euclaise/mathqa_programs huggingface dataset:
Problem: one pipe can fill a pool 1.5 times faster than a second pipe . when both pipes are opened , they fill the pool in five hours . how long would it take to fill the pool if only the slower pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 12.5 , d ) 9 , e ) 7.2
Rationale: "say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.5 r = 3 r / 2 . since when both pipes are opened , they fill the pool in five hours , then their combined rate is 1 / 5 pool / hour . thus we have that r + 3 r / 2 = 1 / 5 - - > r = 2 / 25 pool / hour - - > time is reciprocal of rate thus it ' s 25 / 2 = 12.5 hours . answer : c ."
Answer: c
Python program:
a = 3 + 2 
b = 1/(a)
c = 1 + 1 
d = b / c
e = 1/(d)
f = e / 1
Problem: a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 35 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 27.7
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 35 % of the final price - - > ( final price ) * 0.65 = $ 18 - - > ( final price ) = $ 27.7 . answer : e ."
Answer: e
Python program:
a = 100 + 35 
b = a / 100
c = 15 * b
d = 100 + 20 
e = d / 100
f = c * e
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 11 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 21 so a + b = 7 total number of people = 7 answer : b"
Answer: b
Python program:
a = 11 + 10 
b = 2 + 1 
c = a / b
Problem: a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 684 , what is the reduced price for kg ?
Options: a ) 72 , b ) 27 , c ) 34 , d ) 28 , e ) 20
Rationale: "684 * ( 20 / 100 ) = 136 - - - - 4 ? - - - - 1 = > rs . 34 answer : c"
Answer: c
Python program:
a = 684 * 20
b = a / 100
c = b / 4
Problem: if 522 x is a 3 digit no . with as a digit x . if the no . is divisible by 6 , what is the value of the digit x is ?
Options: a ) 1 , b ) 6 , c ) 4 , d ) 7 , e ) 9
Rationale: if a number is divisible by 6 , it must be divisible by both 2 and 3 in 522 x , to this number be divisible by 2 , the value of x must be even . so it can be 2,4 or 6 from given options 552 x is divisible by 3 , if sum of its digits is a multiple of 3 . 5 + 5 + 2 + x = 12 + x , if put x = 2 , 12 + 2 = 14 not a multiple of 3 if put x = 4 , 12 + 6 = 18 is a multiple of 3 if put x = 6 , 12 + 2 = 14 not a multiple of 3 the value of x is 6 . b
Answer: b
Python program:
a = 522 * 10
b = a + 6 
c = 522 * 10
d = c + 6 
e = d / 6
f = b / e
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 8 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 9 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 8 + 1 ) / ( 8 - 1 ) = 9 / 7 answer : e"
Answer: e
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 8
d = c / 100
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 7 , d ) 2 : 6 , e ) 1 : 4
Rationale: "2 % is 3 % - points below 5 % and 10 % is 5 % - points above 5 % . the ratio of a : b should be 3 : 5 . the answer is b ."
Answer: b
Python program:
a = 5 - 2
b = 10 - 5
c = a / b
Problem: the side of a rhombus is 28 m and length of one of its diagonals is 12 m . the area of the rhombus is ?
Options: a ) 326.2 , b ) 324.2 , c ) 328.2 , d ) 338.2 , e ) 328.9
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 28 ; p = 12 a = 1 / 2 * 12 * √ 4 ( 28 ) 2 - ( 12 ) 2 = 1 / 2 * 12 * √ 3136 - 144 = 1 / 2 * 12 * √ 2992 a = 328.2 answer : c"
Answer: c
Python program:
a = 2 * 28
b = a ** 2
c = 12 ** 2
d = b - c
e = math.sqrt(d)
f = 12 * e
g = f / 2
Problem: the product of two numbers is 2028 and their hcf is 13 . what are the number of such pairs ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 23 , e ) 25
Rationale: "let the numbers be 13 x and 13 y ( hcf of the numbers = 13 ) 13 x × 13 y = 2028 xy = 12 co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) ( we need to take only co - primes with product 12 . if we take two numbers with product 12 , but not co - prime , the hcf will not remain as 13 ) hence the numbers with hcf 13 and product 2028 = ( 13 × 1 , 13 × 12 ) and ( 13 × 3 , 13 × 4 ) = ( 13 , 156 ) and ( 39 , 52 ) so , there are 2 pairs of numbers with hcf 13 and product 2028 answer is b"
Answer: b
Python program:
a = 2 * 2028
b = 13 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 2028
f = d + e 
g = math.sqrt(f)
Problem: at deluxe paint store , fuchsia paint is made by mixing 6 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: in 24 liters , red = 6 / 9 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 4 / 5 or , x = 12 ( answer b )
Answer: b
Python program:
a = 6 + 3 
b = 6 / a
c = 24 * b
d = 6 + 3 
e = 4 / d
f = c / e
g = 6 + 3 
h = 5 / g
i = f * h
j = 6 + 3 
k = 6 / j
l = 24 * k
m = 24 - l
n = i - m
Problem: if x is a positive integer with fewer than 3 digits , what is the probability w that x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability w that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Python program:
a = 100 / 4
b = a * 2
c = 100 / 5
d = c * 2
e = b + d 
f = e - 4
g = 100 - 1
h = f / g
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 2 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 22.5 % , d ) 33.3 % , e ) 37.5 %
Rationale: "say morks income is - 100 so tax paid will be 40 say mindys income is 2 * 100 = 200 so tax paid is 30 % * 200 = 60 total tax paid = 40 + 60 = 100 . combined tax % will be 100 / 100 + 200 = 33.3 %"
Answer: d
Python program:
a = 40 / 100
b = 30 / 100
c = 2 * b
d = a + c 
e = 1 + 2 
f = d / e
g = 100 * f
Problem: two employees m and n are paid a total of rs . 550 per week by their employer . if m is paid 120 percent of the sum paid to n , how much is n paid per week ?
Options: a ) rs . 220 , b ) rs . 250 , c ) rs . 280 , d ) rs . 300 , e ) rs . 320
Rationale: let the amount paid to m per week = x and the amount paid to n per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 550 ⇒ y [ 12 / 10 + 1 ] = 550 ⇒ 22 y / 10 = 550 ⇒ 22 y = 5500 ⇒ y = 5500 / 22 = 500 / 2 = rs . 250 b )
Answer: b
Python program:
a = 550 * 2
b = a - 120
c = b / 2
d = c / 2
e = 10 / 2
f = d + e
Problem: a certain bag of gemstones is composed of two - thirds diamonds and one - third rubies . if the probability of randomly selecting two diamonds from the bag , without replacement , is 5 / 12 , what is the probability of selecting two rubies from the bag , without replacement ?
Options: a ) 5 / 36 , b ) 5 / 24 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4
Rationale: 2 / 3 * ( 2 x - 1 ) / ( 3 x - 1 ) = 5 / 12 = > x = 3 so total gems = 9 and probability of ruby = 1 / 3 * 2 / 8 = 1 / 12 answer 1 / 12 c
Answer: c
Python program:
a = 1 / 2
b = 5 / 12
c = a - b
Problem: one man adds 5 liters of water to 10 liters of milk and another 4 liters of water to 20 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?
Options: a ) 4 : 5 , b ) 9 : 11 , c ) 2 : 3 , d ) 4 : 7 , e ) 3 : 7
Rationale: strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 10 / 15 strength of the milk 2 nd mixture = 20 / 24 the ratio of their strengths = 10 / 15 : 20 / 24 = 4 : 5 answer is b
Answer: b
Python program:
a = 5 + 10 
b = 10 / a
c = 4 + 20 
d = 20 / c
e = b / d
Problem: the average of 9 observations was 6 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 36 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 6 = 54 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 54 = 36 option a"
Answer: a
Python program:
a = 10 * 5
b = 6 * 5
c = a + b 
d = 6 * 9
e = c - d
Problem: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 60 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 125 , d ) 150 , e ) 100
Rationale: explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 60 + 2 / 3 of 60 80 / 100 x = 100 x = 125 . answer : option c
Answer: c
Python program:
a = 2 / 3
b = 60 * a
c = 60 + b 
d = 20 / 100
e = 1 - d
f = c / e
Problem: two pipes a and b can fill a tank in 24 and 48 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 , b ) 16 , c ) 19 , d ) 20 , e ) 22
Rationale: "part filled by a in 1 min . = 1 / 24 part filled by b in 1 min . = 1 / 48 part filled by ( a + b ) in 1 min . = 1 / 24 + 1 / 48 = 1 / 16 . both the pipes can fill the tank in 16 minutes . answer : b"
Answer: b
Python program:
a = 24 * 100
b = 1 / 24
c = 1 / 48
d = b + c 
e = d * 2
f = 1 - e
g = f * 24
h = g * const_60
i = a + h
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 1000 . then his monthly salary is
Options: a ) rs . 5000 , b ) rs . 6000 , c ) rs . 4000 , d ) rs . 3000 , e ) rs . 2000
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 1000 â ‡ ” 20 / 100 x = 1000 â ‡ ” x = 1000 ã — 5 = 5000 . answer a"
Answer: a
Python program:
a = 4 + 1 
b = 1000 * a
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 36 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 36 / 3 = 12 kmph . answer : a"
Answer: a
Python program:
a = 36 * 2
b = a / 3
c = 36 - b
Problem: find the average of first 7 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 20
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 ) / 7 = 20 answer is e"
Answer: e
Python program:
a = 7 + 1 
b = 7 + 1 
c = b + 2 
d = a + c 
e = 5 - 7
f = 5 - 2
g = e + f 
h = d + g 
i = h / 7
Problem: robert ' s salary was decreased by 40 % and subsequently increased by 40 % . how much percentage does he lose ?
Options: a ) 16 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 40 % = 100 - 100 x 40 / 100 = $ 60 salary after increasing 40 % on $ 60 = 60 + 60 x 40 / 100 = $ 84 percentage of loss = 100 - 84 = 16 % answer : a"
Answer: a
Python program:
a = 100 * 100
b = 100 - 40
c = 100 + 40 
d = b * c
e = a - d
f = 100 * 100
g = e / f
h = g * 100
Problem: rs . 1560 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 528 , d ) s . 720 , e ) s . 549
Rationale: "a + b + c = 1560 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1560 = rs . 720 answer : d"
Answer: d
Python program:
a = 4 + 2 
b = a + 3 
c = 1560 / b
d = 4 * c
Problem: the average runs of a cricket player of 12 innings was 48 . how many runs must he make in his next innings so as to increase his average of runs by 10 ?
Options: a ) 12 , b ) 142 , c ) 164 , d ) 178 , e ) 84
Rationale: "explanation : average after 13 innings = 58 required number of runs = ( 58 * 13 ) – ( 48 * 12 ) = 754 – 576 = 178 answer d"
Answer: d
Python program:
a = 12 + 1 
b = 48 + 10 
c = a * b
d = 48 * 12
e = c - d
Problem: tickets numbered from 1 to 22 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 ) 3 / 7 , e ) 7 / 22
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 ] p ( e ) = n ( e ) / n ( s ) = 7 / 22 the answer is e ."
Answer: e
Python program:
a = 22 / 3
b = a / 22
Problem: a present value of a machine is $ 900 . its value depletiation rate is 25 % per annum then find the machine value before 2 years ?
Options: a ) $ 1500 , b ) $ 1200 , c ) $ 1600 , d ) $ 1000 , e ) $ 1350
Rationale: "p = $ 900 r = 25 % t = 2 years machine value before 2 years = p / [ ( 1 - r / 100 ) ^ t ] = 900 * 4 / 3 * 4 / 3 = $ 1600 answer is c"
Answer: c
Python program:
a = 25 / 100
b = 1 - a
c = b ** 2
d = 900 * c
Problem: how many positive integers less than 100 are neither multiples of 3 or 5 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 32 , d ) d ) 53 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 5 till 100 = 100 / 5 = 20 2 ) multiples of 3 till 100 = 100 / 3 = 33.33 = 33 add the two 20 + 33 = 53 ; subtract common terms that are multiple of both 5 and 3 . . lcm of 5 and 3 = 15 multiples of 15 till 100 = 100 / 15 = 6 so total multiples of 5 and 3 = 53 - 6 = 47 ans = 100 - 47 = 53 d"
Answer: d
Python program:
a = 4 + 3 
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: 122 * 252 - 12234 = ?
Options: a ) 15310 , b ) 18870 , c ) 24510 , d ) 18510 , e ) 42510
Rationale: "d ? = 122 * 252 - 12234 = 30744 - 12234 = 18510"
Answer: d
Python program:
a = 122 * 252
Problem: a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 72 minutes and a model y computer can complete the same task in 36 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model x computers were used ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: let ' s say 1 work is processing 72 gb of data . model x : 1 gb per min model y : 2 gb per min working together , 1 x and 1 y = 3 gb per min so , 24 times as many computers would work at 72 gb per min . so no . of x = 24 answer is c
Answer: c
Python program:
a = 72 * 36
b = 72 + 36 
c = a / b
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 360 oranges . how many oranges he had originally ?
Options: a ) 700 , b ) 710 , c ) 600 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 360 100 % of oranges = ( 360 × 100 ) / 6 = 600 total oranges = 700 answer : c"
Answer: c
Python program:
a = 40 / 100
b = 360 * a
c = 360 + b
Problem: of the goose eggs laid at a certain pond , 1 / 2 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 800 , b ) 840 , c ) 880 , d ) 920 , e ) 960
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 2 ) x = 120 ( 6 / 40 ) x = 120 x = 800 the answer is a ."
Answer: a
Python program:
a = 2 / 5
b = 1 - a
c = 120 / b
d = 2 / 4
e = c / d
f = 1 / 2
g = e / f
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "et 100 be the total volume . total salt = 10 salt taken out = 10 / 4 = 2.5 to make solution 16 % , total salt = 16 salt added = 16 - 7.5 = 8.5 solution had = 8.5 / 25 * 100 = 34 % sugar answer : a"
Answer: a
Python program:
a = 16 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 10 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 420 , what is the least possible value of n ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "420 = 2 * 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is b ."
Answer: b
Python program:
a = 420 / 2
b = a / 3
c = b / 4
d = 10 / 2
e = c / d
Problem: if x = 5 - q and y = 3 q - 1 , then for what value of q , x is three times to y ?
Options: a ) 0 , b ) 1 , c ) - 1 , d ) - 8 , e ) 8
Rationale: "explanation : x = 3 y < = > 5 - q = 3 ( 3 q - 1 ) < = > 5 - q = 9 q - 3 < = > 8 q = 8 < = > q = 1 . answer : b"
Answer: b
Python program:
a = 5 - 5
b = 1 + a
Problem: express a speed of 16 kmph in meters per second ?
Options: a ) 10 mps , b ) 8 mps , c ) 4 mps , d ) 7 mps , e ) 2 mps
Rationale: "16 * 5 / 18 = 4 mps answer : c"
Answer: c
Python program:
a = const_0_2778 * 16
Problem: xavier starts from p towards q at a speed of 90 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 51 km , then how much time does he take to cover the distance ?
Options: a ) 30 , b ) 32 , c ) 30 , d ) 36 , e ) 40
Rationale: "first 12 min = 90 * 12 / 60 = 18 km 2 nd 12 min = 100 * 12 / 60 = 20 km 3 rd 12 min = 110 * 12 / 60 = 22 km total time 12 * 3 = 36 min d"
Answer: d
Python program:
a = 12 + 12 
b = a + 12 
c = b + 12
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 30 paisa . if the share of y is rs . 63 , what is the total amount ?
Options: a ) 166 , b ) 105 , c ) 178 , d ) 177 , e ) 245
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 63 35 - - - ? = > 245 answer : e"
Answer: e
Python program:
a = 100 / 45
b = a * 63
c = 30 / 45
d = c * 63
e = b + d 
f = e + 63
Problem: how many multiples of 2 are there between 0 and 100 , exclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 49
Rationale: "2 * 50 = 100 total multiples = ( 50 - 1 ) + 1 = 50 exclude 0 and 100 = 50 - 1 = 49 answer is e ."
Answer: e
Python program:
a = 100 - 0
b = a / 2
c = b + 1
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 68 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 68 ) = 1180 kgs actual average weight is 1180 / 20 = 59 kgs d"
Answer: d
Python program:
a = 58 * 4
b = 68 - 56
c = a + b 
d = c / 20
Problem: what is the probability that a two digit number selected at random will be a multiple of ' 3 ' and not a multiple of ' 5 ' ?
Options: a ) 2 / 15 , b ) 4 / 15 , c ) 1 / 15 , d ) 4 / 90 , e ) 5 / 60
Rationale: solution : there are a total of 90 two digit numbers . every third number will be divisible by ' 3 ' . therefore , there are 30 of those numbers that are divisible by ' 3 ' . of these 30 numbers , the numbers that are divisible by ' 5 ' are those that are multiples of ' 15 ' . i . e . numbers that are divisible by both ' 3 ' and ' 5 ' . there are 6 such numbers - - 15 , 30,45 , 60,75 and 90 . we need to find out numbers that are divisible by ' 3 ' and not by ' 5 ' , which will be : 30 â ˆ ’ 6 = 24 24 out of the 90 numbers are divisible by ' 3 ' and not by ' 5 ' . the required probability is therefore , = 24 / 90 = 4 / 15 answer is b
Answer: b
Python program:
a = 5 * 2
b = a * 3
c = 3 * 2
d = b - c
e = 5 * 2
f = 3 * 3
g = e * f
h = d / g
Problem: tom , working alone , can paint a room in 12 hours . peter and john , working independently , can paint the same room in 6 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 5 / 3 , b ) 1 / 3 , c ) 7 / 3 , d ) 4 / 9 , e ) 3 / 5
Rationale: let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 12 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 6 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 12 * ( t + 4 ) + 1 / 6 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 12 - - > ( t + 4 ) + ( 2 t + 2 ) + 6 t = 12 - - > t = 2 / 3 ; hence peter has done 1 / 6 * ( 2 / 3 + 2 ) = 1 / 6 * 8 / 3 = 8 / 18 = 4 / 9 answer : d
Answer: d
Python program:
a = 4 * 2
b = a + 1 
c = 4 / b
Problem: p and q started a business investing rs 50000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 12 : 5 , b ) 17 : 3 , c ) 10 : 6 , d ) 17 : 7 , e ) 10 : 3
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 50000 : 15000 = 50 : 15 = 10 : 3 option e"
Answer: e
Python program:
a = 50000 / 15000
Problem: there are many numbers that can be expressed as the sum of 3 squares in 3 different ways . can you find out the smallest of such number ?
Options: a ) 87 , b ) 54 , c ) 29 , d ) 30 , e ) 70
Rationale: b 54 7 ^ 2 + 2 ^ 2 + 1 ^ 1 6 ^ 2 + 3 ^ 2 + 3 ^ 2 2 ^ 2 + 5 ^ 2 + 5 ^ 2
Answer: b
Python program:
a = 3 * 3
b = a * 4
c = b + 12 
d = c + 4 
e = d + 2
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 100 metres ?
Options: a ) 16 seconds , b ) 20 seconds , c ) 14 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 100 m = 100 / 5 = 20 seconds . answer : b"
Answer: b
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 100 / b