euclaise/mathqa_programs huggingface dataset:
Problem: if x is to be chosen at random from the integers between 1 to 5 , inclusive , and y is to be chosen at random from the integers between 7 and 10 , inclusive , what is the probability that x + y will be even ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 2 / 5 * 2 / 4 = 1 / 5 p ( x and y are both odd ) = 3 / 5 * 2 / 4 = 3 / 10 p ( x + y is even ) = 1 / 5 + 3 / 10 = 1 / 2 the answer is a .
Answer: a
Python program:
a = 2 * 2
b = 3 * 2
c = a + b 
d = 5 - 1
e = 5 * d
f = c / e
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 8 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 62 , d ) 14 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 8 ^ 2 - 2 = 62 . thus , the answer is c ."
Answer: c
Python program:
a = 2 ** 2
b = a - 2
Problem: the perimeter of a rhombus is 52 units . one of its diagonal is 24 units . what is its second diagonals length ?
Options: a ) 5
b ) 10
c ) 15
d ) 20
e ) 25
Rationale: when the perimeter of a triangle is 52 units each side is 13 units next , the diagonal of a rhombus bisect each other at 90 degree thus the half of the diagonal is 12 units now in a right angle triangle so formed , the perpendicular is 12 and the hypptenuse is 13 ( that is the side of the triangle ) finding the base ( which is half of the other diagonal ) : 13 ^ 2 - 12 ^ 2 = 25 thus half of the diagonal is 5 and the diagonal is 10 units answer : b
Answer: b
Python program:
a = 52 / 4
b = a ** 2
c = 24 / 2
d = c ** 2
e = b - d
f = math.sqrt(e)
g = f * 2
Problem: how much is 60 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 4 , b ) 6 , c ) 10 , d ) 8 , e ) 13
Rationale: "60 / 100 ) * 40 â € “ ( 4 / 5 ) * 25 24 - 20 = 4 answer : a"
Answer: a
Python program:
a = 60 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: if x and y are integers , what is the least positive number of 24 x + 18 y ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "24 x + 21 y = 6 ( 4 x + 3 y ) which will be a minimum positive number when 4 x + 3 y = 1 . 4 ( 1 ) + 3 ( - 1 ) = 1 then 6 ( 4 x + 3 y ) can have a minimum positive value of 6 . the answer is b ."
Answer: b
Python program:
a = 24 - 18
Problem: the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.2 minutes , b ) 5.21 minutes , c ) 5.25 minutes , d ) 5.28 minutes , e ) 6 minutes
Rationale: let both of them meet after tt min 4500 m are covered by suresh in 60 m . in tt min he will cover 4500 t 604500 t 60 likewise , in tt min suresh ' s wife will cover 3750 t 603750 t 60 given , 4500 t 60 + 3750 t 60 = 7264500 t 60 + 3750 t 60 = 726 tt = 5.28 minutes option ( d ) is correct
Answer: d
Python program:
a = 4 * 5
b = 3 * 75
c = a + b 
d = c / const_60
e = 726 / d
Problem: a boatman goes 3 km against the current of the stream in 3 hour and goes 1 km along the current in 30 minutes . how long will it take to go 3 km in stationary water ?
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 1 hours
Rationale: "explanation : speed upstream = 3 / 3 = 1 km / hr speed downstream = 1 / ( 30 / 60 ) = 2 km / hr speed in still water = 1 / 2 ( 2 + 1 ) = 3 / 2 km / hr time taken to travel 3 km in still water = 3 / ( 3 / 2 ) = 6 / 3 = 2 hours answer : option d"
Answer: d
Python program:
a = 1 / 30
b = a * const_60
c = 3 / 3
d = b + c 
e = d / 2
f = 3 / e
Problem: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years . find the average age of the women ?
Options: a ) 39 , b ) 27 , c ) 30 , d ) 26 , e ) 29
Rationale: "20 + 24 + 8 * 2 = 60 / 2 = 30 answer : c"
Answer: c
Python program:
a = 20 + 24 
b = 8 * 2
c = a + b 
d = c / 2
Problem: how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 20 m long and 16 1 / 2 m board ?
Options: a ) 66 , b ) 18 , c ) 16 , d ) 10 , e ) 15
Rationale: "20 * 33 / 2 = 5 / 2 * 2 * x = > x = 66 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 16 + a 
c = 20 * b
d = 1 / 2
e = 2 + d 
f = e * 2
g = c / f
Problem: a corporation paid $ 5 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 140 % , e ) 43 %
Rationale: difference in ratios = ( 30 / 150 ) - ( 5 / 50 ) = ( 5 / 50 ) % change = ( change ( 5 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 140 % answer - d
Answer: d
Python program:
a = 30 + 5 
b = a / 150
c = 5 / 50
d = b - c
e = 5 / 50
f = d / e
g = f * 100
Problem: a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 69 / 70 ) â ˆ ’ 150000 ã — ( 69 / 70 ) â ˆ ’ 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,000 = > rs . 5,000 . answer : d
Answer: d
Python program:
a = 5 * 1000
b = a * 100
c = 75000 * 2
d = c + 75000 
e = b - d
f = 70 - 1
g = f / 70
h = 5 * 1000
i = h * 100
j = g * i
k = 75000 * 2
l = 70 - 1
m = l / 70
n = k * m
o = j - n
p = o - 75000
q = e - p
Problem: there are 5 thieves , each loot a bakery one after the other such that the first one takes 1 / 2 of the total no . of the breads plus 1 / 2 of a bread . similarly 2 nd , 3 rd , 4 th and 5 fth also did the same . after the fifth one no . of breads remained are 3 . initially how many breads were there ?
Options: a ) 124 , b ) 125 , c ) 126 , d ) 127 , e ) 128
Rationale: let the number of breads initial be x you should go in reverse order as left bread is 3 i . e x = ? after 1 st person ate a = x - ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - x ) / 2 - ( 1 / 2 ) i . e a = ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - 2 ) / 4 i . e a = ( x - 1 ) / 2 like wise - - - - after 2 nd person ate b = ( a - 1 ) / 2 like wise - - - - after 3 rd person ate c = ( b - 1 ) / 2 like wise - - - - after 4 th person ate d = ( c - 1 ) / 2 like wise - - - - after 5 th person ate e = ( d - 1 ) / 2 now as after 5 th person ate the value of remaining bread is - - - 3 therefore the value of e = 3 ; now go reverse from botom to top to get the value of x after calcuating value of d = 7 value of c = 15 value of b = 31 value of a = 63 value of x = 127 so the final answer is 127 breads were there answer : d
Answer: d
Python program:
a = 5 * 4
b = 5 * a
c = 5 * 4
d = b + c 
e = d + 5 
f = e + 2
Problem: in an examination 35 % of the students passed and 260 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 650 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 260 65 x / 100 = 260 x = 260 * 100 / 65 = 400 answer is b"
Answer: b
Python program:
a = 260 * 100
b = 100 - 35
c = a / b
Problem: if 8 women can color 400 m long cloth in 5 days , then 10 women can color 500 m long cloth in ?
Options: a ) 6 days , b ) 4 days , c ) 5 days , d ) 15 days , e ) 10 days
Rationale: "the length of cloth painted by one woman in one day = 400 / 8 × 5 = 10 m no . of days required to paint 500 m cloth by 10 women = 500 / 10 × 10 = 5 days answer : c"
Answer: c
Python program:
a = 8 * 5
b = 400 / a
c = 10 * b
d = 500 / c
Problem: average of 6 numbers comes out to be 3.95 . average of two of the numbers is 3.4 while the average of other two is 3.85 . determine the average of the two numbers left .
Options: a ) 4.7 , b ) 4.8 , c ) 4.3 , d ) 4.6 , e ) 4.9
Rationale: explanation : in the given question we have taken average of 6 numbers taken 2 at a time which makes 3 numbers . = > 3.95 ( average of 1 st and 2 nd number ) = > 3.85 ( average of 3 rd and 4 th number ) = > 3.4 ( average of 5 th and 6 th number ) 3.95 = ( 3.4 + 3.85 + x ) / 3 x = 4.6 answer d
Answer: d
Python program:
a = 2 / 6
b = 3 * 4
c = 2 / 6
d = 3 * 85
e = b + d 
f = 3 - 95
g = 2 / 6
h = f / g
Problem: the average weight of 8 person ' s increases by 4 kg when a new person comes in place of one of them weighing 55 kg . what might be the weight of the new person ?
Options: a ) 80 kg , b ) 87 kg , c ) 90 kg , d ) 100 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 55 + 32 ) kg = 87 kg . b )"
Answer: b
Python program:
a = 8 * 4
b = a + 55
Problem: a 900 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 1000 , b ) 1050 , c ) 1060 , d ) 370 , e ) 380
Rationale: "speed = 900 / 18 = 50 / 1 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 50 / 1 = > x = 1950 m . l = 1950 - 900 = 1050 answer : option b"
Answer: b
Python program:
a = speed * (
b = a - 39
Problem: a horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2
b ) 308 m 2
c ) 150 m 2
d ) 407 m 2
e ) none of these
Rationale: area of the shaded portion = 1 ⁄ 4 × π × ( 14 ) 2 = 154 m 2 answer a
Answer: a
Python program:
a = 14 ** 2
b = a * math.pi
c = b / 4
Problem: reeya obtained 55 , 67 , 76 , 82 and 55 out of 100 in different subjects , what will be the average
Options: a ) 70 , b ) 75 , c ) 67 , d ) 85 , e ) 90
Rationale: "explanation : ( 55 + 67 + 76 + 82 + 55 / 5 ) = 67 option c"
Answer: c
Python program:
a = 55 + 67 
b = a + 76 
c = b + 82 
d = c + 55 
e = 4 + 1 
f = d / e
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 8 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1
b ) 2
c ) 4
d ) 8
e ) 16
Rationale: as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 8 ( pir ^ 2 ) pir ^ 2 = 16 pir r = 16 answer : e
Answer: e
Python program:
a = 8 ** 2
b = math.sqrt(a)
c = 2 * b
Problem: at the end of the first quarter , the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 60 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 33.33 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 60 = 20 + b + 20 b / 100 b = 33.33 answer ( d )"
Answer: d
Python program:
a = 100 + 60 
b = 100 + 20 
c = a / b
d = c - 1
e = d * 100
Problem: the class mean score on a test was 50 , and the standard deviation was 15 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 20 , b ) 31 , c ) 45 , d ) 90 , e ) 89
Rationale: "1 sd from the mean ranges from 35 to 65 , where 65 is within sd above the mean and 35 within 1 sd below the mean 2 sd = 15 twice = 30 from the the mean , which is 80 to 20 , where 80 is within 2 sd above the mean and 20 is within 2 sd below the mean . answer = a"
Answer: a
Python program:
a = 2 * 15
Problem: find the area of a cuboid of length 4 cm , breadth 6 cm . and height 5 cm .
Options: a ) 120 cm cube
b ) 110 cm cube
c ) 220 cm cube
d ) 430 cm cube
e ) 480 cm cube
Rationale: area of a cuboid = lxbxh = 4 cm x 6 cm x 5 cm = 120 cm cube answer : a
Answer: a
Python program:
a = 4 * 6
b = a * 5
Problem: a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 660 , b ) 680 , c ) 720 , d ) 760 , e ) 800
Rationale: "total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 600 = 1800 5 x / 3 = 1200 x = 720 km the answer is c ."
Answer: c
Python program:
a = 1800 * 2
b = a / 3
c = b * 3
d = 2 + 3 
e = c / d
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 55000 . what is the share of c ?
Options: a ) rs . 12250 , b ) rs . 13375 , c ) rs . 16750 , d ) rs . 15000 , e ) none of these
Rationale: explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 55000 ] = rs . 15000 answer : option d
Answer: d
Python program:
a = 2 / 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 1 
f = 1/(e)
g = 55000 * f
Problem: the average runs of a cricket player of 5 innings was 20 . how many runs must he make in his next innings so as to increase his average of runs by 3 ?
Options: a ) 12 , b ) 42 , c ) 44 , d ) 76 , e ) 84
Rationale: "explanation : average after 6 innings = 23 required number of runs = ( 24 * 6 ) – ( 20 * 5 ) = 144 – 100 = 44 answer c"
Answer: c
Python program:
a = 5 + 1 
b = 20 + 3 
c = a * b
d = 20 * 5
e = c - d
Problem: the sum of three consecutive even numbers is 20 more than the first of these numbers . what is the middle number ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) can not be determined , e ) none of these
Rationale: "solution let the numbers be x , x + 2 and x + 4 . then , x + ( x + 2 ) + ( x + 4 ) = x + 20 ⇔ 2 x = 14 ⇔ x = 7 . ∴ middle number = x + 2 = 9 . answer b"
Answer: b
Python program:
a = 20 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 20 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 20 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 20 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 600 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 2778 , d ) 2800 , e ) 5000
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 600 = > 36 x / 100 - 24 x / 100 = 600 = > 12 x / 100 = 600 = > x = 5000 . answer : e"
Answer: e
Python program:
a = 18 - 12
b = a * 2
c = b / 100
d = 600 / c
Problem: there are 100 freshmen at a particular college , all of whom must take at least one of the 3 core classes : art , biology , and calculus . of these freshmen , 17 take only biology , 10 take only calculus , 9 take all 3 classes , and 20 take art and exactly one of the other two core classes . if the number of freshmen who take only art is 3 times the number of freshmen who take every core class except art , how many freshmen take art ?
Options: a ) 25 , b ) 32 , c ) 36 , d ) 48 , e ) 62
Rationale: make a venn diagram to get a clear picture . look at the diagram : each letter represents only one color . b represents the people who take only art . d represents people who take only art and bio etc . d + f = 20 ( people who take art and one other class ) b = 3 e ( people who take only art is 3 times the people who take bio and calculus ) 17 + 10 + 9 + b + d + e + f = 100 ( total people ) b + b / 3 = 44 b = 33 number of freshmen who take art = 33 + 20 + 9 = 62 answer e
Answer: e
Python program:
a = 17 + 10 
b = a + 9 
c = b + 20 
d = 100 - c
e = d * 3
f = e / 4
g = f + 20 
h = g + 9
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 4 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 512 , b ) 656 , c ) 740 , d ) 896 , e ) 972
Rationale: "there are 2 ^ 4 = 16 possibilities for the true - false answers . however we need to remove two cases for tttt and ffff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 14 * 64 = 896 . the answer is d ."
Answer: d
Python program:
a = 3 ** 4
b = a - 3
c = 4 * 4
d = b * c
Problem: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 228 , b ) 2000 , c ) 267 , d ) 270 , e ) 274
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 250 ) / 26 = 20 x = 270 m . answer : d"
Answer: d
Python program:
a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 250
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.0168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 5 digits after decimal total no . of decimals = 7 req . no . of digits = ( n - 1 ) = ( 7 - 1 ) = 6 answer : b"
Answer: b
Python program:
a = 52 / 416
Problem: a goods train runs at the speed of 72 km / hr and crosses a 150 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 277 , c ) 276 , d ) 370 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 150 ) / 26 = 20 x = 370 m . answer : d"
Answer: d
Python program:
a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 150
Problem: if w is the set of all the integers between 49 and 76 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 19 , b ) 91 , c ) 41 , d ) 18 , e ) 14
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 75 , the smallest is 51 ) : 75 - 51 = 24 step 2 . divide by 3 : 24 / 3 = 8 step 3 . add 1 : 8 + 1 = 9 . so there are 9 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 76 , the smallest is 50 ) : 76 - 50 = 26 step 2 . divide by 2 : 26 / 2 = 13 step 3 . add 1 : 13 + 1 = 14 . so there are 14 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 9 multiples of 3 and the 14 multiples of 2 : 9 + 14 = 23 . 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 9 + 14 = 23 . 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 23 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 72 - 54 = 18 step 2 . divide by 6 : 18 / 6 = 3 step 3 . add 1 : 3 + 1 = 4 . so there are 4 multiples of 6 within the range : we counted 4 numbers twice . subtract the 4 multiples of 6 from the sum of the multiples of 2 and 3 : = 9 + 14 - 4 = 23 - 4 = 19 therefore , the final number of multiples of 2 , 3 or 6 is 19 . hence , this is the correct answer . ( a )"
Answer: a
Python program:
a = 76 - 49
b = a / 3
c = math.floor(b)
d = 76 - 49
e = d / 2
f = c + e 
g = 76 - 49
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
Problem: the ratio between the sale price and the cost price of an article is 10 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 3 : 7 , d ) 2 : 0 , e ) 2 : 1
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 10 x . then , gain = rs . 3 x required ratio = 3 x : 7 x = 3 : 7 answer : c"
Answer: c
Python program:
a = 10 - 7
b = a / 7
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 300 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 50 sec , e ) 1 min
Rationale: they meet every 300 / 7 + 8 = 20 sec answer is a
Answer: a
Python program:
a = 8 + 7 
b = 300 / a
Problem: what annual installment will discharge a debt of rs . 1344 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 345 , c ) 325 , d ) 335 , e ) 400
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1344 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1344 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1344 * 25 ) x = ( 1344 * 25 ) / 84 = rs . 400 . therefore , each installment = rs . 400 . answer is e ."
Answer: e
Python program:
a = 12 / 1344
b = 100 * 0
c = b * 3
Problem: city x has a population 5 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 10 : 1
Rationale: "x = 5 y , y = 2 * z x : y , y : z 5 : 1 , 2 : 1 10 : 2 , 2 : 1 so , x : z = 10 : 1 ( e )"
Answer: e
Python program:
a = 5 * 2
Problem: a working mom wakes up every day at 7 am and goes to sleep at 11 pm . she works 8 hours a day . spends 2 hours working out at the gym . she spends 1.5 hours cooking dinner and doing dishes . she spends . 5 of an hour giving her daughter a bath . she spends 1 hour helping with homework and getting her daughter ready for bed . she spends another . 5 of an hour packing lunches for the family for the next day . she spends . 5 of an hour cleaning the house and 2 hours taking a shower and reading or watching t . v . before she goes to sleep . what percent of her day does she spend at work ?
Options: a ) 60 , b ) 50 , c ) 70 , d ) 55 , e ) 40
Rationale: 8 + 2 + 1.5 + . 5 + 1 + . 5 + . 5 + 2 = 16 = total number of hours 8 / 16 = . 05 = 50 percemt the answer is b
Answer: b
Python program:
a = 3 * 4
b = a - 7
c = b + 11 
d = 8 / c
e = d * 100
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1400 employees , then the no . of female employees who are computer literate ?
Options: a ) 588 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1400 female employees , 60 % of 1400 . = ( 60 * 1400 ) / 100 = 840 . then male employees , = 560 50 % of male are computer literate , = 280 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1400 ) / 100 = 868 computer literate . thus , female computer literate = 868 - 280 = 588 . answer : option a"
Answer: a
Python program:
a = 62 / 100
b = 60 / 100
c = 1 - b
d = 50 / 100
e = c * d
f = a - e
g = f * 1400
Problem: sales price is $ 81 , gross profit is 170 % of cost , what is the value of gross profit ?
Options: a ) 32 , b ) 33 , c ) 39 , d ) 40 , e ) 51
Rationale: "cost + profit = sales cost + ( 170 / 100 ) cost = 81 cost = 30 profit = 81 - 30 = 51 answer ( e )"
Answer: e
Python program:
a = 170 / 100
b = 1 + a 
c = 81 / b
d = 81 - c