euclaise/mathqa_programs huggingface dataset:
Problem: given that g and h are events such that q ( g ) = 0.30 q ( h ) = 0.9 q ( gnh ) = 0.9 find q ( g | h ) and q ( g | h )
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 6 , e ) 1 / 3
Rationale: here , g and h are events q ( g | h ) = q ( gnh ) / q ( h ) = 0.9 / 0.9 = 1 q ( g | h ) = q ( gnh ) / q ( g ) = 0.9 / 0.30 = 1 / 3 answer is c
Answer: c
Python program:
a = 0 * 3
b = a + 0 
c = b - const_0_25
d = c - const_0_25
e = 0 / 9
f = d / e
Problem: 6000 − ( 105 ÷ 21.0 ) = ?
Options: a ) 6100 , b ) 5100 , c ) 550 , d ) 598 , e ) 5995
Rationale: "explanation : = 6000 − ( 105 / 21 ) = 6000 − 5 = 5995 option e"
Answer: e
Python program:
a = 105 / 21
b = 6000 - a
Problem: a boats man can row in still water at speed of 7 km / hr . it takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km / hr . what is the distance between the two destinations ?
Options: a ) 40 , b ) 87 , c ) 126 , d ) 18 , e ) 91
Rationale: explanation : x = 7 km / hr ; y = 3 km / hr ds = 10 km / hr ; us = 4 km / hr distance ( d ) is same . therefore , if time taken for downstream is t hours , the time for upstream is ( t + 6 ) hours . 10 * t = 4 * ( t + 6 ) 6 t = 24 ; t = 4 hours d = 10 * 4 = 40 km answer : a
Answer: a
Python program:
a = 6 * 4
b = a / 6
c = b * 10
Problem: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 3 m + n ?
Options: a ) 11 , b ) 18 , c ) 20 , d ) 45 , e ) 33
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 3 * 10 + 15 = 45 answer : d"
Answer: d
Python program:
a = 3 ** 3
b = 4 * a
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 24 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 6
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 104 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 24 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 24 r 2 = ( 24 * 2 ) / 3 = 16 = > r = 4 rate = 4 % answer : option d"
Answer: d
Python program:
a = math.sqrt(24)
Problem: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 76 . how tall is the fourth person ?
Options: a ) 76 , b ) 78 , c ) 80 , d ) 82 , e ) 84
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 76 ) = 304 x = 72 and the fourth person has a height of 72 + 10 = 82 inches the answer is d ."
Answer: d
Python program:
a = 76 * 4
b = 4 + 6 
c = 6 + b 
d = a - c
e = d / 4
f = 4 + 6 
g = e + f
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 65 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,960 , e ) $ 27,360
Rationale: for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.65 * 12000 = 12000 - 7800 x = 4200 earning becomes 9360 + 3 x = 9360 + 3 * 4200 = 21960 ans : d
Answer: d
Python program:
a = 100 * 3
b = a + const_60
Problem: how many prime numbers between 1 and 100 are factors of 7150 ?
Options: a ) 238 , b ) 100 , c ) 299 , d ) 270 , e ) 111
Rationale: "ans : 7 , 150 = 2 × 52 × 11 × 13 so there are 4 distinct prime numbers that are below 100 answer : b"
Answer: b
Python program:
a = 4 * 1
Problem: in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.8 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 228.9 $ , c ) 343.7 $ , d ) 395.05 $ , e ) 412.12 $
Rationale: service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.8 = 384.8 total cost = fuel + service = 384.8 + 10.25 = 395.05 answer is d
Answer: d
Python program:
a = 65 * 120
b = a / 100
c = 65 + b 
d = c * 2
e = d * 0
f = 65 * 3
g = f * 0
h = e + g
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 88 and rs . 80 respectively . the sum is :
Options: a ) 880 , b ) 1450 , c ) 1600 , d ) 1800 , e ) none
Rationale: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 88 * 80 / ( 88 - 80 ) = rs . 880 . answer a"
Answer: a
Python program:
a = 88 * 80
b = 88 - 80
c = a / b
Problem: machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 3 hours and machine y produces k bottles in 2 hours . how many hours does it take machines x and y , working simultaneously , to produce 12 k bottles ?
Options: a ) 16 , b ) 20 , c ) 15 , d ) 72 / 5 , e ) 24
Rationale: x rate = k / 3 y rate = k / 2 k / 3 + k / 2 = 12 k / t solving t = 72 / 5 answer d
Answer: d
Python program:
a = 3 + 2 
b = a / 2
c = 12 * b
d = c / 2
Problem: a family pays $ 800 per year for an insurance plan that pays 65 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,500 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 35 % of first 1000 $ in expense = 350 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 350 = 1150 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1500 $ ( since insurance plan will pay 100 % of amount that exceeds 1150 $ ) answer d"
Answer: d
Python program:
a = 1 - 0
Problem: by how much is 3 - fifth of 390 greater than 4 - seventh of 210 ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 114 , e ) 130
Rationale: explanation : 3 / 5 of 390 - 4 / 7 of 210 = 234 - 120 = 114 . answer : d
Answer: d
Python program:
a = 2 + 3 
b = 3 / a
c = b * 390
d = 3 + 4 
e = 4 / d
f = e * 210
g = c - f
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 51 then sum is
Options: a ) rs . 5000 , b ) rs . 5100 , c ) rs . 5800 , d ) rs . 6000 , e ) rs . 6200
Rationale: p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 51 5100 answer : b
Answer: b
Python program:
a = 10 / 100
b = 10 / 100
c = a * b
d = 51 / c
Problem: a box measuring 27 inches long by 15 inches wide by 6 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 90
b ) 180
c ) 210
d ) 240
e ) 864
Rationale: least number of cubes will be required when the cubes that could fit in are biggest . 3 is the biggest number that could divide all three , 27 , 15 and 6 . thus side of cube must be 3 , and total number of cubes = 27 / 3 * 15 / 3 * 6 / 3 = 90 ans a it is .
Answer: a
Python program:
a = 27 * 15
b = a * 6
c = 6 / 2
d = b / volume_cube
Problem: if x is 30 percent more than y and y is 50 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 65 % , d ) 125 % , e ) 60 %
Rationale: "z = 100 ; y = 50 so x = 65 x as % of z = 65 / 100 * 100 = > 65 % answer will be ( c )"
Answer: c
Python program:
a = 30 / 100
b = 1 + a 
c = 100 - 50
d = b * c
Problem: in an examination 35 % of the students passed and 481 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 740 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 481 65 x / 100 = 481 x = 481 * 100 / 65 = 740 answer is d"
Answer: d
Python program:
a = 481 * 100
b = 100 - 35
c = a / b
Problem: a certain number of men can do a work in 20 days . if there were 4 men more it could be finished in 5 days less . how many men are there ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 20 , e ) 18
Rationale: "original number of workers = 4 * ( 20 - 5 ) / 5 = 12 men answer is b"
Answer: b
Python program:
a = 20 + 5 
b = a * 4
c = b / 5
Problem: a farmer spent $ 38 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 41.80
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 38 = $ 15.2 on chicken feed , thus he spent the remaining 38 - 15.2 = $ 22.8 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 15.2 - - > x = $ 19 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 19 + 22.8 = $ 41.8 . answer : e ."
Answer: e
Python program:
a = 40 / 100
b = 38 * a
c = b + 38
Problem: 10 men and 15 women together can complete a work in 7 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 127 days , b ) 667 days , c ) 177 days , d ) 187 days , e ) 350 days
Rationale: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 7 15 women ' s 1 day work = ( 1 / 7 - 10 / 100 ) = 3 / 70 1 woman ' s 1 day work = 1 / 350 1 woman alone can complete the work in 350 days . answer : e"
Answer: e
Python program:
a = 1 * 100
b = 1 * 100
c = 10 * 7
d = b - c
e = a / d
f = 15 * 7
g = e * f
Problem: a can do a work in 60 days . he works for 15 days and later b alone completes the work in 30 days . in what time will they together complete the work ?
Options: a ) 24 days , b ) 25 days , c ) 30 days , d ) 32 days , e ) none of these
Rationale: let a can do a work in = 1 / 60 days he does 15 days so work done by a in 15 days = ( 15 ) * ( 1 / 60 ) = 1 / 4 remaining work is = 1 - 1 / 4 = 3 / 4 b ' s one day work is = 1 / 30 so 3 / 4 work is done by b in = ( 3 / 4 ) * ( 1 / 30 ) = 1 / 40 days time require to complete the work is = 1 / 60 + 1 / 40 = 5 / 120 5 / 120 = 1 / 24 so 24 days require to complete the work together . answer : a
Answer: a
Python program:
a = 30 + 10 
b = 1/(a)
c = 1/(60)
d = b + c 
e = 1/(d)
Problem: jerry and beth each drove from smallville to crown city by different routes . jerry drove an an average speed of 40 miles per hour and completed the trip in 30 minutes . beth ' s route was 5 miles longer , and it took her 20 minutes more than jerry to complete the trip . how many miles per hour was beth ' s average speed on this trip ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 75
Rationale: speed = distance / time distance for jerry = speed * time = 40 * 1 / 2 = 20 miles distance for beth = distance for jerry + 5 = 20 + 5 = 25 miles time taken by beth = time taken by jerry + ( 1 / 3 hour ) = 1 / 2 + 1 / 3 = 5 / 6 speed of beth = d / t = 25 / ( 5 / 6 ) = 25 * 6 / 5 = 30 miles per hour hence , b is the answer .
Answer: b
Python program:
a = 40 / const_60
b = a * 30
c = b + 5 
d = 30 + 20 
e = speed * (
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 3 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 8 / 15 , e ) 13 / 20
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 3 = 105 remaining work is 300 - 105 = 195 remaining fraction of work is = 195 / 300 = 13 / 20 answer e"
Answer: e
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = c * 3
e = 1 - d
Problem: a certain company had a total annual expenditure of 1.47 ∗ 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ?
Options: a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: given : total annual expenditure of 1.47 ∗ 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 3.5 = 1470 therefore try to bring the numerator in terms of 1470 average salary = ( 1470 * 10 ^ 4 ) / 420 = 3.5 * 10 ^ 4 = 35,000 option c
Answer: c
Python program:
a = 10 * 7
b = 1 * 47
c = b / 420
d = c * 100
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 12 hours , and machine с can finish the job in 8 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 15 / 4 , b ) 18 / 7 , c ) 21 / 8 , d ) 24 / 11 , e ) 28 / 13
Rationale: "the combined rate is 1 / 4 + 1 / 12 + 1 / 8 = 11 / 24 of the job per hour . the time to complete the job is 24 / 11 hours . the answer is d ."
Answer: d
Python program:
a = 1/(4)
b = 1/(12)
c = a + b 
d = 1/(8)
e = c + d 
f = 1/(e)
Problem: the number 130 can be written as the sum of the squares of 2 different positive integers . what is the sum of these 2 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "11 ^ 2 + 3 ^ 2 = 130 - - > 11 + 3 = 14 . d"
Answer: d
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 2
Problem: if 10000 microns = 1 decimeter , and 1000000000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 0.01 , b ) 1 , 000,000 , c ) 0.001 , d ) 1,000 , e ) 1.0 e - 05
Rationale: given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b
Answer: b
Python program:
a = 1 / 1
Problem: pipe a can fill a tank in 24 minutes . pipe b can fill the same tank 6 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 32 / 7 minutes , c ) 192 / 7 minutes , d ) 3 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 24 minutes - - > the rate of a = 1 / 24 tank / minute ; pipe b can fill the same tank 6 times fasterthan pipe a - - > the rate of b = 1 / 24 + 6 / 24 = 7 / 24 tank / minute . their combined rate = 1 / 24 + 7 / 24 = 1 / 3 tank / minute ; therefore , a and b can fill the tank in 3 minutes . answer : d"
Answer: d
Python program:
a = 1 / 24
b = 1 / 24
c = 6 / 24
d = b + c 
e = a + d 
f = 1/(e)
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 24 , what is the value of r - p ?
Options: a ) 28 , b ) 10 , c ) 30 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 48 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 28 hence , the correct answer is a"
Answer: a
Python program:
a = 24 * 2
b = 10 * 2
c = a - b
Problem: the ratio of three numbers is 6 : 7 : 5 and their sum is 108 . the second number of the three numbers is ?
Options: a ) 12 , b ) 42 , c ) 30 , d ) 36 , e ) none of these
Rationale: "explanation : 6 : 7 : 5 total parts = 18 18 parts - - > 108 1 part - - - - > 6 the second number of the three numbers is = 7 7 parts - - - - > 42 answer : option b"
Answer: b
Python program:
a = 5 ** 2
b = 6 ** 7
c = 7 ** 7
d = b + c 
e = a + d 
f = 108 / e
g = math.sqrt(f)
Problem: a room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room ?
Options: a ) 110 , b ) 124 , c ) 96 , d ) 117 , e ) 127
Rationale: "length = 6 m 24 cm = 624 cm width = 4 m 32 cm = 432 cm hcf of 624 and 432 = 48 number of square tiles required = ( 624 * 432 ) / ( 48 * 48 ) = 13 * 9 = 117 answer : d"
Answer: d
Python program:
a = 6 * 100
b = a + 24 
c = 4 * 100
d = c + 32 
e = b * d
f = 6 * 100
g = f + 24 
h = 4 * 100
i = h + 32 
j = math.gcd(g, i)
k = 6 * 100
l = k + 24 
m = 4 * 100
n = m + 32 
o = math.gcd(l, n)
p = j * o
q = e / p
Problem: the average of first five prime numbers greater than 61 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 74.6 , d ) 32.8 , e ) 32.4
Rationale: "67 + 71 + 73 + 79 + 83 = 373 / 5 = 74.6 answer : c"
Answer: c
Python program:
a = 61 + 1
Problem: a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km
Options: a ) 200 km , b ) 222 km , c ) 224 km , d ) 248 km , e ) none of these
Rationale: "explanation : let time taken to travel the first half = x hr then time taken to travel the second half = ( 10 - x ) hr distance covered in the the first half = 21 x [ because , distance = time * speed ] distance covered in the the second half = 24 ( 10 - x ) distance covered in the the first half = distance covered in the the second half so , 21 x = 24 ( 10 - x ) = > 45 x = 240 = > x = 16 / 3 total distance = 2 * 21 ( 16 / 3 ) = 224 km [ multiplied by 2 as 21 x was distance of half way ] option c"
Answer: c
Python program:
a = 21 * 24
b = a * 10
c = 21 + 24 
d = b / c
e = 2 * d
Problem: calculate how many seconds it will take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 9 , 10 , 14 and 18 seconds . ?
Options: a ) 636 , b ) 631 , c ) 633 , d ) 610 , e ) 630
Rationale: lcm of 9 , 10 , 14 and 18 is 630 lcm = 630 answer : e
Answer: e
Python program:
a = 14 / 2
b = 9 * 10
c = a * b
Problem: the size of a flat - screen tablet is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 8 - inch flat - screen tablet than a square 7 - inch flat - screen tablet ?
Options: a ) 7.6 , b ) 7.3 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 8 - inch flat - screen television the diagonal ( hypotenuse ) = 8 so , we can apply the pythagorean theorem to get x ² + x ² = 8 ² simplify : 2 x ² = 8 ² divide both sides by 2 to get : x ² = 8 ² / 2 since the area of the square = x ² , we can see that the area of this square is 8 ² / 2 square 7 - inch flat - screen television the diagonal ( hypotenuse ) = 7 so , we can apply the pythagorean theorem to get x ² + x ² = 7 ² simplify : 2 x ² = 7 ² divide both sides by 2 to get : x ² = 7 ² / 2 since the area of the square = x ² , we can see that the area of this square is 7 ² / 2 difference in areas = 8 ² / 2 - 7 ² / 2 = ( 8 ² - 7 ² ) / 2 = ( 64 - 49 ) / 2 = 15 / 2 = 7.5 d"
Answer: d
Python program:
a = 8 ** 2
b = a / 2
c = 7 ** 2
d = c / 2
e = b - d
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1672 cm is ?
Options: a ) 22 , b ) 28 , c ) 19 , d ) 12 , e ) 88
Rationale: "2 * 22 / 7 * 14 * x = 1672 = > x = 19 answer : c"
Answer: c
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 1672 / g
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2016 ) = ?
Options: a ) 2017 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2016 ) = 2017 ans : a
Answer: a
Python program:
a = 1 + 2016
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and six times as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 2 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 6 y solve equation # 2 for z : z = y - 12 now , we can replace both x and z with y in equation # 1 6 y + y + ( y - 12 ) = 100 8 y - 12 = 100 5 y = 112 y = 14 there are 14 blue balls . this is 12 more than the number of white balls , so z = 2 . that ' s the answer . just as a check , x = 84 , and 84 + 14 + 2 = 100 . answer = 2 , ( c )"
Answer: c
Python program:
a = 12 * 3
b = 100 - a
c = b / 4
Problem: 75 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 48 , b ) 180 / 7 , c ) 50.4 , d ) 60 , e ) 90
Rationale: 75 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 75 ) * 100 = 48 square feet answer : option a
Answer: a
Python program:
a = 4 * 9
b = 75 / 100
c = a / b
Problem: there are 408 boys and 264 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 28 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 264 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 264 / 24 = 17 + 11 = 28 answer : a"
Answer: a
Python program:
a = 408 + 264 
b = 2 * 2
c = b * 2
d = c * 3
e = a / d
Problem: the speed at which a woman can row a boat in still water is 120 kmph . if she rows downstream , where the speed of current is 60 kmph , what time will he take to cover 500 metres ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: speed of the boat downstream = 120 + 60 = 180 kmph = 180 * 5 / 18 = 50 m / s hence time taken to cover 500 m = 500 / 50 = 10 seconds . answer : c
Answer: c
Python program:
a = 120 + 60 
b = a * const_0_2778
c = 500 / b
Problem: a company that ships boxes to a total of 15 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 9
Rationale: "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - d"
Answer: d
Python program:
a = 15 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 15 / 2
i = h - 1
j = g - i