While it is possible for a test-taker to prove that a very large integer is not prime -- if the integer is even, if the integer is a multiple of 3, etc. -- it is NOT possible for a test taker to prove that a very large integer IS prime.
Implication:
If a DS problem asks whether a very large integer is prime, the answer must be NO.

BTGmoderatorDC wrote:Is integer k a prime number?

(1) k = 10! + m, where 1 < m < 8
(2) k is a multiple of 7

Statement 1:
Here, k is a very large integer.
Since the question stem asks whether this very large integer is prime, the answer must be NO.
SUFFICIENT.

Statement 2:
If k=7, the answer to the question stem is YES.
If k=14, the answer to the question stem is NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.

The correct answer is A.