euclaise/mathqa_programs huggingface dataset:
Problem: the average age of 21 students of a class is 21 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 21 th student is
Options: a ) 164 , b ) 152 , c ) 100 , d ) 182 , e ) 195
Rationale: "explanation : age of the 21 th student = [ 21 * 21 - ( 14 * 5 + 16 * 9 ) ] = ( 378 - 214 ) = 164 years . answer : a"
Answer: a
Python program:
a = 21 * 21
b = 5 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 40 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 10
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 40 + q = > q = 10 answer : e"
Answer: e
Python program:
a = 10 * 3
b = 40 - a
Problem: the difference between a number and its two - fifth is 510 . what is 30 % of that number ?
Options: a ) 158 , b ) 200 , c ) 255 , d ) 400 , e ) 280
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 10 % of 850 = 255 . answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 510 * a
c = 1 + 2 
d = b / c
Problem: john and jacob set out together on bicycle traveling at 18 and 15 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 18 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 3 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 4 1 / 3
Rationale: "john ' s speed - 18 miles / hr jacob ' s speed - 15 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 18 x 2 / 3 = 12 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 15 x 5 / 3 = 25 miles . now , when john starts riding back , the distance between them is 13 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 18 - 15 = 3 miles / hr . thus , to cover 13 miles at 3 miles / hr , john will take 13 / 3 = 4 1 / 3 hours answer e"
Answer: e
Python program:
a = 18 - 15
b = 40 / const_60
c = b * 18
d = 40 / const_60
e = d * 15
f = c - e
g = 15 - f
h = a + g 
i = 40 / const_60
j = i * 18
k = 40 / const_60
l = k * 15
m = j - l
n = h / m
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 56 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 42 , d ) 24 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of ( 48 / 112 ) * 56 = 24 cubic inches answer d"
Answer: d
Python program:
a = 48 / 112
b = a * 56
Problem: 800 is increased by 110 % . find the final number .
Options: a ) 1200 , b ) 1210 , c ) 1180 , d ) 1190 , e ) 1680
Rationale: explanation final number = initial number + 110 % ( original number ) = 800 + 110 % ( 800 ) = 800 + 880 = 1680 . answer e
Answer: e
Python program:
a = 110 / 100
b = 800 * a
c = 800 + b
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 40 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 82 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 40 % more than company a ' s assets which is 140 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 70 a + b = 170 kw = 140 kw / ( a + b ) * 100 = 140 / 170 * 100 = 82.35 % or 82 % c"
Answer: c
Python program:
a = 100 + 40 
b = 100 + 40 
c = b / 2
d = 100 + c 
e = a / d
f = e * 100
Problem: if a : b = 2 : 3 , b : c = 4 : 5 and c : d = 5 : 9 then a : d is equal to :
Options: a ) 11 : 17 , b ) 8 : 27 , c ) 5 : 9 , d ) 2 : 9 , e ) none
Rationale: "solution : a / d = ( a / b ) * ( b * c ) * ( c / d ) = ( 2 / 3 ) * ( 4 / 5 ) * ( 5 / 9 ) = ( 2 * 4 * 5 ) / ( 3 * 5 * 9 ) = 8 / 27 . answer : option b"
Answer: b
Python program:
a = 2 * 4
b = a * 5
c = 3 * 5
d = c * 9
e = b / d
Problem: if an integer n is to be selected at random from 1 to 105 , inclusive , what is probability n ( n + 1 ) will be divisible by 7 ?
Options: a ) 1 / 7 , b ) 3 / 14 , c ) 1 / 2 , d ) 2 / 7 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 7 , either n or n + 1 has to be a multiple of 7 . thus n must be of the form 7 k or 7 k - 1 . the probability is 2 / 7 . the answer is d ."
Answer: d
Python program:
a = 2 / 7
Problem: two numbers are respectively 20 % and 50 % more than a third number . the ratio of the two numbers is
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 6 : 5 , e ) 7 : 5
Rationale: "explanation : let the third number be x . first number ( 120 / 100 ) * x = 6 x / 5 second number ( 150 / 100 ) * x = 3 x / 2 ratio = 6 x / 5 : 3 x / 2 = > 4 : 5 option c"
Answer: c
Python program:
a = 20 + 100 
b = 50 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: the sum of the first 50 positive even integers is 2,000 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 8,050 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 50 positive even integers = 2000 sum of 1 st 100 odd numbers = 5050 - 2000 = 3050 so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 5000 + 3050 = 8050 c is the answer ."
Answer: c
Python program:
a = 200 + 101 
b = a / 2
c = 200 - 101
d = c / 2
e = d + 1 
f = b * e
Problem: rain is falling at a rate of 3 centimeters per hour all over springfield . somewhere downtown in springfield a group of pigeons is waiting for the rain to stop . if the rain filled a round puddle the with a base area of 350 square centimeters and a depth of 13.5 centimeters , how long did the pigeons wait for the rain to stop ?
Options: a ) 3 hours and 12 minutes .
b ) four hours and 30 minutes
c ) four hours and 45 minutes
d ) five hours and 10 minutes
e ) five hours and 30 minutes
Rationale: the volume of the puddle is irrelevant and only height matters since rain fell all over the city . thus , it takes only . 13.5 / 3 = 4.5 hours of rain to fill the puddle answer is : b , 4 hours and 30 mins
Answer: b
Python program:
a = 13 / 5
Problem: what is the sum of all possible solutions to | x + 3 | ^ 2 + | x + 3 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: "denote | x + 3 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x + 3 | , so it ' s an absolute value and thus can not be negative . y = | x + 3 | = 4 - - > x = 7 . the sum = 7 . answer : c ."
Answer: c
Python program:
a = 4 + 3 
b = 3 - 4
c = a + b
Problem: a small pool filled only with water will require an additional 800 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 800 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 2000 , e ) 2250
Rationale: "since pumping in additional 800 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 800 = 0.8 * { total } - - > { total } = 2,250 . answer : e ."
Answer: e
Python program:
a = 800 * 100
b = a / 30
c = b + 800 
d = 80 / 100
e = c / d
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 2500 more than d , what is b ' s share ?
Options: a ) a ) 8239 , b ) b ) 2900 , c ) c ) 4500 , d ) d ) 2393 , e ) e ) 5000
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 2500 = > x = 2500 . b ' s share = rs . 2 x = 2 * 2500 = rs . 5000 . answer : e"
Answer: e
Python program:
a = 4 - 3
b = a * 2500
c = b * 3
Problem: the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 182.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 184 cm - ( 166 cm - 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b"
Answer: b
Python program:
a = 35 * 184
b = a - 166
c = b + 106 
d = c / 35
e = math.floor(d)
Problem: all the students of class are told to sit in circle shape . here the boy at the 7 th position is exactly opposite to 27 th boy . total number of boys in the class ?
Options: a ) 25 , b ) 40 , c ) 35 , d ) 30 , e ) 28
Rationale: "as half the circle shape consist of 27 - 7 = 20 boys , so total number of boys in full circle = 2 * 20 = 40 answer : b"
Answer: b
Python program:
a = 27 - 7
b = a * 2
Problem: on my sister ' s birthday , she was 132 cm in height , having grown 10 % since the year before . how tall was she the previous year ?
Options: a ) 130 cm , b ) 126 cm , c ) 120 cm , d ) 116 cm , e ) 112 cm
Rationale: "let the previous year ' s height be x . 1.1 x = 132 x = 120 the answer is c ."
Answer: c
Python program:
a = 132 * 10
b = a / 100
c = 132 - b
Problem: a $ 72.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 18 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: listed selling price of chair = 72.95 $ discounted selling price of chair = 59.95 $ discount = 72.95 - 59.95 = 13 $ % decrease in price of chair = ( 13 / 72.95 ) * 100 % = 18 % approx answer a
Answer: a
Python program:
a = 72 - 95
b = a / 72
c = b * 100
Problem: if shares of two persons in profits are rs . 400 and rs . 800 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 400 : 800 = 1 : 2 answer : e"
Answer: e
Python program:
a = 400 / 800
Problem: if an investor puts $ 1000 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 1100.25 , b ) $ 1100.75 , c ) $ 1101.25 , d ) $ 1101.75 , e ) $ 1102.50
Rationale: "1.05 * 1.05 * 1000 = $ 1102.50 the answer is e ."
Answer: e
Python program:
a = 10 / 2
b = a / 100
c = 1 + b 
d = c ** 2
e = 1000 * d
Problem: at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 7 : 3 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
Options: a ) 45 / 21 , b ) 46 / 2 , c ) 13 / 30 , d ) 23 / 6 , e ) 4 / 6
Rationale: "red : blue = 7 : 3 let red = 7 x and blue = 3 x 1 / 3 of red are left handed = > 1 / 3 * 7 x = 7 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 3 x = 6 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 7 x / 3 + 6 x / 3 ) / ( 7 x + 3 x ) = 13 / 30 answer : c"
Answer: c
Python program:
a = 7 * const_0_33
b = 2 / 3
c = 3 * b
d = a + c 
e = 7 + 3 
f = d / e
Problem: a reduction of 23 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.99 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1
Rationale: "100 * ( 23 / 100 ) = 23 - - - 10 ? - - - 1 = > rs . 2.3 100 - - - 77 ? - - - 2.3 = > rs . 2.99 answer : a"
Answer: a
Python program:
a = 23 / 100
b = a * 100
c = b / 10
d = 23 / 100
e = d * 100
f = c / e
g = f * 100
Problem: if 60 % of a number is greater than 30 % of 10 by 27 , what is the number ?
Options: a ) 50 , b ) 100 , c ) 30 , d ) 75 , e ) 5
Rationale: explanation : 60 / 100 * x - 30 / 100 * 10 = 27 60 / 100 * x - 3 = 27 60 / 100 * x = 30 x = 30 * 100 / 60 x = 50 answer : option a
Answer: a
Python program:
a = 10 / 100
b = a * 30
c = 27 + b 
d = c / 60
e = 100 * d
Problem: how many integers from 0 to 53 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 52 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 52 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 51 or , n - 1 = 17 or , n = 18 d"
Answer: d
Python program:
a = 53 / 10
Problem: a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 4 : 3 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: "originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 3 / 9 ) * 1350 = 450 acres were planted with tobacco . the answer is b ."
Answer: b
Python program:
a = 100 * 10
b = 3 * 100
c = a + b 
d = 5 * 10
e = c + d 
f = 3 + 2 
g = f + 2 
h = 3 / g
i = e * h
j = 100 * 10
k = 3 * 100
l = j + k 
m = 5 * 10
n = l + m 
o = 5 + 2 
p = o + 2 
q = 2 / p
r = n * q
s = i - r
Problem: ( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + 0.096 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.68 , b ) 0.086 , c ) 0.86 , d ) 0.068 , e ) none of them
Rationale: "given expression = ( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + ( 0.96 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.96 - 0.1 ) = 0.86 answer is c ."
Answer: c
Python program:
a = 0 ** 96
b = 0 ** 1
c = a - b
d = 0 ** 96
e = d + 0 
f = 0 ** 1
g = e + f 
h = c / g
Problem: a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 450 bolts ?
Options: a ) 36 , b ) 72 , c ) 120 , d ) 144 , e ) 108
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 450 bolts 450 * 6 / 25 = 108 mins ans e"
Answer: e
Python program:
a = 100 / const_60
b = 150 / const_60
c = a + b 
d = 450 / c
Problem: a man ' s speed with the current is 21 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 20 , c ) 16 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 21 km / hr = > speed of the man + speed of the current = 21 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 21 - 2.5 = 18.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 18.5 - 2.5 = 16 km / hr answer is c ."
Answer: c
Python program:
a = 21 - 2
b = a - 2
Problem: a train 275 m long , running with a speed of 90 km / hr will pass a tree in
Options: a ) 11 sec , b ) 15 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 90 x 5 / 18 ) m / sec . = 25 m / sec . time taken = ( 275 x 1 / 25 ) sec = 11 sec answer a"
Answer: a
Python program:
a = 90 * 1000
b = 275 / a
c = b * 3600
Problem: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and danny have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and danny submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Python program:
a = 80 * 0
b = 2 * a
c = 100 - 25
d = c / 100
e = 160 * d
f = e * 0
g = b - f
h = g / 2
Problem: 28 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 70
Rationale: "i came up with ( e ) 70 think of 100 people total : from the first fact , 28 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 28 equals the number of fair haired men , which is 42 men with fair hair . add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women . 70 % e"
Answer: e
Python program:
a = 28 / 40
b = a * 100
Problem: a jogger running at 9 km / hr along side a railway track is 150 m ahead of the engine of a 100 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 88 , b ) 27 , c ) 36 , d ) 80 , e ) 25
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 150 + 100 = 250 m . time taken = 250 / 10 = 25 sec . answer : e"
Answer: e
Python program:
a = 150 + 100 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: a train running at the speed of 60 km / hr crosses a pole in 12 sec . what is the length of the train ?
Options: a ) 200 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 150 m
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 200 m answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 12
Problem: if x + 1 / x = 5 then find out the value of x ^ 5 + 1 / x ^ 5 = ?
Options: a ) 2515 , b ) 2525 , c ) 2535 , d ) 2545 , e ) 2555
Rationale: "given , ( x + 1 / x ) = 5 x ^ 2 + 1 / x ^ 2 = ( x + 1 / x ) ^ 2 - 2 * x * 1 / x = 5 ^ 2 - 2 = 23 - - - - - - - ( 1 ) x ^ 3 + 1 / x ^ 3 = ( x + 1 / x ) ^ 3 - 3 * x * 1 / x * ( x + 1 / x ) = 5 ^ 3 - 3 * 5 = 110 - - - - - - - ( 2 ) multiplying ( 1 ) & ( 2 ) , we get = > ( x ^ 2 + 1 / x ^ 2 ) * ( x ^ 3 + 1 / x ^ 3 ) = 23 * 110 = > x ^ 5 + 1 / x + x + 1 / x ^ 5 = 2530 = > x ^ 5 + 1 / x ^ 5 + ( x + 1 / x ) = 2530 = > x ^ 5 + 1 / x ^ 5 + 5 = 2530 = > ( x ^ 5 + 1 / x ^ 5 ) = 2525 answer : b"
Answer: b
Python program:
a = 5 / 1
Problem: a student traveled 30 percent of the distance of the trip alone , continued another 40 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "let x be the total length of the trip . 0.3 x + 40 miles + 0.5 x = x 40 miles = 0.2 x x = 200 miles the answer is e ."
Answer: e
Python program:
a = 1/(30)
b = 1 - a
c = 1 / 2
d = b - c
e = 40 / d
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 10 : 00 am and pipe b at 11 : 00 am , at what time will the pool be full ?
Options: a ) 22 : 00 , b ) 20 : 00 , c ) 21 : 00 , d ) 18 : 00 , e ) 17 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 10 : 00 a . m and pipe b at 11 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 11 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 10 : 00 a . m , pool is full at 20 : 00 hrs answer : b"
Answer: b
Python program:
a = 3 / 4
b = 1 / 4
c = 1 / 6
d = b - c
e = 1 / d
f = a * e
Problem: a number , x is chosen at random from the set of positive integers less than 20 . what is the probability that ( 18 / x ) > x ?
Options: a ) 1 / 5 , b ) 2 / 9 , c ) 3 / 19 , d ) 4 / 19 , e ) 7 / 9
Rationale: "number x has to be chosen from numbers 1 - 19 ( 18 / x ) > x = > 18 > x ^ 2 = > x ^ 2 - 18 < 0 x can have 2 values only 1 , 2 , 3 , 4 therefore , probability = 4 / 19 answer d"
Answer: d
Python program:
a = 20 - 18
b = a / 18
Problem: a , b , c hired a car for rs . 520 and used it for 7 , 8 and 11 hours respectively . hire charges paid by b were ?
Options: a ) 127 , b ) 160 , c ) 287 , d ) 237 , e ) 111
Rationale: a : b : c = 7 : 8 : 11 . hire charges paid by b = rs . ( 520 * 8 / 26 ) = rs . 160 . answer : b
Answer: b
Python program:
a = 7 + 8 
b = a + 11 
c = 8 / b
d = 520 * c
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 256,000 locusts ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 15 , e ) 11
Rationale: "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 + 12 hours : 256,000 answer : a"
Answer: a
Python program:
a = 4 ** 4
b = a / 2
c = math.log(b)
d = c * 2
e = d - 4
Problem: there are 2 white plates , 6 green plates , 8 red plates , 4 pink plates , and 10 purple plates in the cabinet . what is the least number of plates that you have to pull out to make sure that you will have a matching pair ? ( assume that all the plates are identical except for the color )
Options: a ) 2 , b ) 4 , c ) 12 , d ) 7 , e ) 6
Rationale: since there are 5 colors , if you take 5 plates , you could still have 1 plate per color and not have a match . therefore , upon taking the 6 th plate , you will definitely have a match since the 6 th plate will form at least a pair with the 1 st 5 so 5 + 1 = 6 answer is e
Answer: e
Python program:
a = 2 + 4
Problem: the smallest number which when diminished by 7 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none
Rationale: "solution required numbers = ( l . c . m of 12 , 16,18 , 21,28 ) + 7 ‹ = › 1008 + 7 = 1015 . answer b"
Answer: b
Python program:
a = 3 ** 2
b = 2 ** 0
c = a * b
d = 3 + 4 
e = c * d
f = e + 7