Hi Neha,

Before we start discussing this question, lets discuss the below rule to find the number of factors.

Given a number, N,

If prime factorization of N = p^x * q^y * r^z

Then the number of factors of N would be,

(x+1) * (y+1) * (z+1)

For example, the number of factors of 40 is,

40 = 2^3 * 5

So, number of factors are (3+1)*(1+1) = 8.

So let’s get back to the original question,

Question: Number of factors of 20k ?

So according the above rule,

20k = 2^2 * 5 * k

Statement I is insufficient:

Given, k is prime.

If k = 5 , then the number of factors would be,

100 = 2^2 * 5^2

Number of factors are (2+1)* (2+1) = 9

But if, k = 11

220 = 2^2 * 5 * 11

Number of factors are (2+1)*(1+1)*(1+1) = 12.

So it changes accordingly with the prime, not sufficient.

Statement II is sufficient:

K = 7

It says specifically what’s the prime is , so sufficient.

140 = 2^2 * 5 * 7

So, number of factors are (2+1)*(1+1)*(1+1) = 12.

So the answer is B.

Hope this helps.