euclaise/mathqa_programs huggingface dataset:
Problem: a study group consists of 4 english majors , 6 biological sciences majors , and 5 engineers . in how many ways can 3 english majors , 3 biological science majors and 3 engineers selected from the given group ?
Options: a ) 987 ways , b ) 346 ways , c ) 600 ways , d ) 200 ways , e ) 134 ways
Rationale: the number of ways of selecting three english majors , two biological science majors and three engineers is : = ⁴ c ₃ * ⁶ c ₂ * ⁵ c ₃ = ( 4 * 3 * 2 ) / ( 3 * 2 * 1 ) * ( 6 * 5 ) / ( 3 * 2 * 1 ) * ( 5 * 4 * 3 ) / ( 3 * 2 * 1 ) = 4 * 5 * 10 = 200 ways . answer : d
Answer: d
Python program:
a = math.factorial(6)
b = math.factorial(3)
c = math.factorial(3)
d = b * c
e = a / d
f = math.factorial(5)
g = math.factorial(3)
h = 2 * g
i = f / h
j = e * i
Problem: a man swims downstream 35 km and upstream 20 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 6.5 , b ) 5.5 , c ) 5.2 , d ) 4.6 , e ) 9.7
Rationale: "35 - - - 5 ds = 7 ? - - - - 1 20 - - - - 5 us = 4 ? - - - - 1 m = ? m = ( 7 + 4 ) / 2 = 5.5 answer : b"
Answer: b
Python program:
a = 20 / 5
b = 35 / 5
c = a + b 
d = c / 2
Problem: in the third grade of windblown school there are 90 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 90 failed in math = 90 / 3 = 30 failed in literature = 90 / 6 = 15 the least failed in both can be 0 while max can be 15 answer a"
Answer: a
Python program:
a = 90 / 3
b = 90 / 6
c = min(a)
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 9 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.25 % , c ) 14.14 % , d ) 13.33 % , e ) 11.71 %
Rationale: "( 100 % + 9 % ) * ( 100 % - 19 % ) = 1.09 * . 81 = 0.8829 . 1 - 0.8829 = 11.71 % lost = - 11.71 % the answer is e the organization has lost 11.71 % of its total volunteers from fall to spring ."
Answer: e
Python program:
a = 9 / 100
b = 1 + a 
c = 19 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: a theater box office sold an average ( arithmetic mean ) of 64 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 76 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 15 : 19 , e ) 64 : 76
Rationale: "deviation from the mean for the daytime staff = 76 - 64 = 12 . deviation from the mean for the evening staff = 64 - 60 = 4 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 4 : 12 = 1 : 3 . the answer is c ."
Answer: c
Python program:
a = 64 - 60
b = 76 - 64
c = a / b
Problem: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.988 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 54 , e ) can not be determined
Rationale: "it can not be determined . as we do not know the actual value of k . however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer k = [ lcm of 80 and 45 ] * ( any integer ) for value of k ( 60 ) * any integer unit value will be always zero . a"
Answer: a
Python program:
a = 3 * 2
b = 3 * 2
c = a * b
d = 3 * 2
e = c * d
f = e / 4
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is ?
Options: a ) 12 , b ) 27 , c ) 24 , d ) 29 , e ) 11
Rationale: "each row contains 12 plants . there are 11 gapes between the two corner trees ( 11 x 2 ) metres and 1 metre on each side is left . therefore length = ( 22 + 2 ) m = 24 m . answer : c"
Answer: c
Python program:
a = 12 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: 5 n + 2 > 12 and 7 n - 5 < 30 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 5 , e ) 2 and 9
Rationale: "5 n > 10 - - > n > 2 7 n < 35 - - > n < 5 2 < n < 5 answer : d"
Answer: d
Python program:
a = 2 * 10
b = 30 + 5 
c = b / 7
d = a + c
Problem: how long does a train 110 m long traveling at 36 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 28 , b ) 16.0 , c ) 16.4 , d ) 16.8 , e ) 16.1
Rationale: "d = 110 + 170 = 280 m s = 36 * 5 / 18 = 10 t = 280 * 1 / 10 = 28 sec answer : a"
Answer: a
Python program:
a = 110 + 170 
b = 36 * const_0_2778
c = a / b
Problem: how many positive integer solutions does the equation 2 x + 5 y = 100 have ?
Options: a ) 50 , b ) 33 , c ) 16 , d ) 35 , e ) 10
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 5 ) = 10 answer : e"
Answer: e
Python program:
a = 5 / 2
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 34 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 66.90 % , c ) 68.57 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 34 % of 1100 ) + ( 32 % of 900 ) = 374 + 288 = 662 failed = 2000 - 662 = 1338 failed % = [ ( 1338 / 2000 ) x 100 ] % = 66.9 % . answer : b"
Answer: b
Python program:
a = 100 * 10
b = 2 * a
c = 34 / 100
d = 100 * 10
e = 2 * d
f = e - 900
g = c * f
h = b - g
i = 32 / 100
j = i * 900
k = h - j
l = 100 * 10
m = 2 * l
n = k / m
o = n * 100
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 88 feet , b ) 86 feet , c ) 84 feet , d ) 82 feet , e ) 83 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 680 = > breadth = 34 feet area to be fenced = 2 b + l = 2 * 34 + 20 = 88 feet answer : option a"
Answer: a
Python program:
a = 680 / 20
b = a * 2
c = b + 20
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 330 . how much does c have ?
Options: a ) 50 , b ) 78 , c ) 30 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 330 - - - - - - - - - - - - - - a + b + 2 c = 530 a + b + c = 500 - - - - - - - - - - - - - - - - c = 30 answer : c"
Answer: c
Python program:
a = 200 + 330 
b = a - 500
Problem: when positive integer x is divided by positive integer y , the remainder is 4 . if x / y = 96.16 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 4 / y . the remainder in decimal form is given as . 16 therefore , 4 / y = . 16 solve for y and get 25 . d"
Answer: d
Python program:
a = math.floor(96, 16)
b = 96 - 16
c = 4 / b
Problem: the present ages of 3 persons are in proportions 4 : 7 : 9 . 7 years ago , the sum of their ages was 79 . find their present ages .
Options: a ) 20 , 28 , b ) 28 , 36 , c ) 35 , 45 , d ) 35 , 55 , e ) of these
Rationale: let their present ages be 4 x , 7 x and 9 x years respectively . then , ( 4 x - 7 ) + ( 7 x - 7 ) + ( 9 x - 7 ) = 79 20 x = 100 = > x = 5 their present ages are 20 , 35 and 45 years respectively . answer : c
Answer: c
Python program:
a = 7 * 3
b = 79 + a 
c = 4 + 7 
d = c + 9 
e = b / d
f = e * 7
g = f - 7
Problem: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability e this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability e of cgd / ( cg ) - > 3 / 19 answer d
Answer: d
Python program:
a = 1 / 8
b = 2 / 3
c = a / b
d = 1 / 8
e = 2 / 3
f = d / e
g = f + 1 
h = c / g
Problem: a car dealership has 40 cars on the lot , 15 % of which are silver . if the dealership receives a new shipment of 80 cars , 30 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the number of silver cars is 0.15 * 40 + 0.3 * 80 = 30 the percentage of cars which are silver is 30 / 120 = 25 % the answer is b ."
Answer: b
Python program:
a = 15 / 100
b = 40 * a
c = 30 / 100
d = 80 * c
e = b + d 
f = 40 + 80 
g = e / f
h = g * 100
Problem: two train each 500 m long , and running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 20 sec , b ) 25 sec , c ) 24 sec , d ) 30 sec , e ) 22 sec
Rationale: speed = ( 45 + 30 ) = 75 * 5 / 18 = = > 125 / 6 req time = 500 * 6 / 125 = 24 sec answer c
Answer: c
Python program:
a = 45 + 30 
b = const_0_2778 * a
c = 1/(b)
d = 500 * c
Problem: geetha ' s home has one tap , working alone at its maximum constant rate , can fill a certain sink in 210 seconds . a second tap , working alone at its maximum constant rate , can fill the same sink in 214 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to
Options: a ) 106 seconds , b ) 130 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 210 secs tap 2 : 214 secs considering the average of these 2 taps : 212 secs . so 1 tap can fill the tank in 212 secs , so 2 taps can fill the tank in 212 / 2 = 106 secs . closest answer is a .
Answer: a
Python program:
a = 1 / 210
b = 1 / 214
c = a + b 
d = 1/(c)
Problem: a bucket contains 2 mixtures a and b in the ratio 3 : 2 . if 5 liters of the mixture is replaced by 5 liters of liquid b , then the ratio of the two liquids becomes 3 : 5 . how much of the liquid a was there in the bucket ?
Options: a ) 8 liters , b ) 10 liters , c ) 12 liters , d ) 15 liters , e ) 18 liters
Rationale: "1 st ratio = 3 : 2 2 nd ratio = 3 : 5 difference of cross products ratio = 3 * 5 - 3 * 2 = 9 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 5 / 5 ) + ( 5 * 3 / 9 ) = 1 + 5 / 3 = 2.67 quantity of a = 3 * 2.67 = 8 liters approximately answer is a"
Answer: a
Python program:
a = 3 + 2 
b = 3 / a
c = b * 5
d = 5 * c
e = 3 + 2 
f = 2 / e
g = f * 5
h = 5 - g
i = 3 * h
j = d + i 
k = 5 * 3
l = 2 * 3
m = k - l
n = j / m
o = n * 3
Problem: 34 : 43 : : 25 : ?
Options: a ) 49 , b ) 52 , c ) 36 , d ) 64 , e ) 56
Rationale: "ans 52 reverse of 25 answer : b"
Answer: b
Python program:
a = 34 / 43
b = 25 * a
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 2 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 18
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 2 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 2 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 2 x = 3 since you need a 15 l solution , you must evaporate 18 of the original 50 l solution to get a 2 % solution . answer is e ."
Answer: e
Python program:
a = 50 / 100
b = a * 2
c = 50 - b
Problem: how much more would rs . 40000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 482 , b ) 725 , c ) 964 , d ) 837 , e ) 923
Rationale: "40000 ( 11 / 10 ) 4 - 40000 ( 6 / 5 ) 2 = 964 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a / 2
c = 1 + b 
d = c ** 4
e = d * 40000
f = 20 / 100
g = f + 1 
h = g ** 2
i = h * 40000
j = e - i
Problem: fresh grapes contain 80 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 80 = 20 % of whole weight ) , so 20 * 0.75 = x * 0.2 - - > x = 75 . answer : a ."
Answer: a
Python program:
a = 100 - 25
b = 20 * a
c = b / 100
d = c + 80
Problem: a can finish a work in 6 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 6 , b ) 5 , c ) 5.5 , d ) 2 , e ) 8
Rationale: "b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 6 therefore 1 work is done by a in ( 6 x 1 ) = 2 days . d"
Answer: d
Python program:
a = 1 / 15
b = a * 10
c = b * 6
d = c / 2
Problem: one night 25 percent of the female officers on a police force were on duty . if 500 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 500 number of female officers on duty on that night = 500 / 2 = 250 ( 25 / 100 ) * f = 250 = > f = 1000 answer e"
Answer: e
Python program:
a = 500 / 2
b = 25 / 100
c = a / b
Problem: two bullet trains of equal lengths take 10 seconds and 50 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 13 sec . , b ) 15 sec . , c ) 12 sec . , d ) 17 sec . , e ) 16.7 sec .
Rationale: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 50 m / sec = 2.4 m / sec . relative speed = ( 12 + 2.4 ) = 14.4 m / sec . required time = ( 120 + 120 ) / 14.4 sec = 16.7 sec . e"
Answer: e
Python program:
a = 120 + 120 
b = speed + ( 
c = a / b
Problem: if $ 935 are divided between worker a and worker b in the ratio 5 : 12 , what is the share that worker b will get ?
Options: a ) 62.15 % , b ) 64.26 % , c ) 66.37 % , d ) 68.48 % , e ) 70.59 %
Rationale: "worker b will get 12 / 17 = 70.59 % the answer is e ."
Answer: e
Python program:
a = 5 + 12 
b = 935 / a
Problem: a shop owner sells 30 mtr of cloth and gains sp of 10 metres . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 65 % , e ) 72 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 30 m cloth ) – ( c . p . of 30 m cloth ) selling price of 20 m cloth = selling price of 30 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 20 m cloth = rs . 2000 and s . p . of 20 m cloth = rs . rs . 3000 profit % = 10 × 100 = 50 % 20 profit of 50 % was made by the merchant . c"
Answer: c
Python program:
a = 30 - 10
b = 10 / a
c = b * 100
Problem: if n is a positive integer and n ^ 2 is divisible by 50 , then what is the largest positive integer that must divide n ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 20 , e ) 25
Rationale: "50 = 2 * 5 ^ 2 if 50 divides n ^ 2 , then n must be divisible by 2 * 5 = 10 the answer is c ."
Answer: c
Python program:
a = 50 / 2
b = math.sqrt(a)
c = b * 2
Problem: the sum of present age of abe and the age before 7 years is 29 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 29 2 x - 7 = 29 2 x = 29 + 7 x = 36 / 2 x = 18 z = x + 7 = 18 + 7 = 25 answer : a"
Answer: a
Python program:
a = 29 + 7 
b = a / 2
c = b + 7
Problem: if both 5 ^ 2 and 3 ^ 3 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 49 , b ) 75 , c ) 150 , d ) 225 , e ) 343
Rationale: "the number a must include at least 3 * 5 ^ 2 = 75 the answer is b ."
Answer: b
Python program:
a = 5 * 2
b = a * 2
c = 5 * 2
d = c * 2
e = b + d 
f = 5 * 2
g = f * 2
h = e + g 
i = h + 2 
j = i + 4 
k = j + 4
Problem: a and b can finish a work in 16 days while a alone can do the same work in 32 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 98 days , d ) 32 days , e ) 22 days
Rationale: b = 1 / 16 – 1 / 32 = 1 / 32 = > 32 days answer : d
Answer: d
Python program:
a = 1/(16)
b = 1/(32)
c = a - b
d = 1/(c)
Problem: of 60 applicants for a job , 28 had at least 4 years ' experience , 36 had degrees , and 6 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "60 - 6 = 54 54 - 28 - 36 = - 10 then 10 are in the intersection between 4 years experience and degree . answer : a"
Answer: a
Python program:
a = 28 + 36 
b = 60 - 6
c = a - b
d = 36 - 28
e = c + d
Problem: if log 0.317 = 0.3332 and log 0.318 = 0.3364 , then find log 0.319
Options: a ) 0.3396 , b ) 0.3496 , c ) 0.3596 , d ) 0.3696 , e ) 0.3796
Rationale: "log . 318 - log . 317 = . 0032 log . 318 + log . oo 1 = log . 319 . 3364 + . 0032 = . 3396 answer : a"
Answer: a
Python program:
a = 0 / 3332
b = 0 * 3332
Problem: a bicycle wheel has a diameter of 0.81 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 448 , c ) 393 , d ) 710 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.81 m ) = 393.2 . hence 393 complete revolutions . answer c"
Answer: c
Python program:
a = 1000 * 1
b = 3 * 4
c = b + 2 
d = 4 * 2
e = d + 2 
f = e ** 2
g = c / f
h = 3 + g 
i = h * 0
j = a / i
Problem: if there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 30 % of the total . what fraction of the total is men who own cars ?
Options: a ) 3 ⁄ 20 , b ) 31 ⁄ 60 , c ) 9 ⁄ 40 , d ) 1 ⁄ 3 , e ) 11 ⁄ 20
Rationale: consider a group of 100 women and 200 men , a total of 300 people . 30 % of them , which is 90 , form a group of people who do n ' t own a car . half of them are men , and the other half are women , more precisely 45 . it means that there are 200 - 45 = 155 men who own a car , and this represents 155 / 300 = 31 / 60 of the total . answer b
Answer: b
Python program:
a = 100 - 30
b = a / 2
c = b - 4
d = 30 * 2
e = c / d
Problem: 12 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 150 , b ) 131 , c ) 115 , d ) 90 , e ) 45
Rationale: "there are 12 business exec and in each handshake 2 business execs are involved . hence 12 c 2 = 66 also , each of 12 exec will shake hand with every 7 other chairmen for total of 84 handshake . total = 66 + 84 = 150 ans : a"
Answer: a
Python program:
a = 12 - 1
b = 12 * a
c = b / 2
d = 12 * 7
e = c + d
Problem: if the function q is defined by the formula q = 5 w / ( 4 d ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , d is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: "we just need to find the factor thats all , w - > quadrupled - > 4 w d - > doubled - > 2 d z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and d * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b"
Answer: b
Python program:
a = 3 ** 2
b = 2 * a
c = 4 / b
Problem: a pipe can fill a cistern in 88 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 8 min , d ) 1 min , e ) 10 min
Rationale: full cistern filled in = 88 minutes 1 / 11 part filled in = 88 * 1 / 11 = 8 minutes answer is c
Answer: c
Python program:
a = 1 / 11
b = 88 * a
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 20 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 950 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 20 minutes = 15 / 18 * 20 * 60 = 1000 m answer is d"
Answer: d
Python program:
a = 15 * 1000
b = a / const_60
c = b * 20
Problem: a total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ?
Options: a ) 32 , b ) 60 , c ) 27 , d ) 29 , e ) 21
Rationale: let the number of boys be x . number of girls is 120 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 120 - x ) = 300 = > 360 - x = 300 = > x = 60 . so , the number of boys or girls is 60 . answer : b
Answer: b
Python program:
a = 3 * 120
b = 3000 / 10
c = a - b
Problem: how many figures are required to number the pages the pages of a book containing 365 pages ?
Options: a ) 987 , b ) 977 , c ) 967 , d ) 897 , e ) 997
Rationale: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 365 = 266 * 3 = 798 - - - - - - - - - - - 987 answer : a"
Answer: a
Python program:
a = 365 / 10
b = a / 10
c = b - 1
d = 365 / 10
e = d - 1
f = 365 / 10
g = f / 10
h = g - 1
i = e - h
j = c + i 
k = 365 - 1
l = 365 / 10
m = l - 1
n = k - m
o = n * 3
p = j + o
Problem: a mixture contains milk and water in the ratio 3 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 2 : 3 . total quantity of milk & water before adding water to it ?
Options: a ) 30 , b ) 40 , c ) 20 , d ) 10 , e ) 25
Rationale: milk : water = 3 : 2 after adding 10 liters of water milk : water = 2 : 3 olny water patrs increase when mixture of water milk : wate = 3 : 2 = 2 * ( 3 : 2 ) = 6 : 4 after adding 10 liters of water milk : water = 2 : 3 = 3 * ( 2 : 3 ) = 6 : 9 option ' c '
Answer: c
Python program:
a = 2 / 3
b = 10 * a
c = 3 + 2 
d = 3 / c
e = 3 + 2 
f = 2 / e
g = 2 / 3
h = f * g
i = d - h
j = b / i
Problem: 16 men can complete a piece of work in 30 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 77 days , c ) 20 days , d ) 24 days , e ) 44 days
Rationale: "16 * 30 = 20 * x = > x = 24 days answer : d"
Answer: d
Python program:
a = 30 * 16
b = a / 20
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 160 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 5.0 , b ) 5.5 , c ) 6.0 , d ) 6.5 , e ) 7.0
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 1.5 hours to travel 240 km , so c leaves 6.5 hours after a . the answer is d ."
Answer: d
Python program:
a = 40 - 30