euclaise/mathqa_programs huggingface dataset:
Problem: a bowl was half full of water . 4 cups of water were then added to the bowl , filling the bowl to 70 % of its capacity . how many cups of water are now in the bowl ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: lets say total volume of the container = v initial water content is half of total volume = v / 2 then 4 cups of water were added . current water content = ( v / 2 ) + 4 cups = ( 70 / 100 ) v = > v = 20 cups = > current water content is equivalent to = v / 2 + 4 cups = 20 / 2 + 4 = 14 cups ; answer : a
Answer: a
Python program:
a = 70 / 100
b = 4 * 100
c = 70 / 100
d = 100 / 2
e = d / 100
f = c - e
g = f * 100
h = b / g
i = a * h
Problem: two numbers are in the ratio of 5 : 7 . if 25 be subtracted from each , they are in the ratio of 35 : 59 . find the numbers ?
Options: a ) 60,88 , b ) 60,86 , c ) 60,82 , d ) 60,84 , e ) 60,83
Rationale: "( 5 x - 25 ) : ( 7 x - 25 ) = 35 : 59 x = 12 = > 60,84 answer : d"
Answer: d
Python program:
a = 5 * 25
Problem: the number 189 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 20 , d ) 27 , e ) 39
Rationale: "4 ^ 3 + 5 ^ 3 = 189 the number is 4 * 5 = 20 c"
Answer: c
Python program:
a = 189 / 2
b = 1 / 3
c = a ** b
d = math.floor(c)
e = 189 / 2
f = 1 / 3
g = e ** f
h = math.floor(g)
i = h ** 3
j = 189 - i
k = 1 / 3
l = j ** k
m = d * l
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 36000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "0.037 * 10 ^ 5 can be written as 3600 74000 * 10 ^ ( - 3 ) can be written as 36 required = 3600 / 36 = 100 answer : a"
Answer: a
Python program:
a = 1000 * 100
b = a * 0
c = 36000 / 1000
d = b / c
Problem: in 120 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 24 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 120 / 45 x 9 m = 24 m . a beats b by 24 metres . answer : option a"
Answer: a
Python program:
a = 120 / 45
b = 45 - 36
c = a * b
Problem: how many seconds will a 450 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 20 , b ) 27 , c ) 42 , d ) 32 , e ) 60
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 450 * 3 / 50 = 27 sec . answer : option b"
Answer: b
Python program:
a = 63 - 3
b = a * const_0_2778
c = 450 / b
Problem: fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 40 %
Rationale: "x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 10 ( 0.22 - x ) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ."
Answer: e
Python program:
a = 22 / 100
b = 22 / 100
c = 18 * 2
d = b * c
e = 9 - d
f = 10 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: a taxi leaves point a 3 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 60 , b ) 72 , c ) 48 , d ) 36 , e ) 64
Rationale: let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 3 hrs . hence 6 * ( v - 30 ) = 3 v 6 v - 180 = 3 v 3 v = 180 v = 60 mph a
Answer: a
Python program:
a = 3 * 30
b = 3 * 30
c = a + b 
d = 3 + 3 
e = d - 3
f = c / e
Problem: a train 100 m long crosses a platform 250 m long in 7 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 180 kmph , e ) 59 kmph
Rationale: "d = 100 + 250 = 350 t = 7 s = 350 / 7 * 18 / 5 = 180 kmph answer : d"
Answer: d
Python program:
a = const_60 * 0
b = 7 * a
c = b - 100
Problem: what is the greatest positive integer x such that 6 ^ x is a factor of 216 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "216 ^ 10 = ( 6 ^ 3 ) ^ 10 = 6 ^ 30 answer : e"
Answer: e
Python program:
a = 216 - 10
b = a * 10
Problem: simple interest on a certain sum at a certain annual rate of interest is 1 / 4 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 4 % . , b ) 25 / 4 % . , c ) 5 % , d ) 6 % . , e ) 3 % .
Rationale: "explanation : let sum = x . then , s . i . = x / 4 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 4 ? r ^ 2 = 100 / 4 = 25 r = 5 hence , rate of interest = 5 % . answer : c"
Answer: c
Python program:
a = 1 / 4
b = a * 100
c = math.sqrt(b)
d = math.floor(c)
e = d * 10
f = e + 1 
g = f / 3
Problem: ravish has to secure 40 % marks to clear his board exam of class 10 th . he got 40 marks and failed by 40 marks . what is the maximum marks ?
Options: a ) 150 , b ) 135 , c ) 160 , d ) 200 , e ) 155
Rationale: d 200 to pass the exam ravish needs 40 + 40 = 80 marks . = > ( 80 / 40 ) * 100 = 200
Answer: d
Python program:
a = 40 + 40 
b = 40 / 100
c = a / b
Problem: there are 172 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 83 , b ) 85 , c ) 87 , d ) 79 , e ) 89
Rationale: "editing my solution : number of switches = 172 number of switches turned on by a : 3 , 6 , . . . 171 = 57 number of switches turned on by b : 5 , 10 , . . . . 170 = 34 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 57 - 6 ) + ( 34 - 6 ) = 79 answer : d"
Answer: d
Python program:
a = 172 / 3
b = math.floor(a)
c = 1 + 4 
d = 172 / c
e = math.floor(d)
f = b + e 
g = 1 + 4 
h = 3 * g
i = 172 / h
j = math.floor(i)
k = j * 2
l = f - k
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 41 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 140 , b ) 175 , c ) 210 , d ) 245 , e ) 280
Rationale: "in 72 minutes , car x travels 42 miles . car y gains 6 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d ."
Answer: d
Python program:
a = 72 / const_60
b = a * 35
c = 41 - 35
d = b / c
e = 35 * d
Problem: a man swims downstream 36 km and upstream 48 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 5 , b ) 24 , c ) 7 , d ) 42 , e ) 6
Rationale: "36 - - - 6 ds = 6 ? - - - - 1 48 - - - - 6 us = 8 ? - - - - 1 m = ? m = ( 6 + 8 ) / 2 = 7 answer : c"
Answer: c
Python program:
a = 48 / 6
b = 36 / 6
c = a + b 
d = c / 2
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100
Rationale: c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 17 - 2 cmb = 100 b - cb - mb - 2 cmb = 27 hence the probability = 27 / 100 d
Answer: d
Python program:
a = 50 + 40 
b = a - 17
c = 100 - b
d = c / 100
Problem: the original price of a suit is $ 150 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 130 , b ) $ 136 , c ) $ 144 , d ) $ 150 , e ) $ 160
Rationale: "0.8 * ( 1.2 * 150 ) = $ 144 the answer is c ."
Answer: c
Python program:
a = 150 * 20
b = a / 100
c = 150 + b 
d = 150 * 20
e = d / 100
f = 150 + e 
g = f * 20
h = g / 100
i = c - h
Problem: convert 350 inches into centimeter ?
Options: a ) 812 cm , b ) 820 cm , c ) 850 cm , d ) 889 cm , e ) 854 cm
Rationale: "1 inch = 2.54 cm 350 inches = 100 * 2.54 = 889 cm answer is d"
Answer: d
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 350
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ?
Options: a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ) 22.5 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b"
Answer: b
Python program:
a = 624 / 4
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: a is twice as fast as b . if b alone can do a piece of work in 10 days , in what time can a and b together complete the work ?
Options: a ) 10 / 3 , b ) 8 , c ) 9 , d ) 7 / 3 , e ) 12
Rationale: "a can do the work in 10 / 2 i . e . , 5 days . a and b ' s one day ' s work = 1 / 5 + 1 / 10 = ( 2 + 1 ) / 10 = 10 / 3 so a and b together can do the work in 10 / 3 days . answer : a"
Answer: a
Python program:
a = 1 / 10
b = 1 / 10
c = b * 2
d = a + c 
e = 1/(d)
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 36 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.4 = 1.5 km = 1500 m . required time = 1500 * 3 / 125 = 36 sec . answer : b"
Answer: b
Python program:
a = 1 * 10
b = 60 * 1000
c = b / 3600
d = a / c
e = 0 * 4
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: how much time does a train 225 metres long running at 90 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 9 s , e ) 7.4 s
Rationale: "explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 225 / t t = 9 s answer : d"
Answer: d
Python program:
a = 225 / 1000
b = a / 90
c = b * 3600
Problem: of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1000 , b ) 1200 , c ) 1400 , d ) 1600 , e ) 1800
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 3 ) x = 120 ( 6 / 60 ) x = 120 x = 1200 the answer is b ."
Answer: b
Python program:
a = 3 / 5
b = 1 - a
c = 120 / b
d = 3 / 4
e = c / d
f = 1 / 3
g = e / f
Problem: the price of lunch for 20 people was $ 300 including a 20 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12.5 , c ) 13.8 , d ) 14 , e ) 15.87
Rationale: "clearly b is the answer i used poe here lets consider option ( b ) 20 * 12.5 = 250 now 250 ( 120 / 100 ) = 300 = > possible answer imo b"
Answer: b
Python program:
a = 100 - 20
b = 300 * a
c = b / 100
d = c / 20
Problem: the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 28 - inch flat - screen television than a square 25 - inch flat - screen television ?
Options: a ) 79.5
b ) 89.3
c ) 85.5
d ) 75.4
e ) 72.5
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 28 - inch flat - screen television the diagonal ( hypotenuse ) = 28 so , we can apply the pythagorean theorem to get x ² + x ² = 28 ² simplify : 2 x ² = 28 ² divide both sides by 2 to get : x ² = 28 ² / 2 since the area of the square = x ² , we can see that the area of this square is 28 ² / 2 square 25 - inch flat - screen television the diagonal ( hypotenuse ) = 25 so , we can apply the pythagorean theorem to get x ² + x ² = 25 ² simplify : 2 x ² = 25 ² divide both sides by 2 to get : x ² = 25 ² / 2 since the area of the square = x ² , we can see that the area of this square is 25 ² / 2 difference in areas = 28 ² / 2 - 25 ² / 2 = ( 28 ² - 25 ² ) / 2 = ( 784 - 625 ) / 2 = 159 / 2 = 79.5 a
Answer: a
Python program:
a = 28 ** 2
b = a / 2
c = 25 ** 2
d = c / 2
e = b - d
Problem: the sector of a circle has radius of 14 cm and central angle 144 o . find its perimeter ?
Options: a ) 60 cm , b ) 63.2 cm , c ) 70 cm , d ) 80 cm , e ) 90 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 144 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 35.2 + 28 = 63.2 cm answer : b"
Answer: b
Python program:
a = 14 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 14
Problem: a number is doubled and 4 is added . if the resultant is divided by 5 , it becomes 25 . what is that number ?
Options: a ) 73.5 , b ) 68 , c ) 60.5 , d ) none of these , e ) can not be determined
Rationale: "solution let the number be x . then , ( 2 x + 4 ) / 5 ‹ = › 25 ‹ = › 2 x + 4 = 125 ‹ = › 2 x = 121 x = 60.5 answer c"
Answer: c
Python program:
a = 3 * 4
b = 5 - a
c = 3 * 2
d = b / c
Problem: chris mixed 4 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 4 lbs of raisin = $ 4 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 4 = 16 fraction of the value of raisin = 4 / 16 = 1 / 4 ans : c"
Answer: c
Python program:
a = 4 * 3
b = a + 4 
c = 4 / b
Problem: how many 3 digit numbers are divisible by 6 in all ?
Options: a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) 172
Rationale: "explanation : required numbers are 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then , a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 . answer is b"
Answer: b
Python program:
a = 1000 - 10
b = 3 * 3
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: 1907 x 1907 = ?
Options: a ) a ) 3623216 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3636649 , e ) e ) 3625216
Rationale: "1907 x 1907 = ( 1907 ) 2 = ( 1900 + 7 ) 2 = ( 1900 ) 2 + ( 7 ) 2 + ( 2 x 1900 x 7 ) = 3610000 + 49 + 26600 . = 3636649 . d )"
Answer: d
Python program:
a = 1907 / 1907
b = a * 100
Problem: an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) 720 , b ) 360 , c ) 250 , d ) 280 , e ) 290
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 3120 = rs . 720 answer : a"
Answer: a
Python program:
a = 2 + 3 
b = a + 4 
c = 3120 / b
d = c * 4
Problem: a certain company ’ s profit in 1996 was 10 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 32 % , d ) 35 % , e ) 38 %
Rationale: profit in 1995 - 100 profit in 1996 - 110 % increae profit in 1997 in comparison to 1995 = 10 + 110 * 20 % = 32 correct option : c
Answer: c
Python program:
a = 20 / 100
b = a + 1 
c = 10 / 100
d = 1 + c 
e = b * d
f = e - 1
g = f * 100
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 11 .
Options: a ) 8 , b ) 5 , c ) 1 , d ) 3 , e ) 4
Rationale: "6 * 15 * 11 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 11 + 1 ) = ( √ 8 * 18 ) / 12 = ( √ 144 ) / 12 = 12 / 124 = 1 . answer is c"
Answer: c
Python program:
a = 6 + 2 
b = 15 + 3 
c = a * b
d = math.sqrt(c)
e = 11 + 1 
f = d / e
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 8 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 8 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2400 . hence , ( r - p ) = ( 2400 - 900 ) = 1500 answer : b"
Answer: b
Python program:
a = 1500 / 5
b = 8 - 3
c = a * b
Problem: in a caravan , in addition to 50 hens , there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads in the caravan , the number of keepers is
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: explanation : let number of keepers be x . then , total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2 x = 2 x + 312 . total number of heads = 50 + 45 + 8 + x = 103 + x . therefore ( 2 x + 312 ) = ( 103 + x ) + 224 or x = 15 . answer : d
Answer: d
Python program:
a = 50 + 45 
b = a + 8 
c = b + 224 
d = 2 * 50
e = 4 * 45
f = d + e 
g = 4 * 8
h = f + g 
i = c - h
Problem: a 1500 m long train crosses a tree in 120 sec , how much time will it take to pass a platform 500 m long ?
Options: a ) 288 , b ) 160 , c ) 188 , d ) 188 , e ) 12
Rationale: "l = s * t s = 1500 / 120 s = 12.5 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 12.5 t = 160 sec answer : b"
Answer: b
Python program:
a = 1500 + 500 
b = 1500 / 120
c = a / b
Problem: n is a positive integer . when n + 1 is divided by 6 , the remainder is 4 . what is the remainder when n is divided by 2 ?
Options: a ) 6 , b ) 5 , c ) 1 , d ) 3 , e ) 2
Rationale: n + 1 = 6 a + 4 i . e . n + 1 = 10 , 16 , 22 , 28 , . . . etc . i . e . n = 9 , 15 , 21 , 27 , . . . etc . when n is divided by 2 remainder is always 1 answer : c
Answer: c
Python program:
a = 4 + 2 
b = 6 / a
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 2999 , b ) 1350 , c ) 2677 , d ) 2898 , e ) 2787
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 2 = rs . 1350 answerb"
Answer: b
Python program:
a = 2 * 5
b = 75 + a 
c = 2 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: if 9 / ( 5 + 3 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 3 / 4 , d ) - 1 / 3 , e ) - 3
Rationale: the expression 9 / ( 5 + 3 / x ) = 1 should have been equal to something . if 9 / ( 5 + 3 / x ) = 1 = > 9 x / ( 5 x + 3 ) = 1 = > 9 x = 5 x + 3 = > 4 x = 3 = > x = 3 / 4 correct option : c
Answer: c
Python program:
a = 9 - 5
b = 3 / a
Problem: if price of t . v set is reduced by 25 % , then its sale increases by 75 % , find net effect on sale value
Options: a ) 31 , b ) 32 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 25 + 75 + ( - 25 * 75 ) / 100 = - 25 + 75 - 19 = 31 answer : a"
Answer: a
Python program:
a = 100 - 25
b = a / 100
c = 100 + 75 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: 25 , 50 , 100 , 175 , 275 , ( . . . . )
Options: a ) 400 , b ) 300 , c ) 425 , d ) 450 , e ) 325
Rationale: "explanation : the pattern is 25 , 50 , 75 , 100 , etc . hence 125 = 400 answer : a"
Answer: a
Python program:
a = negate - (
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 9 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 9 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 9 * ( 2 / 3 ) ) days = > 20 days answer : b"
Answer: b
Python program:
a = 15 * 21
b = a * 8
c = 21 * 9
d = 2 / 3
e = c * d
f = b / e
Problem: kathleen can paint a room in 3 hours , and anthony can paint an identical room in 4 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 4 / 3 , c ) 15 / 8 , d ) 24 / 7 , e ) 15 / 4
Rationale: "( 1 / 3 + 1 / 4 ) t = 2 t = 24 / 7 answer : d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 4
c = a + b 
d = 1 / c
e = d * 2
Problem: how many prime numbers are between 25 / 8 and 213 / 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "25 / 8 = 4 - 213 / 6 = 36 - prime numbers between 4 and 36 are 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , and 31 - sign signifies that the number is marginally less . answer d"
Answer: d
Python program:
a = math.floor(2)
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 4 . if p is less than – 2 , what is the value of p ?
Options: a ) – 14 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 4 = 6 since number p is twice as many units from - 2 as - 2 is from 4 , therefore p can be - 14 since , p is less than - 2 , the value of p = - 14 answer a"
Answer: a
Python program:
a = negate - (
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 18 : 13 , b ) 16 : 13 , c ) 19 : 13 , d ) 14 : 11 , e ) 13 : 11
Rationale: "vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 375 , water = 125 ; vessel a + b = 800 gallons - - > milk = 475 , water 325 . the ratio = 475 / 325 - - > 19 / 13 answer : c"
Answer: c
Python program:
a = 1 ** 3
Problem: a bus travels first half distance between two places with a speed of 40 kmph and the rest half distance with a speed of 60 kmph . the average speed of the bus is ?
Options: a ) 48 kmph , b ) 78 kmph , c ) 28 kmph , d ) 18 kmph , e ) 98 kmph
Rationale: explanation : we know that speed = distance traveled / time taken let the total distance traveled by the car is 2 x km . then time taken by it to cover first half is hour . and for second half is hour . then average speed = total distance travelled / total time taken . i . e . = > = 48 kmph . answer : a
Answer: a
Python program:
a = 40 + 60 
b = a / 2
Problem: in a hostel there were 100 students . to accommodate 20 more students the average is decreased by rupees 5 . but total expenditure increased by rs . 400 . find the total expenditure of the hostel now ?
Options: a ) 54888 , b ) 2777 , c ) 5400 , d ) 1278 , e ) 2881
Rationale: "100 x + 400 = 12 ( x – 5 ) x = 50 100 * 50 + 400 = 5400 answer : c"
Answer: c
Python program:
a = 100 + 20 
b = a * 5
c = b + 400 
d = c / 20
e = d - 5
f = 100 + 20 
g = e * f