Bunuel wrote:

If n is a positive integer, what is the greatest common factor of n and 64?

Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).

(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

Answer: D.

Hope it's clear.

Hi

Bunuel what if the n is in the form of

2^p where none of the two factors of 2^p will add to a prime number. but we do not know what is the value of P so we certainly can not determine GCF .So statement 1 is not sufficient.