euclaise/mathqa_programs huggingface dataset:
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is b ' s share ?
Options: a ) a ) 8239 , b ) b ) 2900 , c ) c ) 1000 , d ) d ) 2393 , e ) e ) 2009
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 500 = > x = 500 . b ' s share = rs . 2 x = 2 * 500 = rs . 1000 . answer : c"
Answer: c
Python program:
a = 4 - 3
b = a * 500
c = b * 3
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 19.1 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 20 = 10 * 3 = 30 time difference = 19.1 ans : d"
Answer: d
Python program:
a = 55 + 10 
b = a - 1
c = 10 / 20
d = 10 / 55
e = c - d
f = b * e
g = max(f)
Problem: a 21 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 210 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 21 , money invested = rs . ( 100 / 10 x 21 ) = rs . 210 . â ˆ ´ market value of rs . 100 stock = rs . 210 answer b"
Answer: b
Python program:
a = 100 / 10
b = a * 21
Problem: which no . need to add to 859622 to get a no . exactly divisible by 456 ?
Options: a ) 546577 , b ) 674645 , c ) 566578 , d ) 465766 , e ) 859622
Rationale: dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e
Answer: e
Python program:
a = 859622 - reminder
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 864 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 4 ( 9 horizontal dots and 4 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 4 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 3 c 1 , ( 4 - 1 = 3 as 1 vertical dot is already occupied by a ) . 9 c 1 * 4 c 1 * 8 c 1 * 3 c 1 = 864 . answer : c ."
Answer: c
Python program:
a = 4 - 1
b = 4 * a
c = 9 * 4
d = b * c
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "well , first let ’ s take care of the “ totals ” . the numbers in the “ totals ” row must add up . if 90 are females , the other 250 – 90 = 160 must be males . similarly , the numbers in the “ totals ” column must add up . if 40 are managers , then the other 250 – 40 = 210 must be associates . now , in the “ associate ” row , 135 + e = 210 , which means e = 75 — the other 75 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the “ female ” column : b + 75 = 90 , which means b = 15 . there are fifteen female managers in this company . thus , the answer = ( a ) ."
Answer: a
Python program:
a = 40 * 1
Problem: a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is
Options: a ) 15 % , b ) 12 % , c ) 8 % , d ) 7 % , e ) 5 %
Rationale: "explanation : simple interest for 3 years = ( rs . 12005 - rs . 9800 ) = rs . 2205 simple interest for 5 years = 22053 × 5 = rs . 3675 principal ( p ) = ( rs . 9800 - rs . 3675 ) = rs . 6125 r = 100 × si / pt = 100 × 3675 / 6125 × 5 = 12 % answer : option b"
Answer: b
Python program:
a = 12005 - 9800
b = 9800 * 8
c = 5 * 12005
d = b - c
e = a / d
f = e * 100
Problem: if 3 / p = 5 & 3 / q = 15 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 2 / 15 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 3 / 5 , q = 3 / 15 = > q = 1 / 5 therefore p - q = ( 3 / 5 ) - ( 1 / 5 ) = 2 / 15 answer : c"
Answer: c
Python program:
a = 3 / 5
b = 3 / 15
c = a - b
Problem: a invested some money in 8 % stock at 96 . if b wants to invest in an equally good 10 % stock , he must purchase a stock worth of :
Options: a ) rs . 120 , b ) rs . 60 , c ) rs . 128 , d ) rs . 130 , e ) rs . 140
Rationale: "solution for an income of rs . 8 , investment = rs . 96 . for an income of rs . 10 , investment = rs . ( 96 / 8 x 10 ) = rs . 120 answer a"
Answer: a
Python program:
a = 96 / 8
b = a * 10
Problem: how many digits 2 ^ 400 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 99 , e ) 121
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 120 therefore 121 digits would be my best guess e"
Answer: e
Python program:
a = math.log(2)
b = math.log(10)
c = a / b
d = c * 400
e = 1 + d 
f = math.floor(e)
Problem: a committee is reviewing a total of 40 x black - and - white films and 4 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 20 / 11 , b ) 16 / 11 , c ) 17 / 11 , d ) 10 / 11 , e ) 19 / 11
Rationale: "say x = y = 10 . in this case we would have : 40 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 40 color films , thus total of 44 films were selected . color films thus compose 40 / 44 = 10 / 11 of the selected films . answer : d"
Answer: d
Python program:
a = 40 / 100
b = a + 4 
c = 4 / b
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 6 / 25 , b ) 5 / 16 , c ) 4 / 9 , d ) 3 / 7 , e ) 2 / 5
Rationale: let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 8 ( 1 - x ) p 12 xp = 8 p - 8 xp 20 xp = 8 p x = 2 / 5 the answer is e .
Answer: e
Python program:
a = 12 / 8
b = a + 1 
c = 1/(b)
Problem: if x is equal to the sum of the integers from 50 to 70 , inclusive , and y is the number of even integers from 50 to 70 , inclusive , what is the value of x + y ?
Options: a ) 1211 , b ) 1231 , c ) 1251 , d ) 1271 , e ) 1291
Rationale: "x = 50 + 51 + . . . + 70 = 21 ( 60 ) = 1260 y = 11 x + y = 1271 the answer is d ."
Answer: d
Python program:
a = 50 + 70 
b = a / 2
c = 70 - 50
d = c + 1 
e = b * d
f = 70 - 50
g = f / 2
h = g + 1 
i = e + h
Problem: 12 times a positive integer is more than its square by 36 , then the positive integer is
Options: a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 12 x = x 2 + 36 = > x 2 - 12 x + 36 = 0 = > ( x - 6 ) ( x - 6 ) = 0 = > x = 6 answer : a"
Answer: a
Python program:
a = 12 ** 2
b = 36 * 4
c = a - b
d = 12 + c 
e = d / 2
Problem: renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 4 days . in what time suma can do it alone ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 8 suma â € ™ s one day â € ™ s work = 1 / 4 - 1 / 8 = 1 / 8 suma can do it alone in 8 days . answer : a"
Answer: a
Python program:
a = 1 / 4
b = 1 / 8
c = a - b
d = 1/(c)
Problem: 90 percent of the members of a study group are women , and 60 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.34 , b ) 0.44 , c ) 0.54 , d ) 0.64 , e ) 0.74
Rationale: "say there are 100 people in that group , then there would be 0.9 * 0.60 * 100 = 54 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 54 / 100 . answer : c"
Answer: c
Python program:
a = 5 * 5
b = a * 4
c = 90 / b
d = 5 * 5
e = d * 4
f = 60 / e
g = c * f
Problem: a train covers a distance of 12 km in 10 min . if it takes 12 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 m , b ) 188 m , c ) 240 m , d ) 178 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 12 = 240 m . answer : c"
Answer: c
Python program:
a = 12 / 10
b = a - 12
c = 12 / b
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 310000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,292 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 12,917 , e ) $ 20,796
Rationale: 0.04 x + 0.09 y = 310000 [ 1 ] 0.04 x = 0.80 * 310000 = 248000 [ 2 ] 248000 + 0.09 y = 310000 - - > 0.09 y = 62000 [ 3 ] 248000 / 12 = 258333.3333 [ 4 ] 62000 / 12 = 5166.67 [ 5 ] adding [ 4,5 ] we get : 25833 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.292 , ans a
Answer: a
Python program:
a = 4 + 9 
b = a + 100 
c = b / 100
d = math.log(c)
e = d / 12
f = 2 ** e
Problem: x and y started a business by investing rs . 5000 / - and rs . 15000 / - respectively . find the x ’ s share out of a total profit of rs . 1600 :
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: x = rs . 5000 / - y = rs . 15000 / - x share 1 part & y share 3 parts total 4 parts - - - - - > rs . 1600 / - - - - - > 1 part - - - - - - - > rs . 400 / - x share = 1 part - - - - - > rs . 400 / - e
Answer: e
Python program:
a = 5000 + 15000 
b = 1600 / a
c = 5000 * b
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 48 / r years . if pat ' s parents invested $ 5,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 48 / r years , then for r = 8 it ' ll double in 48 / 8 = ~ 6 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 3 = $ 15,000 . answer : b ."
Answer: b
Python program:
a = 2 + 3 
b = a * 1000
c = b * 8
d = c / 2
Problem: how many multiples of 7 are there between 9 and 89 , 9 and 89 inclusive ?
Options: a ) 11 , b ) 17 , c ) 16 , d ) 13 , e ) 12
Rationale: "7 multiples are . . . 14 , 21,28 , 35,42 , 49,56 , 63,70 , 77,84 , . . . , . . . , the answer is = 11 answer is a"
Answer: a
Python program:
a = 89 - 9
b = a / 7
c = b + 1
Problem: 5 men are equal to as many women as are equal to 7 boys . all of them earn rs . 90 only . men ’ s wages are ?
Options: a ) 8 rs . , b ) 7 rs . , c ) 6 rs . , d ) 4 rs . , e ) 5 rs .
Rationale: 5 m = xw = 7 b 5 m + xw + 7 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : c
Answer: c
Python program:
a = 3 * 5
b = 90 / a
Problem: when positive integer n is divided by 4 , the remainder is 2 . when n is divided by 7 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 3 . . c"
Answer: c
Python program:
a = 100 - reminder
Problem: if p ( a ) = 8 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 16 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 2 , e ) 4 / 7
Rationale: "p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 16 / 15 ) / ( 8 / 15 ) = 2 . d"
Answer: d
Python program:
a = 16 / 15
b = 8 / 15
c = a / b
Problem: the speed of a car is 90 km in the first hour and 42 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 92 kmph , c ) 75 kmph , d ) 65 kmph , e ) 66 kmph
Rationale: "s = ( 90 + 42 ) / 2 = 66 kmph e"
Answer: e
Python program:
a = 90 + 42 
b = a / 2
Problem: in how many ways can the integer 48 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "method 1 : listing all multiples since given number is small 48 = 1 * 48 , 2 * 24 , 3 * 16 , 4 * 12 , 6 * 8 = > 5 ways method 2 : express given number as prime factors 48 = 6 * 8 = 2 * 3 * 2 ^ 3 = 2 ^ 4 * 3 total number of factors = ( 4 + 1 ) ( 1 + 1 ) = 5 * 2 = 10 since the given number is not a perfect square , there will be exact 5 pairs possible of the given 10 factors = > 5 ways option c"
Answer: c
Python program:
a = 48 / 1
b = a / 3
c = b - 3
Problem: if w is 40 percent less than x , x is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 x , x = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Python program:
a = 46 / 100
b = 1 - a
c = b * 100
d = 100 - 40
e = 40 / 100
f = 100 - 40
g = e * f
h = d - g
i = c - h
j = 100 - 40
k = 40 / 100
l = 100 - 40
m = k * l
n = j - m
o = i / n
p = o * 100
Problem: a boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 2 hr 30 min , b ) 2 hr , c ) 4 hr , d ) 1 hr 15 min , e ) none of these
Rationale: "explanation : speed upstream = 2 / 2 = 1 km / hr speed downstream = 1 / ( ( 20 / 60 ) ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 5 km in still water = 5 / 2 = 2 ( 1 / 2 ) hours = 2 hour 30 minutes . answer : option a"
Answer: a
Python program:
a = 1 / 20
b = a * const_60
c = 2 / 2
d = b + c 
e = d / 2
f = 5 / e
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 5 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 10210 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 5 = rs 10210 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 5
d = 8000 * c
Problem: pencils , pens and exercise books in a shop are in the ratio of 14 : 4 : 3 . if there are 140 pencils , the number of exercise books in the shop is :
Options: a ) 30 , b ) 27 , c ) 35 , d ) 33 , e ) 37
Rationale: explanation : let pencils = 14 x , pens = 4 x & exercise books = 3 x . now , 14 x = 140 hence x = 10 number of exercise books = 3 x = 30 answer : a
Answer: a
Python program:
a = 140 / 14
b = a * 3
Problem: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 280 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 16 * 20 = 320 = length of train length of platform = 600 - 320 = 280 answer : c"
Answer: c
Python program:
a = 72 * 1000
b = a / 3600
c = b * 30
d = 72 * 1000
e = d / 3600
f = e * 16
g = c - f
Problem: in a quiz the points in each round for the first , second , third and fourth position were 10050 , 2010 . no other points were given . rachel participated in several rounds in the competition and the product of her score was 10000 . in how many rounds did she participate ?
Options: a ) 2 , b ) can not be determined , c ) 4 , d ) 6 , e ) 10
Rationale: correct answer is b because we are given that there wo n ' t be any points awarded for rounds other than 1 st four position . thus , it may happen that she played 150 rounds out of only 8 rounds were there in which she was awarded some points .
Answer: b
Python program:
a = 10050 - 10000
Problem: how many positive integers less than 50 have a reminder 2 when divided by 7 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "take the multiples of 7 and add 2 0 x 7 + 2 = 2 . . . . 6 x 7 + 2 = 44 there are 7 numbers answer e"
Answer: e
Python program:
a = 4 + 2 
b = a - 1
c = math.factorial(b)
d = math.factorial(2)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the area of the field . what is the length of the field ?
Options: a ) 13 , b ) 16 , c ) 34 , d ) 43 , e ) 42
Rationale: "explanation : a / 2 = 8 * 8 = > a = 8 * 8 * 2 x * 2 x = 8 * 8 * 2 x = 8 = > 2 x = 16 answer : option b"
Answer: b
Python program:
a = square_area * (
b = a / 2
c = 1/(2)
d = math.sqrt(b)
Problem: how many three digit numbers n are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Python program:
a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) km / hr = 8 kmph . answer c"
Answer: c
Python program:
a = 11 + 5 
b = a / 2
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 5 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 5 0 = a + d - 4 a + d = 4 a = d ( as they are twin brothers ) a = d = 2 a is the answer"
Answer: a
Python program:
a = 5 - 1
b = a / 2
Problem: a and b go around a circular track of length 900 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 186 sec , d ) 180 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 900 / ( 36 * 5 / 18 ) , 900 / ( 54 * 5 / 18 ) } = lcm ( 90 , 60 ) = 180 sec . answer : d"
Answer: d
Python program:
a = 54 * const_0_2778
b = 36 * const_0_2778
c = a - b
d = 900 / c
Problem: working together , jose and jane can complete an assigned task in 12 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 48 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 12 12 ( x + y ) = xy next , we ' re told 1 job takes 48 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 48 x + y = 96 so xy = 1152 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 36 days for jose and 32 days for jane . answer : e
Answer: e
Python program:
a = 3 * 12
Problem: one fourth of one third of two fifth of a number is 15 . what will be the 40 % of that number is ?
Options: a ) 120 , b ) 130 , c ) 150 , d ) 180 , e ) 250
Rationale: "( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 15 then x = 15 * 30 = 450 40 % of 450 = 180 answer d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 15 / f
h = g * 40
i = h / 100
Problem: the ages of ashley and mary are in the ratio 4 : 7 . the sum of their ages is 22 . find the ages of ashley .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: a : m = 4 : 7 let the ages of a & m be x & 22 - x x / 22 - x = 4 / 7 x = 8 a = 8 yrs answer : b
Answer: b
Python program:
a = 4 + 7 
b = 22 / a
c = b * 4
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 180 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 12 sec , c ) 30 sec , d ) 50 sec , e ) 1 min
Rationale: "they meet every 180 / 7 + 8 = 12 sec answer is b"
Answer: b
Python program:
a = 8 + 7 
b = 180 / a
Problem: a clock shows the time as 12 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 30 minutes , e ) 40 minutes
Rationale: "there are 6 hours in between 12 a . m . to 6 p . m . 6 * 5 = 30 minutes . answer : d"
Answer: d
Python program:
a = 3 + 6 
b = a * 5
Problem: what will be the cost of building a fence around a square plot with area equal to 36 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2882 , c ) 2999 , d ) 2667 , e ) 1392
Rationale: "let the side of the square plot be a ft . a 2 = 36 = > a = 6 length of the fence = perimeter of the plot = 4 a = 24 ft . cost of building the fence = 24 * 58 = rs . 1392 . answer : e"
Answer: e
Python program:
a = math.sqrt(36)
b = square_perimeter * (
Problem: a person want to give his money of $ 4500 to his 4 children a , b , c , d in the ratio 2 : 4 : 5 : 4 . what is the a + b share ?
Options: a ) $ 1000 , b ) $ 2000 , c ) $ 1800 , d ) $ 1500 , e ) $ 1600
Rationale: "a ' s share = 4500 * 2 / 15 = $ 600 b ' s share = 4500 * 4 / 15 = $ 1200 a + b = $ 1800 answer is c"
Answer: c
Python program:
a = 2 + 4 
b = a + 5 
c = 4 / b
d = c * 4500
Problem: if the price of a certain computer increased 30 percent from y dollars to 351 dollars , then 2 y =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = y after 30 % price increase price = y + ( 30 / 100 ) * y = 1.3 y = 351 ( given ) i . e . y = 351 / 1.3 = $ 270 i . e . 2 y = 2 * 270 = 540 answer : option a"
Answer: a
Python program:
a = 100 + 30 
b = a / 100
c = 351 / b
d = c * 2