Answer to the Number Properties DS question

Is the two digit positive integer P a prime number?
1) P + 2 and P – 2 are prime.
2) P – 4 and P + 4 are prime.

Statement (1): P + 2 and P – 2 are prime.
One out of 3 consecutive odd integers, (P - 2), P, and (P + 2) will definitely be a multiple of '3'. If (P + 2) and (P - 2) are prime, then P has to be a multiple of '3', which is not prime. The only exception is if the 3 consecutive odd numbers are 3, 5 and 7. However, we are dealing with two digit positive integers.
SUFFICIENT.

Statement (2): P – 4 and P + 4 are prime.
One out of 3 consecutive odd integers, (P - 4), P, and (P + 4) will definitely be a multiple of '3'. If (P + 4) and (P - 4) are prime, then P has to be a multiple of '3', which is not prime. The only exception is if the 3 consecutive odd numbers are 3, 7 and 11. However, we are dealing with two digit positive integers.
SUFFICIENT.

Hence, the correct answer is D.

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