euclaise/mathqa_programs huggingface dataset:
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 163 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 185.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 163 / 22.50 = 1 = â € º x - 163 = 22.50 = â € º x = 185.50 . hence , price of the third variety = rs . 175.50 per kg . answer c"
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 163 * b
d = 126 + 126 
e = c - d
f = e / 2
Problem: in an examination , 25 % of total students failed in hindi , 40 % failed in english and 35 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 25 + 40 - 35 ) = 100 - 70 = 30 answer : c"
Answer: c
Python program:
a = 25 + 40 
b = a - 35
c = 100 - b
Problem: the total circumference of two circles is 49 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 7.8 , b ) 6.0 , c ) 6.7 , d ) 9.7 , e ) 18.0
Rationale: "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 49 where 2 r = r thus : 2 π r + 4 π r = 49 6 π r = 49 r = approx 2.6 π r + 2 r π = 49 3 π r = 49 r = approx 5.2 r + r = approx 7.8 answer : a"
Answer: a
Python program:
a = 49 / 3
b = a / 3
c = 49 / 3
d = c * 2
e = d / 3
f = b + e 
g = f / 2
Problem: a certain pair of used shoes can be repaired for $ 10.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 30.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 42.85 , b ) 44 , c ) 48 , d ) 38 , e ) 40
Rationale: "1 ) cost of repairing = 10.5 ( for one year ) , therefore for 2 years it would be $ 21 . 2 ) cost of new pair which will last for 2 years is $ 30.00 percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 30 - 21 ) / ( 21 ) * 100 = 42.85 % . ans is a"
Answer: a
Python program:
a = 10 * 50
b = 30 - 0
c = 10 * 50
d = b / c
e = 100 * d
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 17.5 , b ) 7.4 , c ) 7.9 , d ) 12.0 , e ) 7.1
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 6 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i . e . , 12 hrs . answer : d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 6
c = a - b
d = 1 / c
Problem: a and b invests rs . 8000 and rs . 9000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 45 , b ) 32 : 47 , c ) 32 : 45 , d ) 32 : 41 , e ) 32 : 42
Rationale: "a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 9000 * 6 ) + ( 6000 * 6 ) 64000 : 90000 32 : 45 . answer : a"
Answer: a
Python program:
a = 8000 * 4
b = 9000 / 3
c = 2 * 4
d = b * c
e = a + d 
f = 2 * 3
g = 9000 * f
h = 9000 / 3
i = 9000 - h
j = 2 * 3
k = i * j
l = g + k 
m = e / l
Problem: a runs twice as fast as b and gives b a start of 42 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 84 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 42 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 42 m is 42 / 1 = 42 m so the total time taken by a and b to reach = 2 * 42 = 84 m answer : c"
Answer: c
Python program:
a = 42 * 2
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135
Rationale: "the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b ."
Answer: b
Python program:
a = 3 * 2
b = a + 4 
c = b + 5 
d = 330 / c
e = d * 4
Problem: what is the 26 th digit to the right of the decimal point in the decimal form of 6 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "6 / 11 = 0.54545454 . . . the even numbered positions in the decimal expansion are all 4 . the answer is b ."
Answer: b
Python program:
a = 6 / 11
Problem: a can complete a certain job in 9 days . b is 80 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 5 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 4.8
Rationale: "let , total work unit = 90 units a can finish in 9 days = 90 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 80 / 100 ) * 10 = 18 unit work days in which b will complete the work alone = 90 / 18 = 5 days answer : option a"
Answer: a
Python program:
a = 9 * const_60
b = a / 100
Problem: in what time a sum of money double itself at 2 % per annum simple interest ?
Options: a ) 60 % , b ) 58 % , c ) 55 % , d ) 40 % , e ) 50 %
Rationale: p = ( p * 2 * r ) / 100 r = 50 % answer : e
Answer: e
Python program:
a = 100 * 100
b = 2 * 100
c = a / b
Problem: a , b , c can complete a piece of work in 18 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 36 / 11 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 18 + 1 / 6 + 1 / 12 = 11 / 36 a , b , c together will complete the job in 36 / 11 days answer is d"
Answer: d
Python program:
a = 1 / 18
b = 4 + 2 
c = 1 / b
d = a + c 
e = 4 + 2 
f = 2 * e
g = 1 / f
h = d + g 
i = 1 / h
Problem: if the horse can run 10 miles / hour , how many days would it take for a horse to run from new york city to washington . d . c . ? ( 240 miles from nyc to d . c . )
Options: a ) 0.6 , b ) 0.8 , c ) 1 , d ) 1.2 , e ) 1.4
Rationale: the horse runs 10 miles / hour , thus it would take the horse 240 miles / 10 miles / hour to = 24 hours to run from nyc to d . c . there are 24 hours in a day , so days it take would be 24 hours / 24 hours / day = 1 day . correct option : 1
Answer: c
Python program:
a = 240 / 10
b = 240 / 10
c = a / b
Problem: solve below question 2 x + 1 = - 21
Options: a ) - 11 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 21 x = - 11 a"
Answer: a
Python program:
a = 21 + 1 
b = negate / (
Problem: solution for 2.12 + . 004 + . 345
Options: a ) 2.91 , b ) 2.911 , c ) 2.469 , d ) 2.586 , e ) 2.499
Rationale: 2.12 + . 004 + . 345 0 = 0 - 2.12 - 0.004 - 0.345 0 = - 2.469 answer : c
Answer: c
Python program:
a = 4 / 1000
b = 2 + 12 
c = 345 / 1000
d = b + c
Problem: in a throw of dice what is the probability of ge æ « ng number greater than 3
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Rationale: "explanation : number greater than 3 is 4 , 5 , 6 , so only 3 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 3 / 6 = 1 / 2 answer : a"
Answer: a
Python program:
a = 6 - 3
b = a / 6
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1300 , what is the reduced price for kg ?
Options: a ) s . 40 , b ) s . 65 , c ) s . 49 , d ) s . 41 , e ) s . 42
Rationale: "1300 * ( 25 / 100 ) = 325 - - - - 5 ? - - - - 1 = > rs . 65 answer : b"
Answer: b
Python program:
a = 1300 * 25
b = a / 100
c = b / 5
Problem: how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1 / 2 m board ?
Options: a ) 90 , b ) 99 , c ) 97 , d ) 95 , e ) 65
Rationale: "30 * 33 / 2 = 5 / 2 * 2 * x = > x = 99 answer b"
Answer: b
Python program:
a = 1 / 2
b = 16 + a 
c = 30 * b
d = 1 / 2
e = 2 + d 
f = e * 2
g = c / f
Problem: 20 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 4 : 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "let x be the amount of liquid q to be added . ( 2 / 5 ) * 20 + x = ( 3 / 7 ) * ( 20 + x ) 280 + 35 x = 300 + 15 x 20 x = 20 x = 1 the answer is a ."
Answer: a
Python program:
a = 4 + 3 
b = 20 * 3
c = 3 + 2 
d = b / c
e = a * d
f = e / 4
g = f * 3
h = 4 + 3 
i = g / h
j = 20 * 2
k = 3 + 2 
l = j / k
m = i - l
Problem: a sum amounts to rs . 5292 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 4000 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 5800
Rationale: "ci = 5292 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 5292 = p [ 21 / 20 ] ^ 2 5292 [ 20 / 21 ] ^ 2 4800 answer : d"
Answer: d
Python program:
a = 5 / 100
b = a + 1 
c = b ** 2
d = 5292 / c
Problem: express a speed of 56 kmph in meters per second ?
Options: a ) 10.56 mps , b ) 17.56 mps , c ) 97.56 mps , d ) 15.56 mps , e ) 18.56 mps
Rationale: "56 * 5 / 18 = 15.56 mps answer : d"
Answer: d
Python program:
a = const_0_2778 * 56
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 45 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 372 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 45 ) = 21 + 351 = > 372 hence answer will be ( b ) 372"
Answer: b
Python program:
a = 0 * 65
b = a * 12
Problem: a group of men decided to do a work in 12 days , but 6 of them became absent . if the rest of the group did the work in 14 days , find the original number of men ?
Options: a ) 15 , b ) 42 , c ) 44 , d ) 45 , e ) 18
Rationale: "original number of men = 6 * 14 / ( 14 - 12 ) = 42 answer is b"
Answer: b
Python program:
a = 6 * 14
b = 14 - 12
c = a / b
Problem: a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 234 for it , the cost price of the cricket bat for a is :
Options: a ) 156 , b ) 120 , c ) 130 , d ) 160 , e ) 210
Rationale: "125 % of 120 % of a = 234 125 / 100 * 120 / 100 * a = 234 a = 234 * 2 / 3 = 156 . answer a"
Answer: a
Python program:
a = 20 / 100
b = 1 + a 
c = 25 / 100
d = 1 + c 
e = b * d
f = 234 / e
Problem: a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 5 ] = 56 m answer b"
Answer: b
Python program:
a = rectangle_perimeter / (
Problem: in town x , 64 percent of the population are employed , and 49 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 20 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "answer b male - employed - 64 % female - employed - 15 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 15 / 64 = 20 b"
Answer: b
Python program:
a = 64 - 49
b = a / 64
c = b * 100
Problem: the hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 48 , e ) 60
Rationale: for the 12 minutes the motor - cyclist continues to overtake the hiker , she is going at 24 miles per hour faster than the hiker . once the motor - cyclist stops , the hiker is going at 6 miles per hour while the motor - cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds . 24 / 6 * 12 or 48 minutes answer is ( d )
Answer: d
Python program:
a = 30 * const_1_6
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 90 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 90 m = 90 / 5 = 18 seconds . answer : e"
Answer: e
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 90 / b
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 9 seconds . due to some problem , one boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 8.25 sec , e ) none of these
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 9 = 20 m / s now , length of train = 11 ã — 15 = 165 m â ˆ ´ required time = 165 â  „ 20 = 8.25 sec . answer d"
Answer: d
Python program:
a = 12 * 15
b = a - 15
c = 12 * 15
d = c / 9
e = b / d
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 2640 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 45 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 2640 100 r + 120 r = 2640 r = 12 % answer : b"
Answer: b
Python program:
a = 5000 * 2
b = 3000 * 4
c = a + b 
d = 2640 / c
e = d * 100
Problem: tickets numbered from 1 to 26 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 4 / 13 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 ] p ( e ) = n ( e ) / n ( s ) = 8 / 26 = 4 / 13 the answer is d ."
Answer: d
Python program:
a = 26 / 3
b = a / 26
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 56 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 400 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 56 , so 0.14 * { total } = 56 - - > { total } = 400 . answer : b ."
Answer: b
Python program:
a = 100 - 30
b = a / 100
c = 20 / 100
d = b * c
e = 56 / d
Problem: the number 219 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ?
Options: a ) 20 , b ) 21 , c ) 19 , d ) 17 , e ) 15
Rationale: "sum of the squares of 3 different positive integers = 219 13 ^ 2 + 7 ^ 2 + 1 ^ 2 = 219 now , sum of these 3 different integers = 13 + 7 + 1 = 21 ans - b"
Answer: b
Python program:
a = 219 / 2
b = math.sqrt(a)
c = 2 * b
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 7 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 7 / 27 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 7 * x hence , a 1 + a 2 + . . + a 20 + n = 27 x so , the fraction asked = 7 x / 27 x = 7 / 27 answer a"
Answer: a
Python program:
a = 1 * 1
b = 20 / 7
c = b + 21 
d = c / 7
e = d * 2
f = e - 7
g = f - 3
h = a / g
Problem: in a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man . what is weight of new comer ?
Options: a ) 70 , b ) 66 , c ) 68 , d ) 69 , e ) 72
Rationale: solution : member in group * age increased = difference of replacement or , 8 * 1 = new comer - man going out or , new comer = 8 + 60 ; or , new comer = 68 years . answer : option c
Answer: c
Python program:
a = 60 + 8
Problem: the ratio of a and b is 5 : 3 . after 2 years their ratio is 3 : 2 . what is the age of b ?
Options: a ) 5 , b ) 3 , c ) 6 , d ) 7 , e ) 8
Rationale: the ratio of a and b is 5 x and 3 x years . after 2 years , their ratio will be 3 and 2 . ( i . e ) ( 5 x + 2 ) / ( 3 x + 2 ) = 3 / 2 10 x + 4 = 9 x + 6 x = 2 b ' s age = 3 x = 3 ( 2 ) = 6 years answer is option c
Answer: c
Python program:
a = 5 * 2
b = a * 3
c = b / 2
d = 3 * 3
e = c - d
Problem: a train leaves delhi at 7 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 840 , c ) 600 , d ) 888 , e ) 121
Rationale: "d = 30 * 7 = 210 rs = 40 – 30 = 10 t = 210 / 10 = 21 d = 40 * 21 = 840 km answer : b"
Answer: b
Python program:
a = 3 + 2 
b = 30 * a
c = 40 - 30
d = b / c
e = d * 40
Problem: if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 7 , inclusive ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: one case is rainy - rainy - rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 4 = 1 / 16 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 1 / 16 = 1 / 4 the answer is a .
Answer: a
Python program:
a = 1 / 2
b = a ** 4
c = 4 * b
Problem: the length of a rectangle is twice its breadth . if its lengthis decreased by 5 cm & breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?
Options: a ) 25 cm , b ) 30 cm , c ) 40 cm , d ) 45 cm , e ) 60 cm
Rationale: let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x 2 sq . cm . new length = ( 2 x − 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x − 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 5 ) ( x + 5 ) = 2 x 2 + 75 ⇒ 2 x 2 + 10 x − 5 x − 25 = 2 x 2 + 75 ⇒ 5 x − 25 = 75 ⇒ 5 x = 75 + 25 = 100 ⇒ x = 1005 = 20 cm length = 2 x = 2 × 20 = 40 cm c
Answer: c
Python program:
a = 5 * 5
b = 75 + a 
c = 2 * 5
d = c - 5
e = b / d
f = 2 * e
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 51200 ?
Options: a ) 81000 , b ) 81028 , c ) 27772 , d ) 29889 , e ) 64800
Rationale: 51200 * 9 / 8 * 9 / 8 = 64800 . answer : e
Answer: e
Python program:
a = 1 / 8
b = a * 51200
c = 51200 + b 
d = 1 / 8
e = 1 / 8
f = e * 51200
g = 51200 + f 
h = d * g
i = c + h
Problem: set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 4 , while all other numbers remain the same , what is the new average of set s ?
Options: a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9
Rationale: "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 4 then total increased to 62 + 4 = 66 new avg - 66 / 10 = 6.6 . hence answer is a ."
Answer: a
Python program:
a = 10 * 6
b = a + 4 
c = b / 10
Problem: during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 18 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . d"
Answer: d
Python program:
a = 18 / 100
b = a + 1 
c = 20 / 100
d = 1 - c
e = 20 - 14
f = e / 20
g = d * f
h = b / g
i = h - 1
j = i * 100
Problem: how many numbers are divisible by 4 between 1 and 100 .
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 25
Rationale: "numbers divisible by 4 till 100 = ( 100 / 4 ) = 25 but we should not consider 100 as we are asked to find the number between 1 to 100 which are divisible by 4 . so answer is 24 numbers . option : a"
Answer: a
Python program:
a = 4 * 1
b = 100 / a
Problem: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . what is the actual distance travelled by him ?
Options: a ) 33 , b ) 11 , c ) 38 , d ) 50 , e ) 12
Rationale: "assume that the person would have covered x km if travelled at 10 km / hr ⇒ speed = distancetime = x 10 . . . . . ( equation 1 ) give that the person would have covered ( x + 20 ) km if travelled at 14 km / hr ⇒ speed = distancetime = ( x + 20 ) 14 . . . . . ( equation 2 ) from equations 1 and 2 , x 10 = ( x + 20 ) 1414 x = 10 x + 2004 x = 200 x = 2004 = 50 answer : d"
Answer: d
Python program:
a = 14 - 10
b = 20 / a
c = 10 * b
Problem: arjun started a business with rs . 40,000 and is joined afterwards by anoop with rs . 80 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 40000 * 12 = 80000 * ( 12 – x ) = > x = 6 . answer : d"
Answer: d
Python program:
a = 4 * 100
b = a * 100
c = b * 12
d = 2 * 100
e = d * 100
f = e * 12
g = c - f
h = 80 * 100
i = h * 10
j = g / i
Problem: 5555 × 9999 = ?
Options: a ) 55500005 , b ) 55511115 , c ) 55522225 , d ) 55533335 , e ) 55544445
Rationale: "e 55544445 5555 × 9999 = 5555 ( 10000 - 1 ) = 5555 × 10000 - 5555 × 1 = 55550000 - 5555 = 55544445"
Answer: e
Python program:
a = 5555 / 9999
b = a * 100
Problem: 1397 x 1397 = ?
Options: a ) 1951607 , b ) 1951609 , c ) 1951610 , d ) 1951611 , e ) 1951613
Rationale: "1397 x 1397 = ( 1397 ) 2 = ( 1400 - 3 ) 2 = ( 1400 ) 2 + ( 3 ) 2 - ( 2 x 1400 x 3 ) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609 . b )"
Answer: b
Python program:
a = 1397 / 1397
b = a * 100
Problem: if 5 < x < 11 and y = x + 6 , what is the greatest possible integer value of x + y ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "x + y = x + x + 6 = 2 x + 6 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 10.5 then x + y = 10.5 + 16.5 = 27 . the answer is c ."
Answer: c
Python program:
a = 6 + 10 
b = a + 10