euclaise/mathqa_programs huggingface dataset:
Problem: a certain galaxy is known to comprise approximately 4 x 10 ^ 12 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 80,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 4 * 10 ^ 12 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 4 * 10 ^ 12 / 50 * 10 ^ 6 = 40 * 10 ^ 4 / 5 = 80000 therefore answer is c"
Answer: c
Python program:
a = 4 * 10
b = a / 50
c = 10 ** 4
d = b * c
e = d / 1000
f = e * 4
Problem: 12.5 % of 192 = 50 % of ?
Options: a ) 48 , b ) 96 , c ) 24 , d ) none of these , e ) can not be determined
Rationale: "answer let 12.5 % of 192 = 50 % of a , ⇒ ( 12.5 x 192 ) / 100 = ( 50 x a ) / 100 ∴ a = ( 12.5 x 192 ) / 50 = 48 correct option : a"
Answer: a
Python program:
a = 50 * 192
b = a / 100
c = b * 12
d = c / 100
Problem: a 9 % stock yields 25 % . the market value of the stock is :
Options: a ) rs 45 , b ) rs 25 , c ) rs 40 , d ) rs 39 , e ) rs 36
Rationale: "explanation : for an income of rs . 25 , investment = rs . 100 . for an income of rs 9 , investment = rs . 100 / 25 x 9 = rs 36 market value of rs . 100 stock = rs 36 answer is e"
Answer: e
Python program:
a = 100 / 25
b = a * 9
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 asquotient and the 15 as remainder ?
Options: a ) 1245 , b ) 1567 , c ) 1678 , d ) 1335 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Python program:
a = 1365 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: ‘ a ’ completes a work in 12 days . ‘ b ’ completes the same work in 15 days . ‘ a ’ started working alone and after 3 days b joined him . how many days will they now take together to complete the remaining work ?
Options: a ) 5 , b ) 8 , c ) 6 , d ) 4 , e ) none of these
Rationale: work done by ‘ a ’ in 3 days = 1 ⁄ 12 × 3 = 1 ⁄ 4 ∴ remaining work = 1 - 1 ⁄ 4 = 3 ⁄ 4 work done by a and b together = 12 × 15 / 27 = 20 / 3 ∴ remaining work done by a and b together in = 3 ⁄ 4 × 20 ⁄ 3 = 5 days answer a
Answer: a
Python program:
a = 1 / 12
b = a * 3
c = 1 - b
d = 12 * 15
e = 3 ** 3
f = d / e
g = c * f
Problem: the sum of ages of 5 children born 3 years different each is 50 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . x + 12 = 4 + 12 = 16 d"
Answer: d
Python program:
a = 3 + 4 
b = 3 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 50 
g = f / 5
Problem: in a coconut grove , ( x + 2 ) trees yield 40 nuts per year , x trees yield 120 nuts per year and ( x – 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "( x + 2 ) × 40 + x × 120 + ( x − 2 ) × 180 / ( x + 2 ) + x + ( x − 2 ) = 100 ⇒ 340 x − 280 / 3 x = 100 ⇒ 40 x = 280 ⇒ x = 7 answer e"
Answer: e
Python program:
a = 180 * 2
b = 40 * 2
c = a - b
d = 40 + 120 
e = d + 180 
f = 100 * 3
g = e - f
h = c / g
Problem: find value for x from given equation ? x + 1 = - 3
Options: a ) 1 , b ) x = - 4 , c ) - 3 , d ) - 5 , e ) 5
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = - 3 - 1 2 . simplify both sides : x = - 4 b"
Answer: b
Python program:
a = 3 - 1
Problem: rectangular tile each of size 25 cm by 65 cm must be laid horizontally on a rectangular floor of size 150 cm by 390 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 40 , c ) 25 , d ) 36 , e ) 45
Rationale: "area of tile = 25 * 65 = 1625 area of floor = 150 * 390 = 58500 no of tiles = 58500 / 1625 = 36 so , the no of tile = 36 answer : d"
Answer: d
Python program:
a = 150 * 390
b = 25 * 65
c = a / b
Problem: of the 3,600 employees of company x , 1 / 6 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 13 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 4 is 1200 * 1 / 4 so it reduced 150 people , so there is 450 clerical people left but since 150 people left , it also reduced from the total of 3600 so there are 3450 people total since 450 clerical left / 3450 people total you get ( a ) 13 % answer : a"
Answer: a
Python program:
a = 1 / 6
b = 1 / 4
c = 1 - b
d = a * c
e = 1 / 6
f = 1 / 4
g = 1 - f
h = e * g
i = 1 / 6
j = 1 - i
k = h + j 
l = d / k
m = l * 100
Problem: 9886 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9886 = 3314 option : e"
Answer: e
Python program:
a = 13200 - 9886
Problem: if x is a sum of all even integers on the interval 13 . . . 45 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 16 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 44 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 44 ) / 2 * 16 = 29 * 16 . gcd of 16 and 29 * 16 is 16 . answer : b ."
Answer: b
Python program:
a = 13 - 10
b = a + 2 
c = 13 - 10
d = c + 2 
e = b * d
Problem: in a stream running at 2 kmph , a motor boat goes 6 km upstream and back again to the starting point in 33 minutes . find the speed of the motorboat in still water .
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) none of them
Rationale: let the speed of the motarboat in still water be x kmph . then , 6 / x + 2 + 6 / x - 2 = 33 / 60 11 x 2 - 240 x - 44 = 0 11 x 2 - 242 x + 2 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 . answer is a
Answer: a
Python program:
a = 6 + 6 
b = 33 / const_60
c = a / b
Problem: a cistern is filled by a tap in 5 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 66 , e ) 68
Rationale: "filling rate - leak rate = net rate 1 / 5.5 - leak rate = 1 / 6 leak rate = 2 / 11 - 1 / 6 = 1 / 66 the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = 5 + a 
c = 1 / b
d = 1 / 4
e = c - d
f = 1 / e
Problem: ajay bought 15 kg of dal at the rate of rs 14.50 per kg and 10 kg at the rate of rs 13 per kg . he mixed the two and sold the mixture at the rate of rs 15 per kg . what was his total gain in this transaction ?
Options: a ) rs 1.10 , b ) rs 11 , c ) rs 16.50 , d ) rs 27.50 , e ) none of these
Rationale: explanation : cost price of 25 kg = rs . ( 15 x 14.50 + 10 x 13 ) = rs . 347.50 . sell price of 25 kg = rs . ( 25 x 15 ) = rs . 375 . profit = rs . ( 375 — 347.50 ) = rs . 27.50 . answer : d
Answer: d
Python program:
a = 10 + 15 
b = 15 * a
c = 15 * 14
d = 10 * 13
e = c + d 
f = b - e
Problem: speed of a boat in standing water is 10 kmph and speed of the stream is 2 kmph . a man can rows to a place at a distance of 100 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 24 hours , b ) 21 hr 30 min , c ) 20 hr 50 min , d ) 18 hr 15 min , e ) 22 hrs
Rationale: speed upstream = 8 kmph speed downstream = 12 kmph total time taken = 100 / 8 + 100 / 12 = 20 hours 50 min answer is c
Answer: c
Python program:
a = 10 + 2 
b = 10 - 2
c = a + b 
d = c * 100
e = 10 + 2 
f = 100 / e
g = 10 - 2
h = 100 / g
i = f + h 
j = 10 + 2 
k = 10 - 2
l = j + k 
m = i - l
n = m * const_60
o = d + n
Problem: shekar scored 76 , 65 , 82 , 67 and 95 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 77 , c ) 75 , d ) 85 , e ) 90
Rationale: explanation : average = ( 76 + 65 + 82 + 67 + 95 ) / 5 = 385 / 5 = 77 hence average = 77 answer : b
Answer: b
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 95 
e = 1 + 4 
f = d / e
Problem: if in a race of 110 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 22 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 110 * 5 ) / 25 = 22 m hence , a beats b by 22 m . answer d"
Answer: d
Python program:
a = 25 - 20
b = a / 25
c = b * 110
Problem: a small company reduced its faculty by approximately 20 percent to 195 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 244
Rationale: "if x is the original number of employees , then after 20 % reduction in employees number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of employees is 244 correct answer - e"
Answer: e
Python program:
a = 100 - 20
b = a / 100
c = 195 / b
Problem: a part of certain sum of money is invested at 9 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 5 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: "15 : 9 = 5 : 3 answer : c"
Answer: c
Python program:
a = 15 / 100
b = a * 9
Problem: if 3 men or 4 women can reap a field in 43 days how long will 7 men and 5 women take to reap it ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 19
Rationale: "explanation : 3 men reap 1 / 43 field in 1 day 1 man reap 1 / ( 3 x 43 ) 4 women reap 1 / 43 field in 1 day 1 woman reap 1 / ( 43 x 4 ) 7 men and 5 women reap ( 7 / ( 3 x 43 ) + 5 / ( 4 x 43 ) ) = 1 / 12 in 1 day 7 men and 5 women will reap the field in 12 days answer : option b"
Answer: b
Python program:
a = 43 / 3
b = 7 * a
c = 43 / 4
d = 5 * c
e = b + d 
f = 43 / e
Problem: the smallest number when increased by ` ` 3 ` ` is exactly divisible by 510 , 4590 , and 105 is :
Options: a ) 630 , b ) 633 , c ) 150 , d ) 140 , e ) 627
Rationale: lcm = 630 630 - 3 = 627 answer : e
Answer: e
Python program:
a = 4590 / 510
b = 105 / 3
c = a * b
d = 4590 / 510
e = 105 / 3
f = d * e
g = c + f 
h = g - 3
Problem: if the perimeter of square region d and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of d
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pd ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pd = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Python program:
a = 3 * 2
b = 3 + 2 
c = b * 2
d = c / 4
e = d ** 2
f = a / e
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 3 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 5 / 3 = s * 8 / 3 tips = s * 8 / 3 fraction of his income came from tips = ( s * 5 / 3 ) / ( s * 8 / 3 ) = 5 / 8 answer : c"
Answer: c
Python program:
a = 5 / 3
b = 5 / 3
c = b + 1 
d = a / c
Problem: if ( c - a ) / ( c - b ) = 3 , then ( 5 b - 5 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 3.33 , e ) 2.5
Rationale: "let ' s say c = 7 , b = 5 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 3.33 answer d ( hopefully ) ) )"
Answer: d
Python program:
a = 5 - 2
b = a * 5
Problem: rachel and sarah spent $ 8 for gasoline , $ 15.65 for their lunch , and $ 5 apiece for gifts for grandma . grandma gave each of them $ 10 . if the girls left home with a total of $ 50 , how much do they have for the return trip ?
Options: a ) $ 36.35 , b ) $ 26.35 , c ) $ 16.35 , d ) $ 46.35 , e ) $ 56.35
Rationale: $ 50 + $ 20 = $ 70 what they left with plus $ 10 to each $ 8 + $ 15.65 + $ 10 = $ 33.65 what they spent ( gifts are $ 5 + $ 5 ) $ 70 - $ 33.65 = $ 36.35 left correct answer a
Answer: a
Python program:
a = 8 + 15 
b = 5 + a 
c = b - 5
d = 50 - c
e = 10 + d
Problem: in the fifth grade at parkway elementary school there are 420 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 , d ) 65 , e ) 108
Rationale: "total students = 420 boys = 320 , girls = 100 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 100 - 35 = 65 . correct option : d"
Answer: d
Python program:
a = 420 - 320
b = 250 * 86
c = b / 100
d = 250 - c
e = a - d
Problem: p and q invested in a shop . the profits were divided in the ratio of 2 : 4 respectively . if p invested rs . 500000 , the amount invested by q is :
Options: a ) 5000000 , b ) 4000000 , c ) 1000000 , d ) 6000000 , e ) none
Rationale: "suppose q invested rs . y . then , 500000 / y = 2 / 4 or y = [ 500000 x 4 / 2 ] = 1000000 . answer c"
Answer: c
Python program:
a = 500000 / 2
b = a * 4
Problem: 1939392 * 625
Options: a ) 1212120010 , b ) 1212120000 , c ) 1212120011 , d ) 1212121010 , e ) 1212121000
Rationale: "explanation : trick : when multiplying with 5 n 5 n then put n zeros to the right of multiplicand and divide the number with 2 n 2 n so using this we can solve this question in much less time . 1939392 × 5 ( 4 ) = 1939392000016 = 1212120000 option b"
Answer: b
Python program:
a = 1939392 / 625
b = a * 100
Problem: if ( m - 8 ) is a factor of m ^ 2 - qm - 24 , then q =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - qm - 24 a = - 3 q = 8 + a = 5 = b"
Answer: b
Python program:
a = 24 / 8
b = 8 - a
Problem: peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 870 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 650 , c ) 698 , d ) 744 , e ) 700
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 870 - 815 = 55 interest earned for 3 years = 55 * 3 = 165 amount invested = 815 - 165 = 650 answer : b"
Answer: b
Python program:
a = 870 - 815
b = 4 / 100
c = 3 / 100
d = b - c
e = a / d
f = 3 / 100
g = e * f
h = 815 - g
Problem: the ratio of the adjacent angles of a parallelogram is 5 : 13 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 134 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 5 x + 13 x = 180 ° or , 18 x = 180 ° or , x = 10 ° hence the angles of the parallelogram are 50 ° and 130 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 50 ° + 84 ° = 134 ° answer : b"
Answer: b
Python program:
a = 5 * 2
b = a * 10
c = b + 100 
d = c * 2
e = 5 + 6 
f = e + 7 
g = f + 12 
h = d / g
i = h * 13
Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 9 , d ) 3 / 7 , e ) 4 / 7
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Python program:
a = 1 / 2
b = 1 + 3 
c = 1 / b
d = 1 + 3 
e = 3 / d
f = c + e 
g = a + f 
h = 1 + g 
i = 1 + 3 
j = h / i
Problem: half a number plus 5 is 13 . what is the number ?
Options: a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 13 ( 1 / 2 ) x = 13 - 5 ( 1 / 2 ) x = 8 x = 16 correct answer is b"
Answer: b
Python program:
a = 13 - 5
b = a * 2
Problem: a hare and a jackal are running a race . 3 leaps of the hare are equal to 4 leaps of the jackal . for every 6 leaps of the hare , the jackal takes 7 leaps . find the ratio of the speed of the hare to the speed of the jackal .
Options: a ) 64 : 25 , b ) 8 : 7 , c ) 5 : 8 , d ) 25 : 64 , e ) 6 : 7
Rationale: the hare takes 6 leaps and the jackal takes 7 leaps . 1 hare leap = 4 / 3 jackal leaps thus the hare ' s 6 leaps = 6 * ( 4 / 3 ) = 8 jackal leaps . the ratio of their speeds is 8 : 7 . the answer is b .
Answer: b
Python program:
a = 4 + 4 
b = a / 7
Problem: on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 c"
Answer: c
Python program:
a = 109 / 9
b = math.floor(a)
Problem: a , b and c enter into a partnership by investing $ 15000 , $ 21000 and $ 27000 respectively . at the end of 8 months , b receives $ 1540 as his share . find the share of a .
Options: a ) $ 800 , b ) $ 900 , c ) $ 1000 , d ) $ 1100 , e ) $ 1200
Rationale: "the ratio of capital of a , b and c = 15000 : 21000 : 27000 = 5 : 7 : 9 a ' s share = ( 5 / 7 ) * 1540 = $ 1100 the answer is d ."
Answer: d
Python program:
a = 21000 * 8
b = a / 100
c = 1540 / b
d = 15000 * c
e = d * 8
f = e / 100
Problem: a is twice as good as workman as b and together they finish a piece of work in 18 days . in how many days will a alone finish the work ?
Options: a ) 27 , b ) 26 , c ) 29 , d ) 25 , e ) 24
Rationale: "a : b = 2 : 1 ab ' s together wrk in 18 days a ; s alone is 1 / 18 * 2 / 3 = 27 days answer : a"
Answer: a
Python program:
a = 18 * 3
Problem: when a number is divided by 6 & then multiply by 12 the answer is 15 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.6 , d ) 7.5 , e ) 6.5
Rationale: "if $ x $ is the number , x / 6 * 12 = 15 = > 2 x = 15 = > x = 7.5 d"
Answer: d
Python program:
a = 15 / 12
b = a * 6
Problem: by selling 15 pens for a rupee a woman loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 10 , e ) 65
Rationale: "d 85 % - - - 15 125 % - - - ? 85 / 125 * 15 = 10"
Answer: d
Python program:
a = 100 - 25
b = 100 / a
c = b / 15
d = 100 - 25
e = 100 / d
f = e / 15
g = f * 25
h = g / 100
i = c + h 
j = 1/(i)
Problem: if the perimeter of square region z and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of z
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pz ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pz = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Python program:
a = 2 * 3
b = 2 + 3 
c = b / 2
d = c ** 2
e = a / d
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 9 years hence ?
Options: a ) 22 , b ) 77 , c ) 78 , d ) 98 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 9 years , their ages will be 49 and 29 . sum of their ages = 49 + 29 = 78 . answer : c"
Answer: c
Python program:
a = 60 / 9
b = a * 2
c = b + 9 
d = 60 / 9
e = d + 9 
f = c + e
Problem: a , band c can do a piece of work in 35 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 16 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 35 + 1 / 20 = 11 / 140 ( a + c ) ' s 1 day ' s work = 1 / 35 + 1 / 55 = 18 / 385 work done in 2 day ' s = 11 / 140 + 18 / 385 = 48 / 383 48 / 383 th work done in 2 days work done = 383 / 48 * 2 = 16 days ( approx ) answer : e"
Answer: e
Python program:
a = 55 / 35
b = 55 / 20
c = a + b 
d = 55 / 35
e = 55 / 55
f = d + e 
g = c + f 
h = g / 2
i = 55 / h
Problem: aram ’ s car was fined when he gave joe and peter a ride , so they decided to help aram pay the fine . joe paid $ 3 more than 1 / 4 of the fine and peter paid $ 3 less than 1 / 3 of the fine , leaving pay $ 4 less than 1 / 2 the fine to complete the payment . what fraction of the fine did aram pay ?
Options: a ) $ 13 , b ) $ 15 , c ) $ 20 , d ) $ 28 , e ) $ 48
Rationale: as given aram ' payment is [ 1 ] [ / 2 ] * fine - 4 i . e total fine = 2 * ( sam ' s payment + 4 ) now , as everything looks integer , fine should be able to divide by 4 and 3 . because joe ' s contribution has 1 / 4 of the fine and peter ' s contribution has 1 / 3 of the fine so , that leads me to following : options , aram ' s pay , total fine ( f ) , f / 4 , f / 3 a ) , 13 , 34 , no i . e 34 / 4 , no i . e 34 / 3 b ) , 14 , 38 , no , no c ) , 20 , 48 , yes yes , no need to further go on as we have got f / 4 and f / 3 correct , just for confirmation we go further d ) , 28 , 64 , yes , no e ) , 48 , 104 , yes , no correct answer is c
Answer: c
Python program:
a = 3 + 4 
b = a + 3 
c = 1 / 4
d = 1 / 3
e = c + d 
f = 1 / 2
g = e + f 
h = g - 1
i = b / h
j = i - 100
Problem: the mean of 50 observations was 36 . it was found later that an observation 43 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.2 , d ) 36.4 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 43 - 23 ) = 1820 . â ˆ ´ correct mean = 1820 / 50 = 36.4 . answer d"
Answer: d
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50