1000DS is n+2 a prime number --- 1000DS

[rookiez]

10. If n is an integer, is n +2 a prime number?
(1) n is a prime number.
(2) n + 1 is not a prime number.


OA is E
..IMO C

[DanaJ]

1 is insufficient if you consider some examples:
a. say n = 5. In this case, n + 2 = 7, which is indeed a prime number.
b. consider n = 7. This means that n + 2 = 9, which is NOT a prime number.

Since we get two possible outcomes, 1 is not enough.

2 is again insufficient, which can be proven with cases:
a. n = 3, then n + 1 = 4, which is not prime. However, n + 2 = 5, which is prime.
b. n = 8, then n + 1 = 9 is not prime. But n + 2 will be 10, which is NOT prime.

Again, two results, 2 not enough.

Put both together and you still need some more info. To prove this, take n = 5 and n = 3 (case a from statement 1 and case a from statement 2). Again, you'll get two different possibilities, so E is you answer.