The correct Answer would be “(B)”

From Statement 1 one can only deduce that the number will be a prime number. So the statement is “Insufficient”.

Statement 2 says the difference of any 2 distinct positive factor is odd. If N>1, this can happen only when the number is 2. Since all other even numbers will have 2 as a factor (EVEN – EVEN = EVEN) where as all odd numbers will have at least 1 as a factor (ODD – ODD = EVEN). So this statement is “Sufficient”.

Hi SN,

The answer choices which you are referring to here is the question statements. Statements are part of a DS question. We cannot solve any DS question without the statements.

Coming back to the question,

Answer is B.

Statement I is insufficient:

Every prime number has exactly two factors. So N not necessarily has to be 2.

N = 2 (n has two factors and Yes N = 2)

N = 3 (n has two factors and N ≠ 2)

Statement II is sufficient:

N = 2, factors = {1,2} – Difference is odd.

In fact 2 is the only positive integer, where difference between any two distinct factors is odd. We can arrive it by plugging in couple of values.

There is no other number for which this is true.

So statement II is sufficient.

So Answer is B.