euclaise/mathqa_programs huggingface dataset:
Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 4 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 80
b ) 70
c ) 60
d ) 40
e ) 50
Rationale: b : d : w = 4 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 4 / 40 ) = ( 1 / 30 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be c
Answer: c
Python program:
a = 300 / 100
b = 40 / 2
c = a * b
Problem: two vessels contains equal number of mixtures milk and water in the ratio 8 : 2 and 9 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 17 : 3
Rationale: "the ratio of milk and water in the new vessel is = ( 8 / 10 + 9 / 10 ) : ( 2 / 10 + 1 / 10 ) = 17 / 10 : 3 / 10 = 17 : 3 answer is e"
Answer: e
Python program:
a = 9 + 1 
b = 8 + 2 
c = a / b
d = 8 * c
e = d + 9 
f = 9 + 1 
g = 8 + 2 
h = f / g
i = 2 * h
j = i + 1 
k = e / j
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers r are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Python program:
a = 1 + 1
Problem: tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?
Options: a ) 3 / 10 , b ) 3 / 20 , c ) 2 / 5 , d ) 1 / 2 , e ) 1 / 3
Rationale: s = { 1 , 23 , … . 20 } e = { 3 , 6 , 912 , 1518 } p ( e ) = 6 / 20 = 3 / 10 option a
Answer: a
Python program:
a = 3 / 10
Problem: find the ratio between whole surfaces of a sphere and a hemisphere ?
Options: a ) 4 : 3
b ) 3 : 4
c ) 3 : 2
d ) 5 : 2
e ) 4 : 6
Rationale: 4 ï € r 2 : 3 ï € r 2 = > 4 : 3 answer a
Answer: a
Python program:
a = 2 ** 2
b = a * math.pi
c = 4 * b
d = 2 ** 2
e = d * math.pi
f = 3 * e
g = c / f
Problem: some of 10 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 15 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 5
Rationale: "let total paint = 1 let amount replaced = x 10 ( 1 - x ) + 20 x = 15 x = 1 / 2 answer : c"
Answer: c
Python program:
a = 15 / 100
b = 10 / 100
c = a - b
d = 20 / 100
e = 10 / 100
f = d - e
g = c / f
Problem: a person walks from one end to the other of a 100 - meter long moving walkway at a constant rate in 25 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 37 , b ) 39 , c ) 41 , d ) 43 , e ) 45
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 25 ( v + x ) = 100 then 150 ( v + x ) = 600 150 ( v - x ) = 100 when we add the two equations : 300 v = 700 v = 7 / 3 time = 100 / ( 7 / 3 ) = ( 300 / 7 ) seconds which is about 43 seconds the answer is d ."
Answer: d
Python program:
a = 100 / 25
b = 100 / 150
c = a + b 
d = c / 2
e = 100 / d
Problem: a certain number of workers can do a work in 65 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 55 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 65 - 10 ) / 10 = 55 answer is a"
Answer: a
Python program:
a = 65 - 10
b = a * 10
c = 65 - 10
d = 65 - c
e = b / d
Problem: a bag contains 6 black and 9 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 3 / 5
Rationale: "let number of balls = ( 6 + 9 ) = 15 . number of white balls = 9 . p ( drawing a white ball ) = 9 / 15 = 3 / 5 hence answer is e"
Answer: e
Python program:
a = math.factorial(9)
b = 9 - 2
c = math.factorial(b)
d = a / c
e = math.factorial(2)
f = d / e
g = math.factorial(6)
h = 6 - 2
i = math.factorial(h)
j = g / i
k = math.factorial(2)
l = j / k
m = f + l 
n = 6 + 9 
o = math.factorial(n)
p = 6 + 9 
q = p - 2
r = math.factorial(q)
s = o / r
t = math.factorial(2)
u = s / t
v = m / u
Problem: walking at the rate of 8 kmph a man cover certain distance in 4 hr 45 min . running at a speed of 19 kmph the man will cover the same distance in .
Options: a ) 100 min , b ) 110 min , c ) 140 min , d ) 120 min , e ) 150 min
Rationale: "distance = speed * time 8 * 19 / 4 = 38 km new speed = 19 kmph therefore time = d / s = 38 / 19 = 120 min answer : d ."
Answer: d
Python program:
a = 45 / const_60
b = 4 + a 
c = 8 * b
d = c / 19
e = d * const_60
Problem: a train 420 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 20 , e ) 24
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 420 * 2 / 35 = 24 sec answer : option e"
Answer: e
Python program:
a = 63 * 1000
b = 420 / a
c = b * 3600
Problem: every day daniel drives 100 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 28 % , c ) 33 % , d ) 42 % , e ) 52 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 100 miles at 4 miles / hour . d = ( r ) ( t ) 100 = ( 4 ) ( t ) 100 / 4 = 25 = t it takes 25 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 68 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 68 = ( 2 ) ( t ) 68 / 2 = 34 = t it takes 34 hours for the second part total time to drive home on monday = 4 + 34 = 38 hours we ' re asked by what percent 38 hours is greater than 25 hours . 38 / 25 = 1.52 , so it is 52 % greater . e"
Answer: e
Python program:
a = 32 / 2
b = 100 - 32
c = b * 2
d = a + c 
e = d - 100
f = e / 100
g = f * 100
Problem: in what ratio must tea of rs . 42 per kg be mixed with tea of rs . 50 per kg so that cost of mixture is rs . 45 per kg ?
Options: a ) 5 : 3 , b ) 3 : 5 , c ) 2 : 3 , d ) 3 : 4 , e ) 1 : 2
Rationale: 50 - 45 : 45 - 42 = 5 : 3 answer : a
Answer: a
Python program:
a = 50 - 45
b = 45 - 42
c = a / b
Problem: in the biotechnology class of 2000 , there were x graduates . 32 of the graduates found a job , 45 continued on to their second degree and 13 did both . if only 9 people did n ' t do both , what is x equal to ?
Options: a ) 69 . , b ) 71 , c ) 73 , d ) 75 , e ) 76
Rationale: graduates got job = 32 graduates continued to second degree = 45 graduates got job and continued to second degree = 13 graduates did n ' t get job and did n ' t continue to second degree = 9 job no job total second degree 13 32 45 no second degree 19 9 28 total 32 41 x therefore x = 73 answer c
Answer: c
Python program:
a = 32 + 45 
b = a - 13
c = b + 9
Problem: the number 61 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 61 : 1 , 4 , 9 , 16 , 25 , 36 , 49 . now , 61 should be the sum of 3 of those 7 numbers . also to simplify a little bit trial and error , we can notice that as 61 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 61 equals to 9 + 16 + 36 = 3 ^ 2 + 4 ^ 2 + 6 ^ 2 = 61 - - > 3 + 4 + 6 = 13 . answer : e ."
Answer: e
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 3
Problem: the average weight of 6 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 74 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 6 × 1.5 = 9 kg so the weight of new person = 65 + 9 = 74 kg answer a"
Answer: a
Python program:
a = 6 * 1
b = 65 + a
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 54 , what is the total amount ?
Options: a ) 234 , b ) 116 , c ) 117 , d ) 118 , e ) 119
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 54 39 - - - ? = > 234 answer : a"
Answer: a
Python program:
a = 100 / 45
b = a * 54
c = 50 / 45
d = c * 54
e = b + d 
f = e + 54
Problem: from the sale of sleeping bags , a retailer made a gross profit of 14 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.56 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.14 = selling price - - > cost price * 1.14 = $ 28 - - > cost price = $ 24.56 . answer : c ."
Answer: c
Python program:
a = 28 * 100
b = 100 + 14 
c = a / b
Problem: in 150 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 30 m
Rationale: "distance covered by b in 9 sec . = 150 / 45 x 9 m = 30 m . a beats b by 30 metres . answer : option e"
Answer: e
Python program:
a = 150 / 45
b = 45 - 36
c = a * b
Problem: the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.5 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 0.29 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.567 ) / ( 0.5 * 23.25 * 7.57 ) = 25.4303 / 88.00125 = 0.29 answer : d"
Answer: d
Python program:
a = 34 * 31
b = a * 1
c = 7 * 57
d = c * 0
e = b / d
f = e / 10
Problem: if x is 12 percent greater than 70 , then x =
Options: a ) 78.4 , b ) 91.0 , c ) 88.0 , d ) 70.4 , e ) 71.2
Rationale: "12 % of 70 = ( 70 * 0.11 ) = 8.4 12 % greater than 70 = 70 + 8.4 = 78.4 answer is clearly a ."
Answer: a
Python program:
a = 12 / 100
b = a * 70
c = 70 + b
Problem: a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is
Options: a ) 26 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . then â € ¹ = â € º ( x + 28 ) + 2 = 2 ( x + 2 ) â € ¹ = â € º x + 30 = 2 x + 4 x = 26 . answer a"
Answer: a
Python program:
a = 2 * 2
b = a - 2
c = 28 - b
d = 2 - 1
e = c / d
Problem: a and b invests rs . 3000 and rs . 10000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 20 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 10 * 12 ) 54 : 120 = > 9 : 20 . answer : c"
Answer: c
Python program:
a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 10000 * e
g = d / f
Problem: what is the smallest integer that is multiple of 3 , 5,7
Options: a ) a ) 105 , b ) b ) 35 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 3 , 5 and 7 which is 105 . the answer is a ."
Answer: a
Python program:
a = 3 + 4
Problem: a call center has two teams . each member of team a was able to process 7 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 15 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 7 calls , so total calls for team a = 35 fraction for team b = 40 / ( 40 + 35 ) = 8 / 15 = answer = c"
Answer: c
Python program:
a = 8 * 5
b = 8 * 5
c = 5 * 7
d = b + c 
e = a / d
Problem: the speed at which a man can row a boat in still water is 10 kmph . if he rows downstream , where the speed of current is 2 kmph , what time will he take to cover 60 metres ?
Options: a ) 18 seconds , b ) 34 seconds , c ) 14 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 10 + 2 = 12 kmph = 12 * 5 / 18 = 10 / 3 m / s hence time taken to cover 60 m = 60 * 3 / 10 = 18 seconds . answer : a"
Answer: a
Python program:
a = 10 + 2 
b = a * const_0_2778
c = 60 / b
Problem: what is the value of 4 ^ 5 + 4 ^ 4 ?
Options: a ) 4 ^ 12 , b ) 5 ( 4 ^ 4 ) , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 )
Rationale: "4 ^ 5 + 4 ^ 4 = 4 ^ 4 ( 4 + 1 ) = 4 ^ 4 * 5 answer b"
Answer: b
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: the positive numbers w , x , y , and z are such that x is 10 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 16 - answer b"
Answer: b
Python program:
a = 10 + 100 
b = a / 100
c = 10 + 100 
d = c / 100
e = b * d
f = 100 - 10
g = f / 100
h = e * g
i = h - 1
j = 100 * i
Problem: a man misses a bus by 40 minutes if he travels at 30 kmph . if he travels at 40 kmph , then also he misses the bus by 10 minutes . what is the minimum speed required to catch the bus on time ?
Options: a ) 22 , b ) 45 , c ) 66 , d ) 88 , e ) 12
Rationale: let the distance to be travelled to catch the bus be x km x / 30 - x / 40 = 30 / 60 = > ( 4 x - 3 x ) / 120 = 1 / 2 = > x = 60 km by traavelling 30 kmph time taken = 60 / 30 = 2 hours by taking 2 hours , he is late by 40 min . so , he has to cover 60 km in at most speed = 60 / ( 4 / 3 ) = 45 kmph . answer : b
Answer: b
Python program:
a = 40 * 3
b = 30 / const_60
c = a * b
d = 40 * 3
e = 30 / const_60
f = d * e
g = f / 30
h = 40 / const_60
i = g - h
j = c / i
Problem: 5 n + 2 > 12 and 7 n + 2 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9
Rationale: "5 n + 2 > 12 5 n > 10 n > 2 7 n + 2 < 44 7 n < 42 n < 6 so n must be between 2 and 6 2 < n < 6 correct answer b"
Answer: b
Python program:
a = 2 * 10
b = 44 + 2 
c = b / 7
d = a + c
Problem: a committee is reviewing a total of 20 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 ) 26 / 21 , b ) 28 / 21 , c ) 20 / 21 , d ) 40 / 21 , e ) 60 / 21
Rationale: "say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 40 color films , thus total of 42 films were selected . color films thus compose 40 / 42 = 20 / 21 of the selected films . answer : c"
Answer: c
Python program:
a = 20 / 100
b = a + 4 
c = 4 / b
Problem: a jogger running at 9 kmph along side a railway track is 250 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 37 sec , c ) 36 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 250 + 120 ) m = 370 m . ∴ time taken = ( 370 ⁄ 10 ) sec = 37 sec . answer b"
Answer: b
Python program:
a = 250 + 120 
b = a / 1000
c = 45 - 9
d = b / c
e = d * const_60
f = e * const_60
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 11 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 63
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 11 = 63 answer e"
Answer: e
Python program:
a = 1 / 5
b = 2 / 3
c = a + b 
d = 1 - c
e = 1/(d)
f = 11 * e
Problem: a train traveling at 42 kms / hr passes a cyclist going in the same direction in 9 secs . if the cyclist had been going in the opposite direction , the train would have passed him in 5 secs . find the length of the train .
Options: a ) 75 meters , b ) 60 meters , c ) 90 meters , d ) 80 meters , e ) 70 meters
Rationale: let the length of the train be x meter and the speed of the cyclist is y m / s now when the train and the cyclist are in the same direction , the relative speed is : ( 35 / 3 - y ) m / s [ converting 42 km / h to m / s - 35 / 3 m / s ] now distance / relative speed = 9 seconds substituting the values , we get x + 9 y . . . . . . . . . . . . . . . . . . . . . ( 1 ) similarly calculate the relative speed when they are in the opposite direction the relative speed is ( 35 / 3 + y ) now distance / relative speed is equivalent to 5 seconds substituting the values , we get the equation 3 x - 15 y = 175 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2 ) solving ( 1 ) and ( 2 ) , we get x = 75 meters answer : a
Answer: a
Python program:
a = 42 * 1000
b = a / 3600
c = 42 * 1000
d = c / 3600
e = d * 9
f = 42 * 1000
g = f / 3600
h = g * 5
i = e - h
j = 9 + 5 
k = i / j
l = b - k
m = l * 9
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 245 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 455 , e ) none of these
Rationale: "average would be : 350 = ( 245 + x ) / 2 on solving , x = 455 . answer : d"
Answer: d
Python program:
a = 30 * 350
b = 15 * 245
c = a - b
d = c / 15
Problem: in what ratio should a variety of rice costing rs . 5.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 8 , e ) 7 / 6
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5.5 ) = 5 / 8 answer : d"
Answer: d
Python program:
a = 8 - 75
b = 8 - 75
c = a / b
d = 8 - 75
e = 8 - 75
f = d / e
g = 1 - f
h = c / g
Problem: john can complete a given task in 16 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 62 , b ) 64 , c ) 66 / 7 , d ) 10 , e ) 68 / 7
Rationale: "in such questions , you need to start from the end . last 5 days john works alone and completes 5 * ( 1 / 16 ) = 5 / 16 of the work . so 11 / 16 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 16 + 1 / 12 = 7 / 48 time taken to complete 11 / 16 of the work = ( 11 / 16 ) / ( 7 / 48 ) = 33 / 7 days . so total number of days taken to complete the work = 33 / 7 + 5 = 68 / 7 days . e"
Answer: e
Python program:
a = 16 * 12
b = 12 * 5
c = a - b
d = 12 + 16 
e = c / d
f = 5 + e
Problem: what is the least positive integer that is not a factor of 30 ! and is not a prime number ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 62 , e ) 64
Rationale: a ) 31 is prime and per the question stem we can not use this b ) 32 = 2 * 16 - within 30 ! we have a 2 and 16 so 32 will be a factor of 30 ! c ) 33 = 3 * 11 - again within 30 ! we have a 3 and an 11 so 33 will be a factor of 30 ! d ) 62 = 31 * 2 - bingo 31 is not included in 30 ! e ) 64 = 16 * 4 - both 16 and 4 are multiplied in 30 ! answer is d !
Answer: d
Python program:
a = 30 + 1 
b = a * 2
Problem: if the true discount on a sum due 3 years hence at 14 % per annum be rs . 168 , the sum due is :
Options: a ) 698 , b ) 768 , c ) 1430 , d ) 1980 , e ) none
Rationale: "sol . p . w . = 100 * t . d . / r * t = 100 * 168 / 14 * 2 = 600 . ∴ sum = ( p . w . + t . d . ) = rs . ( 600 + 168 ) = rs . 768 . answer b"
Answer: b
Python program:
a = 100 * 168
b = 14 * 2
c = a / b
d = c + 168
Problem: find the slope of the line perpendicular to the line y = ( 1 / 5 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 5 , d ) 4 , e ) 5
Rationale: two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 5 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 5 ) = - 1 solve for m m = - 5 correct answer c ) - 5
Answer: c
Python program:
a = 1 / 5
Problem: each child has 2 pencils and 13 skittles . if there are 9 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 9 = 18 . answer is c .
Answer: c
Python program:
a = 2 * 9
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 400 m long ?
Options: a ) 176 sec , b ) 190 sec , c ) 178 sec , d ) 160 sec , e ) 276 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1600 m t = d / s t = 1600 / 10 t = 160 sec answer : d"
Answer: d
Python program:
a = 1200 + 400 
b = 1200 / 120
c = a / b
Problem: chris age after 14 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 11
Rationale: "chris present age = x after 14 years = x + 14 5 years back = x - 5 x + 14 = 5 ( x - 5 ) x = 11 answer is e"
Answer: e
Python program:
a = 5 * 5
b = a + 14 
c = 5 - 1
d = b / c
e = 5 * 5
f = e + 14 
g = 5 - 1
h = f / g
i = h - 5
j = d - i
Problem: the average of 13 numbers is 59 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 59 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 59 = 767 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 767 = 59 . answer : a"
Answer: a
Python program:
a = 8 * 61
b = 13 * 59
c = 57 * 7
d = b - c
e = a - d
Problem: x is a positive integer less than 400 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 400 n = 23.42 or n = 23 answer : - c
Answer: c
Python program:
a = reminder * (
b = a + 3 
c = b - reminder