S1: n is a prime number

Two Statements S1 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.

Question: 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 above Statements and the Question?

  1. S1 alone is sufficient to answer the Question.
  2. S2 alone is sufficient to answer the Question.
  3. S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
  4. S1 and S2 together are not sufficient to answer the Question.

Answer: D

Explanation

It is given that n is a unique natural number between 10 and 20.

According to S1, n is a prime number.

So, our number n may be: 11, 13, 17 or 19

According to S2, on dividing n by 4 we get a remainder of 1.

So, n can be: 13, 17

Either of the two statements alone is not sufficient to answer the question.

Even if we read both the statements together, we do not get a unique value of n. Instead, we end up with two possible values of n, i.e. 13 & 17.

Hence, we can say that even S1 and S2 together are not sufficient to answer the question.

  • Exam Year: 2020