Quantitative Aptitude - Arithmetic Ability Questions

Two digit numbers: The two digits can be 2 and 9: Two possibilities 29 and 92.

Three-digit numbers: The three digits can be 1, 2 and 9 => 3! Or 6 possibilities.

We cannot have three digits as (3, 3, 2) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.

Every integer is a rational number since Q can be 1.

Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.

Hence, 4 is a rational number in the given options.

Given Karthik’s age = 32 years

Karthik’s son age = 7 years

Difference between their ages = K - S = 32 - 7 = 25 years ….(1)

Now, required K = 2S ……(2)

Put (2) in (1)

2S - S = 25

=> S = 25 years

Hence, at the age of 25 years of Karthik’s son, Karthik will be twice as his son’s age.

25 - 7 = 18 years

Therefore, after 18 years the father be twice as old as the son.