euclaise/mathqa_programs huggingface dataset:
Problem: john makes $ 30 a week from his job . he earns a raise andnow makes $ 40 a week . what is the % increase ?
Options: a ) 16 % , b ) 33.33 % , c ) 33.69 % , d ) 33.98 % , e ) 37 %
Rationale: "increase = ( 10 / 30 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b"
Answer: b
Python program:
a = 40 - 30
b = a / 30
c = b * 100
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 6 , - 4 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) 1
Rationale: "the midpoint of ( 2,8 ) and ( 6 , - 4 ) is ( 4,2 ) . the slope of a line through ( 0 , - 2 ) and ( 4,2 ) is ( 2 - ( - 2 ) ) / ( 4 - 0 ) = 4 / 4 = 1 the answer is e ."
Answer: e
Python program:
a = 8 - 4
b = a / 2
c = b + 2 
d = 2 + 6 
e = d / 2
f = c / e
Problem: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years b in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) 25 , c ) b = 30 , d ) b = 35 , e ) b = 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Python program:
a = 10 * 3
b = 100 - a
c = 39 - 4
d = c / 1000
e = d * 100
f = b / e
Problem: if 36 men can do a piece of work in 5 hours , in how many hours will 15 men do it ?
Options: a ) 12 , b ) 38 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 5 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 5 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 5 } { 15 } = 12 hence , 15 men can do it in 12 hours . answer : a ) 12"
Answer: a
Python program:
a = 36 * 5
b = a / 15
Problem: in business , a and c invested amounts in the ratio 4 : 2 , whereas the ratio between amounts invested by a and b was 4 : 1 , if rs 20,000 was their profit , how much amount did a receive .
Options: a ) 13333 , b ) 26758 , c ) 45896 , d ) 14639 , e ) 89576
Rationale: "explanation : a : b = 4 : 1 = 4 : 1 = > a : c = 4 : 2 = 4 : 2 = > a : b : c = 4 : 1 : 2 a share = ( 4 / 6 ) * 20000 = 13333 option a"
Answer: a
Python program:
a = 1 + 4 
b = a * 1
c = b * 100
d = c * 100
e = 2 + 4 
f = e + 1 
g = 1 / f
h = d * g
Problem: if the average of 10 consecutive integers is 24.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 29 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 24 , integer 6 = 25 . counting up to the tenth integer we get 29 . answer : d"
Answer: d
Python program:
a = 10 * 2
b = 10 * 2
c = 24 - 5
d = c * 10
e = a + d
Problem: the letters o , l and t are rearranged to form the word ' lot ' . find its probability .
Options: a ) 1 / 18 , b ) 1 / 12 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 6
Rationale: explanation : there are total 3 letters . the probability that o gets the first position is 1 / 3 . likewise , probability for l and t are 1 / 2 and 1 / 1 . hence , the required probability is : - = > ( 1 / 3 ) x ( 1 / 2 ) x 1 . = > 1 / 6 . answer : e
Answer: e
Python program:
a = math.factorial(3)
b = 1 / a
Problem: the product of two numbers is 168 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 168 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 168 ) = 625 x + y = 25 . option b"
Answer: b
Python program:
a = 2 * 168
b = 289 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 168
f = d + e 
g = math.sqrt(f)
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 64 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 88
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 64 ( subtracting twice of incorrect from correct ) 3 x = 264 x = 88 answer : e"
Answer: e
Python program:
a = 100 - 64
b = a / 3
c = 100 - b
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 2 ?
Options: a ) 40 , b ) 50 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 2 to 3 it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 so it will from 2 to 7 i . e 3 , 4,5 , 6,7 = 10 * 10 * 10 * 10 * 10 = 10 ^ 5 answer is d"
Answer: d
Python program:
a = 7 - 2
b = 10 ** a
Problem: a wildlife preserve is being planned for 8000 rhinoceroses . the preserve is to contain a total of 10000 acres of watering area , plus 100 acres of grazing area for each rhinoceros . if the number of rhinoceroses is expected to increase by 10 percent , how many 1000 acres should the preserve have in order to provide for the increased population ?
Options: a ) 340 , b ) 330 , c ) 320 , d ) 310 , e ) 890
Rationale: number of rhinos = 8000 watering area = 10,000 acres number of rhino to increase by 10 percent , then number of rhino = 8800 grazing area for a rhino = 100 total grazing area for 8800 rhinos = 8800 * 100 = 8 , 80,000 total area required for the wildlife preserve = 8 , 80,000 + 10,000 = 8 , 90,000 = 890 * 1000 answer e
Answer: e
Python program:
a = 100 * 8000
b = 100 * 8000
c = b / 10
d = a + c 
e = d + 10000 
f = e / 1000
Problem: at a certain organisation , the number of male members went up by 14 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 7
Rationale: "men increase by 14 % = = > 1.14 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.14 m + 0.94 f = 1.012 * ( m + f ) 1.14 m + 0.94 f = 1.012 m + 1.012 f 1.14 m - 1.012 m = 1.012 f - 0.94 f 0.128 m = 0.072 f m / f = ( 0.072 ) / ( 0.128 ) = 72 / 128 = 4 / 7 answer = ( e )"
Answer: e
Python program:
a = 1 / 2
b = 1 + a 
c = b * 1000
d = 6 / 100
e = 1 - d
f = e * 1000
g = c - f
h = 14 / 100
i = 1 + h 
j = i * 1000
k = 1 / 2
l = 1 + k 
m = l * 1000
n = j - m
o = g / n
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 50 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "distance between maxwell ' s and brad ' s home = 50 km maxwell ' s speed = 4 km / h brad ' s speed = 6 km / h relative speed of approach = 10 km / h time = 50 / 10 = 5 hours distance traveled by maxwell when they meet in the middle = 4 * 5 = 20 km answer c"
Answer: c
Python program:
a = 4 + 6 
b = 50 / a
c = 4 * b
Problem: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 10 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 112.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80
Rationale: "correct answer : a the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.1 ( $ 1120 ) = $ 112 . the correct answer is a ."
Answer: a
Python program:
a = 1720 - 600
b = a * 10
c = b / 100
Problem: a man is 37 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 78 years , b ) 22 years , c ) 88 years , d ) 35 years , e ) 65 years
Rationale: "let ' s son age is x , then father age is x + 37 . = > 2 ( x + 2 ) = ( x + 37 + 2 ) = > 2 x + 4 = x + 39 = > x = 35 years answer : d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 37 - b
d = 2 - 1
e = c / d
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 40 - 79 )
Options: a ) 345 , b ) 340 , c ) 343 , d ) 349 , e ) 338
Rationale: "there are 41 digits in 10 ^ 40 when we subtract 79 from it , there will be 40 digits left . 10 ^ 40 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 79 = 9999999 . . . . ( 40 times ) + 1 - 79 = 9999999 . . . . ( 40 times ) - 78 consider the last 2 digits , 99 - 78 = 21 the last 2 digits will be 21 . and our number would be 99999 . . . . . . 99921 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 21 the sum of the digits will be ( 38 * 9 ) + 2 + 1 = 345 answer : - a"
Answer: a
Python program:
a = 10 - 1
b = 40 - 2
c = a * b
d = c + 10
Problem: by investing in 16 % stock at 64 , one earns rs . 1500 . the investment made is :
Options: a ) 5760 , b ) 7667 , c ) 4445 , d ) 4566 , e ) 3344
Rationale: "explanation : to earn rs . , investment = rs . 64 . to earn rs . 1500 , investment = = rs . 5760 . answer : c ) 5760"
Answer: c
Python program:
a = 4 * 2
b = 4 * 2
c = a * b
d = c * 3
e = 100 / 2
f = d / e
g = 4 * 100
h = 1500 - g
i = f * h
Problem: if 80 percent of 600 is 50 percent of x , then x = ?
Options: a ) 960 , b ) 1000 , c ) 1020 , d ) 1080 , e ) 1075
Rationale: 0.8 * 600 = 0.5 * x x = 8 / 5 * 600 = 960
Answer: a
Python program:
a = 80 * 600
b = a / 50
Problem: if a 2 + b 2 + c 2 = 560 and ab + bc + ca = 8 , then a + b + c is
Options: a ) 4 , b ) 52 , c ) 16 , d ) 24 , e ) 64
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 560 and ab + bc + ca = 8 , ( a + b + c ) ^ 2 = 560 + 2 ( 8 ) = 576 = 24 ^ 2 therefore : a + b + c = 24 answer : d"
Answer: d
Python program:
a = 8 * 2
b = 560 + a 
c = math.sqrt(b)
Problem: a man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph , find his average speed for the total journey ?
Options: a ) 1 kmph , b ) 5 kmph , c ) 5.5 kmph , d ) 4 kmph , e ) 7 kmph
Rationale: "explanation : speed of man = 6.5 kmph speed of stream = 2.5 kmph speed in downstream = 9 kmph speed in upstream = 4 kmph average speed = ( 2 x 9 x 4 ) / 13 = 5.5 kmph . answer : c"
Answer: c
Python program:
a = 6 - 5
b = 6 + 5 
c = b / 2
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 15 % profit on the first article and 15 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 768 , c ) 150 , d ) 280 , e ) 279
Rationale: "profit on first article = 150 % of 1000 = 150 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : c"
Answer: c
Python program:
a = 100 - 15
b = 100 / a
c = b * 1000
d = 100 + 15 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 15
l = 100 / k
m = l * 1000
n = 100 + 15 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: a and b can do a work in 8 days , b and c can do the same work in 12 days . a , b and c together can finish it in 6 days . a and c together will do it in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 8 , e ) 9
Rationale: "let the total units of work be 48 . units of work completed by a and b in one day = 6 . units of work completed by b and c in one day = 4 units of work completed by a , b , and c in one day = 8 . from the above information we get the work completed by a and c in one day is 6 units . therefore , the number of days taken by a and c to complete the whole work = 48 / 6 = 8 days . answer : d"
Answer: d
Python program:
a = 8 / 2
b = a + 2 
c = 8 * b
d = c / 6
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 288 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 10,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 288 pi r = 6 so area = 4 . pi . r ^ 2 = 144 . pi = 324 x 3.14 = 400 ( approx ) c"
Answer: c
Python program:
a = const_180 / 1000
Problem: the percentage increase in the area of rectangle , if each of its side is increased by 10 % is ?
Options: a ) 21 % , b ) 30 % , c ) 25 % , d ) 40 % , e ) 50 %
Rationale: "let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 110 x / 100 new breadth = 110 y / 100 = 11 y / 10 new area = 11 x / 10 * 11 y / 10 = 121 xy / 100 m ^ 2 increase percent = 21 xy / 100 * 1 / xy * 100 = 21 % answer is a"
Answer: a
Python program:
a = 100 + 10 
b = a / 100
c = 100 + 10 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: a fill pipe can fill 1 / 2 of cistern in 35 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 20 min , b ) 25 min , c ) 30 min , d ) 35 min , e ) 40 min
Rationale: "required time = 35 * 2 * 1 / 2 = 20 minutes answer is d"
Answer: d
Python program:
a = 35 / 1
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 . 1 per sq m ?
Options: a ) 675 , rs . 1350 , b ) 575 , rs . 675 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 1 = rs . 675 answer : b"
Answer: b
Python program:
a = 2 * 5
b = 75 + a 
c = 2 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: the diameter of a cylindrical tin is 6 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33
b ) 45
c ) 66
d ) 77
e ) 21
Rationale: r = 3 h = 5 π * 3 * 3 * 5 = 45 π cc answer : b
Answer: b
Python program:
a = 6 / 2
b = volume_cylinder / (
Problem: b completes a work in 9 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.73 days , c ) 5.75 days , d ) 6.75 days , e ) 7.73 days
Rationale: "1 / 9 + 1 / 10 = 19 / 90 90 / 19 = 4.73 days answer : b"
Answer: b
Python program:
a = 10 * 9
b = 9 + 10 
c = a / b
Problem: if a ( a + 7 ) = 18 and b ( b + 7 ) = 18 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) − 7 , d ) 46 , e ) 48
Rationale: "a ( a + 7 ) = 18 = > we have a = 2 or - 9 also b ( b + 7 ) = 18 = > b = 2 or - 9 given a ≠ b 1 ) when a = 2 , b = - 9 and a + b = - 7 1 ) when a = - 9 , b = 2 and a + b = - 7 answer choice c"
Answer: c
Python program:
a = 18 / 10
b = 18 / 10
c = 18 / b
d = a + c
Problem: the average ( arithmetic mean ) of the even integers from 0 to 80 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 40 inclusive ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 36 , e ) 40
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 80 is 80 / 2 = 40 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the answer is a ."
Answer: a
Python program:
a = 40 + 0 
b = a / 2
c = 80 + 0 
d = c / 2
e = b - d
Problem: the number of sailors on a ship is 80 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 9 : 5 , c ) 47 : 25 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.80 * officer sailor / officer = 1.80 / 1 = 180 / 100 = 9 / 5 answer will be b"
Answer: b
Python program:
a = 80 + 100 
b = a / 100
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 550 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 23500 answer : a"
Answer: a
Python program:
a = 8 / 100
b = 1 * 0
c = 550 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1
i = math.floor(h)
Problem: a small college reduced its faculty by approximately 20 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 254 , e ) 244
Rationale: "if x is the original number of faculty members , then after 20 % reduction in faculty members number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of faculty members is 244 correct answer - e"
Answer: e
Python program:
a = 100 - 20
b = a / 100
c = 195 / b
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15.5 - 2 * 1.5 = 12.5 . answer : e ."
Answer: e
Python program:
a = 2 * 1
b = 15 - 5
Problem: the greatest number that divides 180 , 565 and 705 leaving remainder 5 , 5 and 5 respectively is :
Options: a ) 31 , b ) 33 , c ) 35 , d ) 38 , e ) 39
Rationale: "explanation : 180 - 5 = 175 , 565 - 5 = 560 and 705 - 5 = 700 highest number that divides 175 , 560 and 700 is hcf of numbers . hcf of 175 , 560 and 700 = 35 answer : c"
Answer: c
Python program:
a = 565 - 5
b = math.gcd(180, 565)
c = a / b
Problem: how many positive integers less than 100 have a remainder of 4 when divided by 13 ?
Options: a ) 6 , b ) 7 , c ) 4 , d ) 9 , e ) 10
Rationale: "we have to include 4 also . as 13 * 0 + 4 = 2 if somebody says to divide 4 by 13 , we will be telling we have 0 quotient and remainder as 4 . answer is c"
Answer: c
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: how many of the positive divisors f of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . f = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Python program:
a = 120 / 4
b = a / 2
c = b / 3
Problem: a circle is inscribed in a triangle of side 6 cm . and a square is inscribed in the circle . what is the area of square ?
Options: a ) 4 cm ^ 2
b ) 6 cm ^ 2
c ) 5 cm ^ 2
d ) 7 cm ^ 2
e ) 8 cm ^ 2
Rationale: the radius of the incircle in a equilateral triangle is a / 2 ( sqrt ) 3 where a = side of triangle = 6 cm so the diameter of the circle would be the diagonal of square so diagonal = 2 * a / 2 ( sqrt ) 3 = a / ( sqrt ) 3 so area of square = 1 / 2 * ( diagonal ) ^ 2 = 6 * 6 / 2 * 3 = 6 cm ^ 2 answer : b
Answer: b
Python program:
a = 6 * 6
b = math.sqrt(a)
Problem: two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 60 km and the other at the rate of 90 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.62
Rationale: "t = ( 111 + 165 ) / ( 60 + 90 ) * 18 / 5 t = 6.62 answer : e"
Answer: e
Python program:
a = 111 + 165 
b = 60 + 90 
c = b * const_0_2778
d = a / c
Problem: what is the average of first 20 multiples of 7 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 79 , d ) d ) 84 , e ) e ) 82
Rationale: "required average = 7 ( 1 + 2 + . . . . + 20 ) / 20 ( 8 / 20 ) x ( ( 20 x 21 ) / 2 ) ( because sum of first 21 natural numbers ) = 84 d"
Answer: d
Python program:
a = 20 + 1 
b = 20 * a
c = b / 2
d = c / 20
e = d * 7
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 148 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1184 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a 1184 b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 148 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 148 = 3 k + 148 = > 2 k = 296 = > k = 148 the initial quantity of milk in a = 8 k = 8 * 148 = 1184 liters ."
Answer: a
Python program:
a = 1/(2)
b = 62 / 5
c = 1 - b
d = a - c
e = 148 / d
Problem: in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the dividend is
Options: a ) 5336 , b ) 4306 , c ) 4236 , d ) 4336 , e ) none
Rationale: sol . divisor = ( 5 × 46 ) = 230 . also , 10 × q = 230 ⇒ q = 23 . and , r = 46 . dividend = ( 230 × 23 + 46 ) = 5336 . answer a
Answer: a
Python program:
a = 5 * 46
b = 5 * 46
c = b / 10
d = a * c
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 9.1 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 15 + 40 = 55 kg alloy is 0.12 * 15 + 0.08 * 40 = 5 kg , so the percentage is 5 / 55 * 100 = 9.1 % . answer : d ."
Answer: d
Python program:
a = 12 * 15
b = a / 100
c = 8 * 40
d = c / 100
e = b + d 
f = 15 + 40 
g = e / f
h = g * 100
Problem: the owner of a furniture shop charges his customer 15 % more than the cost price . if a customer paid rs . 5750 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2299 , b ) 2699 , c ) 2670 , d ) 6725 , e ) 5000
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 5750 ( 100 / 115 ) = rs . 5000 answer : e"
Answer: e
Python program:
a = 15 / 100
b = 1 + a 
c = 5750 / b