euclaise/mathqa_programs huggingface dataset:
Problem: in a river flowing at 2 km / hr , a boat travels 72 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 27 hours , e ) none of these
Rationale: explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 72 km total time taken = time taken downstream + time taken upstream = ( 72 / 8 ) + ( 72 / 4 ) = 27 hr . answer : option d
Answer: d
Python program:
a = 6 - 2
b = 72 / a
c = 6 + 2 
d = 72 / c
e = b + d
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 3.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1140 , c ) s . 999 , d ) s . 1085 , e ) s . 2331
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 3.5 = 2331 answer : e"
Answer: e
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 3
f = e * 3
Problem: if a - b = 5 and a 2 + b 2 = 29 , find the value of ab .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 2
Rationale: 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 25 = 4 ab = 2 . answer : e
Answer: e
Python program:
a = 5 ** 2
b = 29 - a
c = b / 2
Problem: how many miles is 320 km ?
Options: a ) 150 miles , b ) 175 miles , c ) 200 miles , d ) 225 miles , e ) 250 miles
Rationale: "200 miles 320 / 1.6 = 200 answer : c"
Answer: c
Python program:
a = volume_cube / (
Problem: 60 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 8 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 12 days
Rationale: "1 women ' s 1 day work = 1 / 420 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 420 + 10 / 140 ) = 1 / 12 5 women and 10 children will complete the work in 12 days . answer : e"
Answer: e
Python program:
a = 60 * 7
b = 5 / a
c = 60 * 14
d = 60 / c
e = b + d 
f = 1/(e)
Problem: how many seconds will it take for a car that is traveling at a constant rate of 14 miles per hour to travel a distance of 96 yards ? ( 1 mile = 1,160 yards )
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: "speed = 14 miles / hr = 6.84 yard / s distance = 96 yards time = distance / speed = 96 / 6.84 = 14 sec ans - d"
Answer: d
Python program:
a = 14 / 3600
b = 14 + 14 
c = b - 4
d = c * 10
e = a * d
f = 96 / e
Problem: in how many years rs 200 will produce the same interest at 10 % as rs . 400 produce in 5 years at 12 %
Options: a ) 16 , b ) 13 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 400 , time 5 years and rate 12 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 200 * 10 ) = 12 option c"
Answer: c
Python program:
a = 400 * 12
b = a / 100
c = b * 5
d = 10 / 100
e = d * 200
f = c / e
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 196 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 1000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1028 , e ) s : 1400
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 196 100 % - - - - ? = > rs : 1400 answer : e"
Answer: e
Python program:
a = 196 * 100
b = 100 + 4 
c = 100 - 10
d = b - c
e = a / d
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 37 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "37 % is 12 % - points above 25 % and 3 % - points below 40 % . thus the ratio of mixture y to mixture x is 1 : 4 . the percent of mixture x is 4 / 5 = 80 % . the answer is e ."
Answer: e
Python program:
a = 25 + 1 
b = 37 - a
c = 40 / 100
d = 25 + 1 
e = d / 100
f = c - e
g = b / f
Problem: how many cubes of 10 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 10000 cubes , b ) 1000 cubes , c ) 100 cubes , d ) 50 cubes , e ) none of these
Rationale: "explanation : number of cubes = 100 ∗ 100 ∗ 100 / 10 ∗ 10 ∗ 10 = 1000 note : 1 m = 100 cm option b"
Answer: b
Python program:
a = volume_cube / (
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 35 kms . what was the total distance travelled in 12 hours ?
Options: a ) 456 kms , b ) 482 kms , c ) 552 kms , d ) 556 kms , e ) none of these
Rationale: "explanation : total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . . . upto 12 terms ) this is an a . p with first term , a = 35 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 × 35 + { 12 - 1 ) × 2 ] = 6 ( 70 + 23 ) = 552 kms . answer : c"
Answer: c
Python program:
a = 2 * 35
b = 12 - 1
c = b * 2
d = a + c 
e = 12 / 2
f = d * e
Problem: a and b together can do a piece of work in 10 days . b alone can finish it in 20 days . in how many days can a alone finish the work ?
Options: a ) 20 , b ) 10 , c ) 15 , d ) 5 , e ) 7
Rationale: time taken by a to finish the work = xy / ( y - x ) = 10 x 20 / ( 20 - 10 ) = 200 / 10 = 20 days answer : a
Answer: a
Python program:
a = 1/(10)
b = 1/(20)
c = a - b
d = 1/(c)
Problem: the ratio of pens to pencils is 5 to 6 . there are 7 more pencils than pens . how many pencils are there ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 55 , e ) 64
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 7 x = 7 the number of pencils is 42 . the answer is b ."
Answer: b
Python program:
a = 7 * 5
b = a + 7
Problem: the average score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 42 , then find the average for the last 4 matches .
Options: a ) 33.5 , b ) 33.5 , c ) 34.25 , d ) 35 , e ) none of these
Rationale: solution required average = ( 38.9 x 10 ) - ( 42 x 6 ) / 4 = 137 / 4 = 34.25 answer c
Answer: c
Python program:
a = 10 * 38
b = 6 * 42
c = a - b
d = c / 4
Problem: the distance between a & b is 600 km . a person is traveling from a to b at 70 km / hr started at 10 am and another person is traveling from b to a at 80 km / hr and started at same time . then at what time they meet together .
Options: a ) 2 pm , b ) 4 pm , c ) 1 pm , d ) 3 pm , e ) 5 pm
Rationale: let x hours be they will meet together distance covered by 1 st person + distance covered by 2 nd person = 600 km 70 x + 80 x = 600 x = 4 hr they will meet = 10 am + 4 hr = 2 pm answer is a
Answer: a
Python program:
a = 70 + 80 
b = a + 10 
c = b / 80
Problem: a train running at 1 / 4 of its own speed reached a place in 12 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 9 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "time taken if run its own speed = 1 / 4 * 12 = 3 hrs time saved = 12 - 3 = 9 hrs answer : a"
Answer: a
Python program:
a = 1 / 4
b = a * 12
Problem: when a merchant imported a certain item , he paid a 9 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 67.50 , what was the total value of the item ?
Options: a ) $ 1,150 , b ) $ 1,450 , c ) $ 1,750 , d ) $ 2,150 , e ) $ 2,450
Rationale: "let x be the value in excess of $ 1,000 . 0.09 x = 67.5 x = $ 750 the total value was $ 750 + $ 1,000 = $ 1,750 . the answer is c ."
Answer: c
Python program:
a = 9 / 100
b = 67 / 50
c = b + 1 
d = c / 1
e = math.floor(d)
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 37 kg joins the group , the average weight of the group goes up by 1.00001 kg . find the number of boys in the group originally ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 37 kg joins the group , total weight of boys = 30 x + 37 so 30 x + 37 = 31 ( x + 1 ) = > x = 6 . answer : c"
Answer: c
Python program:
a = 30 + 1 
b = 37 - a
c = b + 1
Problem: of 55 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 49 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 55 thrower = 37 rest = 55 - 37 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 37 + 12 = 49 so a . 49 is the right answer"
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 55 - 37
d = b * c
e = 37 + d
Problem: a person want to give his money of $ 900 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 400 , b ) $ 300 , c ) $ 500 , d ) $ 180 , e ) $ 200
Rationale: "b ' s share = 900 * 3 / 9 = $ 300 answer is b"
Answer: b
Python program:
a = 2 + 3 
b = a + 4 
c = 3 / b
d = c * 900
Problem: a can do a piece of work in 21 days and b in 28 days . together they started the work and b left after 4 days . in how many days can a alone do the remaining work ?
Options: a ) 22 , b ) 88 , c ) 27 , d ) 14 , e ) 99
Rationale: "let a worked for x days . x / 21 + 4 / 28 = 1 = > x / 21 = 6 / 7 = > x = 18 a worked for 18 days . so , a can complete the remaining work in 18 - 4 = 14 days . answer : d"
Answer: d
Python program:
a = 1 / 21
b = 4 * a
c = 1 / 28
d = 4 * c
e = b + d 
f = 1 - e
g = 1 / 28
h = f / g
i = h + 4
Problem: if a and b are the two values of t that satisfy the equation t ^ 2 â € “ 12 t + 20 = 0 , with a > b , what is the value of a â € “ b ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: factor the left side of the equation : t ^ 2 â € “ 12 t + 20 = 0 ( t â € “ 2 ) ( t â € “ 10 ) = 0 t = 2 , t = 10 thus , a = 10 and b = 2 . so a â € “ b = 10 â € “ 2 = 8 . the answer is d .
Answer: d
Python program:
a = 20 / 2
b = a - 2
Problem: the average ( arithmetic mean ) of 4 different integers is 74 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 33
Rationale: "total of integers = 74 * 4 = 296 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 296 - ( 90 + 89 + 88 ) = 296 - 267 = 29 answer : c"
Answer: c
Python program:
a = 74 * 4
b = a - 90
c = 90 - 1
d = b - c
e = 90 - 2
f = d - e
Problem: how many numbers from 2 to 11 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 11 / 2 = 5 5 - 1 = 4 4 + 1 = 5 numbers . answer : c"
Answer: c
Python program:
a = 11 / 2
b = math.floor(a)
c = b * 2
d = 2 / 2
e = math.floor(d)
f = e + 1 
g = f * 2
h = c - g
i = h / 2
j = i + 1
Problem: if w is the set of all the integers between 35 and 64 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 18 , b ) 19 , c ) 61 , d ) 31 , e ) 11
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 63 , the smallest is 36 ) : 63 - 36 = 27 step 2 . divide by 3 : 27 / 3 = 9 step 3 . add 1 : 9 + 1 = 10 . so there are 10 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 64 , the smallest is 36 ) : 64 - 36 = 28 step 2 . divide by 2 : 28 / 2 = 14 step 3 . add 1 : 14 + 1 = 15 . so there are 15 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 10 multiples of 3 and the 15 multiples of 2 : 10 + 15 = 25 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 10 + 15 = 25 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 25 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 60 - 30 = 30 step 2 . divide by 6 : 30 / 6 = 5 step 3 . add 1 : 5 + 1 = 6 . so there are 6 multiples of 6 within the range : we counted 6 numbers twice . subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3 : = 10 + 15 - 6 = 25 - 6 = 19 therefore , the final number of multiples of 2 , 3 or 6 is 19 . hence , this is the correct answer . ( b )"
Answer: b
Python program:
a = 64 - 35
b = a / 3
c = math.floor(b)
d = 64 - 35
e = d / 2
f = c + e 
g = 64 - 35
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
Problem: 4 milkmen rented a pasture . a grazed 24 cows for 3 months ; b 10 for 5 months ; c 35 cows for 4 months and d 21 cows for 3 months . if a ' s share of rent is rs . 1440 , find the total rent of the field .
Options: a ) 6500 , b ) 3550 , c ) 4250 , d ) 2250 , e ) 3250
Rationale: ratio of shares of a , b , c , d = ( 24 x 3 ) : ( 10 x 5 ) : ( 35 x 4 ) : ( 21 x 3 ) = 72 : 50 : 140 : 63 . let total rent be rs . x . then , a ’ s share = rs . ( 72 x ) / 325 ( 72 x ) / 325 = 1440 = x = ( 1440 x 325 ) / 72 = 6500 hence , total rent of the field is rs . 6500 . answer is a .
Answer: a
Python program:
a = 24 * 3
b = 10 * 5
c = a + b 
d = 35 * 4
e = c + d 
f = 21 * 3
g = e + f 
h = 24 * 3
i = g / h
j = i * 1440
Problem: how many multiples of 4 are there between 12 and 108 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 3 up to 4 * 27 . 27 - 3 + 1 = 25 . the answer is e ."
Answer: e
Python program:
a = 108 - 12
b = a / 4
c = b + 1
Problem: 123 : 36 : : 221 : ?
Options: a ) 52 , b ) 69 , c ) 72 , d ) 25 , e ) 32
Rationale: "( 1 + 2 + 3 ) ^ 2 = 36 ( 2 + 2 + 1 ) ^ 2 = 25 answer : d"
Answer: d
Python program:
a = 123 / 36
b = 221 * a
Problem: an inspector rejects 0.02 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 10000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3100
Rationale: "let the number of meters to be examined be x then , 0.02 % of x = 2 ( 2 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 10000 answer is b"
Answer: b
Python program:
a = 2 * 100
b = a / 0
Problem: if a - b = 10 and a ^ 2 + b ^ 2 = 150 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 25 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 150 - 100 = 50 = > ab = 25 answer : c"
Answer: c
Python program:
a = math.sqrt(150)
b = a - 10
c = b / 2
d = 10 + c 
e = math.sqrt(150)
f = e - 10
g = f / 2
h = d * g
i = h * 2
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 900 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 4 / 1 , e ) 5 / 3
Rationale: "distance traveled by eddy = 900 km time taken by eddy = 3 hours average speed of eddy = 900 / 3 = 300 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 300 / 75 = 4 / 1 answer d"
Answer: d
Python program:
a = 900 / 3
b = 300 / 4
c = a / b
Problem: if 40 honey bees make 40 grams of honey in 40 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 40 , d ) 49 , e ) 30
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 40 : : 40 : x honey 40 : 1 = > 1 x 40 x x = 40 x 1 x 40 = > x = 40 . answer : c"
Answer: c
Python program:
a = 1 / 40
b = 1 / a
Problem: a dog takes 5 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 25 : 10 , b ) 25 : 8 , c ) 25 : 9 , d ) 8 : 25 , e ) 24 : 8
Rationale: "explanation : dog : hare = ( 5 * 5 ) leaps of hare : 8 leaps of hare = 25 : 8 answer : b"
Answer: b
Python program:
a = 5 * 5
b = a / 8
Problem: of the families in city x in 2001 , 25 percent owned a personal computer . the number of families in city x owning a computer in 2008 was 15 percent greater than it was in 2001 , and the total number of families in city x was 6 percent greater in 2008 than it was in 2001 . what percent of the families in city x owned a personal computer in 2008 ?
Options: a ) 27.12 % , b ) 23.12 % , c ) 25.55 % , d ) 31.22 % , e ) 56.22 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 25 number of families owning computer in 1998 = 25 * 115 / 100 = 28.75 number of families in 1998 = 106 the percentage = 28.75 / 106 * 100 = 27.12 % . answer : a"
Answer: a
Python program:
a = 15 + 100 
b = a * 25
c = b / 100
d = 100 + 6 
e = c / d
f = 100 * e
Problem: the mass of 1 cubic meter of a substance is 100 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "100 kg - 1 cubic meter ; 100,000 g - 1 cubic meter ; 100,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 100,000 = 10 / 1 = 10 cubic centimeters . answer : c ."
Answer: c
Python program:
a = 1 * 0
b = 100 * 1
c = a / b
Problem: two pipes a and b can fill a tank in 12 and 24 minutes respectively . if both the pipes are used together , how long will it take to fill the tank ?
Options: a ) 9 min , b ) 8 min , c ) 4 min , d ) 6 min , e ) none of these
Rationale: "explanation : tank can be filled by pipe a in 12 minutes and pipe b in 24 minutes . = > part filled by a in 1 minute = 1 / 12 = > part filled by b in 1 minute = 1 / 24 = > part filled by both in 1 minute = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 time taken to fill the entire tank = 8 minutes answer b"
Answer: b
Python program:
a = 12 * 100
b = 1 / 12
c = 1 / 24
d = b + c 
e = d * 2
f = 1 - e
g = f * 12
h = g * const_60
i = a + h
Problem: what number is obtained by adding the units digits of 734 ^ 99 and 347 ^ 82 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "the units digit of 734 ^ 99 is 4 because 4 raised to the power of an odd integer ends in 4 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 4 + 9 = 13 . the answer is d ."
Answer: d
Python program:
a = 99 - 82
b = 1 + 10 
c = 99 / b
d = a - c
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 3 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 58
Rationale: et no of sheep and horses are 3 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 3 * 8 ) = 24 answer : a
Answer: a
Python program:
a = 12880 / 230
b = a / 7
c = b * 3
Problem: a pump can fill a tank with a water in 2 hours . because of a leak , it took 2 and 4 / 5 hours to fill the tank . the leak can drain all the water of the full tank in how many hours ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: the rate of the pump + leak = 5 / 14 1 / 2 - leak ' s rate = 5 / 14 leak ' s rate = 1 / 2 - 5 / 14 = 1 / 7 the leak will empty the tank in 7 hours . the answer is d .
Answer: d
Python program:
a = 1 / 2
b = 4 / 5
c = 2 + b 
d = 1 / c
e = a - d
f = 1 / e
Problem: the sum of number of boys and girls in a school is 100 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70
Rationale: "we have x + x % of 100 = 100 x + x / 100 * 100 = 100 2 * x = 100 x = 50 answer is a"
Answer: a
Python program:
a = 100 / 100
b = a + 1 
c = 100 / b
Problem: the food in a camp lasts for 20 men for 50 days . if 20 more men join , how many days will the food last ?
Options: a ) 22 days , b ) 25 days , c ) 28 days , d ) 16 days , e ) 27 days
Rationale: one man can consume the same food in 20 * 50 = 1000 days . 20 more men join , the total number of men = 40 the number of days the food will last = 1000 / 40 = 25 days . answer : b
Answer: b
Python program:
a = 20 * 50
b = 20 + 20 
c = a / b
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 264 . what is their h . c . f . ?
Options: a ) 18 , b ) 22 , c ) 24 , d ) 28 , e ) 32
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 264 x = 22 hcf of 2 x , 3 x and 4 x = x = 22 the answer is b ."
Answer: b
Python program:
a = 2 * 4
Problem: in a class of students , 1 / 2 of the number of girls is equal to 1 / 3 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 3 / 4
Rationale: "( 1 / 2 ) g = ( 1 / 3 ) ( b + g ) 3 g = 2 b + 2 g g = 2 b b / g = 1 / 2 . the answer is a ."
Answer: a
Python program:
a = 1 / 2
b = 1 / 3
c = a - b
d = 1 / 3
e = c / d
Problem: two circles are there one with arc area 60 digree equal to 45 digree of another circle find the area of circle 1 : circle 2 ratio
Options: a ) 3 : 4
b ) 1 : 4
c ) 1 : 2
d ) 2 : 3
e ) 1 : 3
Rationale: area for first circle = ( 3.14 * r ^ 2 ) / 6 area of second circke = ( 3.14 * r ^ 2 ) / 8 therefore , ratio = 3 : 4 answer : a
Answer: a
Python program:
a = 45 / 360
b = a * 2
c = b * math.pi
d = 60 / 360
e = d * 2
f = e * math.pi
g = c / f
Problem: in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 6 of the absentee ballets were thrown out and 3 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 4,000 , d ) 8,000 , e ) 9,000
Rationale: 5 / 6 * 2 / 5 ( total absentee votes ) = 1 / 3 ( total votes ) = 1 / 3 * 12000 = 4000 answer is c
Answer: c
Python program:
a = 3 * 4
b = a * 1000
c = 3 * 4
d = c * 1000
e = 1 / 6
f = d * e
g = b - f
h = 3 * 4
i = h * 1000
j = 3 * 4
k = j * 1000
l = 1 / 6
m = k * l
n = i - m
o = 3 / 5
p = n * o
q = g - p
r = q / 1000
s = r / 4
t = s * 3
Problem: a train 300 m long can cross an electric pole in 30 sec and then find the speed of the train ?
Options: a ) 76 kmph , b ) 54 kmph , c ) 72 kmph , d ) 36 kmph , e ) 91 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 30 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : d"
Answer: d
Python program:
a = 300 / 1000
b = 30 / 3600
c = a / b
Problem: at what rate percent of simple interest will a sum of money double itself in 66 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 1.51 % , d ) 1.94 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 66 ) = 100 / 66 = 1.51 % answer : c"
Answer: c
Python program:
a = 100 / 66
Problem: an = 2 an - 1 + 4 and qn = 4 qn - 1 + 8 for all n > 1 . if a 5 = q 4 and a 7 = 316 , what is the first value of n for which qn is an integer ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assuming i have understood the symbols used correctly answer is c - 3 a 7 = 2 s 6 + 4 = 316 a 6 = 312 / 2 = 156 = 2 a 5 + 4 a 5 = 152 / 2 = 76 = q 4 q 4 = 4 q 3 + 8 = 76 q 3 = 68 / 4 = 17 q 3 = 4 q 2 + 8 = 17 q 2 = 9 / 4 = 2.25 q 2 = 4 q 1 + 8 q 1 will not be integer = c
Answer: c
Python program:
a = 7 - 4