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If n is an integer, is n + 1 a prime number?

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by M7MBA » Sat Mar 31, 2018 8:14 am
If n is an integer, is n + 1 a prime number?

(1) n is a prime number.
(2) n + 2 is not a prime number.

The OA is E.

Why are not sufficient the statements? Can anyone give me some help here? Thanks.
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Source: — Data Sufficiency |

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by [email protected] » Sat Mar 31, 2018 11:56 am
Hi M7MBA,

We're told that N is an INTEGER. We're asked if (N+1) a PRIME number. This is a YES/NO question. We can solve it by TESTing VALUES.

1) N is a PRIME number.

IF...
N=2, then (N+1) = 3 and the answer to the question is YES.
N=7, then (N+1) = 8 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) N + 2 is not a prime number.

IF...
N=2, then (N+2) = 4 and the answer to the question is YES.
N=7, then (N+1) = 9 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that 'fit' both Facts (and produce different answers - one "YES" and one "NO").
Combined, INSUFFICIENT.

Final Answer: E

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