Two Statements Si and S2 are given below followed by a Question:

S1: n is a prime number.

S2: n leaves a remainder of 1 when divided by 4.

If n is a unique natural number between 10 and 20, then what is n?

Which one of the following is correct in respect of the above Statements and the Question?

Neither of the S1 and S2 together or alone can give you the value of n.

Using S1 alone you have four prime numbers between 10 and 20 -> 11, 13, 17, and 19.

Using S2 alone there are two numbers 13 (= 4×3 + 1) and 17 (= 4×4 + 1) are possible.

Even after combining both you will get set of two numbers i.e., 13 and 17. So correct answer is option (d).