GMAT Number Properties DS question

Number Properties is an often tested area as far as Data Sufficiency is concerned. Here is an interesting question.

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.