I need help!

[olylo]

Hi everyone,

I need help please to understand how can I solve this DS within 2 min
The question is :

is the number M a prime number?

1) M+7 is a prime number.

2) M-7 is a prime number.

Thanks

[GmatMathPro]

A useful thing to keep in mind on problems like these is that every prime number besides 2 is odd.

Statement 1: If M is prime, it is either 2 or some odd prime. It can't be 2 because M+7 would then be 9, which is not prime. If M is an odd prime, then M+7 is odd+odd which is always even and greater than 2, and would not be prime. Therefore, M cannot be prime if M+7 is prime. SUFFICIENT

Statement 2: Similar reasoning. M can't be 2 again, because that would make M-7=-5, and M can't be an odd prime because that would make M-7 an even number that is not 2. Therefore, M cannot be prime if M-7 is prime.

So the answer is D

[olylo]

Thank you so much for solving the question.
Your explanation is very clear.

Thanks again