11 / 120 then hcf of numbers is equal to :
Options: a ) 55 , b ) 5 , c ) 10 , d ) 45 , e ) 4
Rationale: let the numbers be a and b and hcf is x , then , a + b = 45 and ab = x * 120 = 120 x required sum = 1 / a + 1 / b = ( a + b ) / ab = 45 / 120 x = 11 / 120 . x = 5 . answer : b
Answer: b
Python program:
a = 45 / 11
b = math.floor(a)
c = b + 1
Problem: find the missing figures : 0.1 % of ? = 0.24
Options: a ) 12 , b ) 120 , c ) 24 , d ) 240 , e ) 36
Rationale: "let 0.1 % of x = 0.24 . then , 0.1 * x / 100 = 0.24 x = [ ( 0.24 * 100 ) / 0.1 ] = 240 . answer is d ."
Answer: d
Python program:
a = 0 / 1
b = 0 / 24
Problem: there has been successive increases of 25 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 23 % , b ) 27 % , c ) 31 % , d ) 35 % , e ) 39 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.25 * p = x * p y = x / ( 1.1 * 1.25 ) which is about 0.73 x which is a decrease of about 27 % . the answer is b ."
Answer: b
Python program:
a = 100 + 25 
b = 100 + 25 
c = b * 10
d = c / 100
e = a + d 
f = 100 / e
g = 1 - f
h = g * 100
Problem: pipe a can fill a tank in 60 min . there is a second pipe in the bottom of the cistern to empty it . if all the two pipes are simultaneously opened , then the cistern is full in 180 min . in how much time , the second pipe alone can empty the cistern ?
Options: a ) 60 min , b ) 45 min , c ) 90 min , d ) 70 min , e ) 30 min
Rationale: work done by the third pipe in 1 min = 1 / 180 - ( 1 / 60 ) = - 1 / 45 . [ - ve sign means emptying ] the third pipe alone can empty the cistern in 45 min . answer : b
Answer: b
Python program:
a = 1 / 180
b = 1 / 60
c = a + b 
d = 1/(c)
Problem: a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 35 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 44 % , b ) 40 % , c ) 68.75 % , d ) 56.25 % , e ) 36 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 35 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.75 . so his profit is $ 6.75 - $ 4 = $ 2 and his profit percent is ( 2.75 / 4 ) * 100 = 68.75 % answer : - c"
Answer: c
Python program:
a = 100 + 35 
b = 100 - 20
c = a / b
d = c - 1
e = d * 100
Problem: nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 2 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 48
Rationale: e its is . let price = x ( x - 2 ) 8 = 6 x x = 8 hence total money = 6 * 8 = 48
Answer: e
Python program:
a = 2 * 8
b = 8 - 6
c = a / b
d = c * 6
Problem: according to a recent student poll , 3 / 4 out of 20 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 1 / 14 , b ) 4 / 49 , c ) 18 / 19 , d ) 45 / 49 , e ) 13 / 14
Rationale: "15 students are interested , 5 are not interested prob = 1 - 5 c 2 / 20 c 2 = 1 - ( 5 * 4 / ( 20 * 19 ) ) = 1 - 1 / 19 = 18 / 19 answer : c"
Answer: c
Python program:
a = math.comb(20, 2)
b = 3 / 4
c = 20 * b
d = 20 - c
e = math.comb(d, 2)
f = a - e
g = math.comb(20, 2)
h = f / g
Problem: there are 4 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 3 , b ) 1 / 14 , c ) 3 / 14 , d ) 1 / 15 , e ) 1 / 16
Rationale: "taking 2 red shoe the probability is 4 c 2 from 8 shoes probability of taking 2 red shoes is 4 c 2 / 8 c 2 = 3 / 14 answer : c"
Answer: c
Python program:
a = math.comb(4, 2)
b = 4 + 4 
c = math.comb(b, 2)
d = a / c
Problem: ram , who is half as efficient as krish , will take 30 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 10 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 30 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 30 days is 30 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 30 w / 3 w = 10 days answer b"
Answer: b
Python program:
a = 1 / 30
b = 30 / 2
c = 1 / b
d = a + c 
e = 1/(d)