If a, b and c are integers, what is the value of a?

[M7MBA]

If a, b and c are integers, what is the value of a?

(1) 2^a+2^b=33
(2) a·c=5

The OA is the option C.

I can't see how, using both statements, we can get an answer. Experts, can you help me? Please.

[DavidG@VeritasPrep]

If a, b and c are integers, what is the value of a?

(1) 2^a+2^b=33
(2) a·c=5

The OA is the option C.

I can't see how, using both statements, we can get an answer. Experts, can you help me? Please.

Statement 1: If we're summing two values to get an ODD result, we know that one of the values must be EVEN and one must be ODD (assuming they're both integers.) The only way we can get an odd value when raising 2 to some exponent is if the exponent is 0, so either a or b is equal to 0.

Case 1: a = 0 and b = 5
Case 2: a = 5 and b = 0
Because we get different values for a, this statement alone is not sufficient.

Statement 2: Case 1: a = 1 and c = 5
Case 2 a = 5 and c = 1
Again, two different values, so not sufficient.

Together. If a*c = 5, then 'a' cannot be 0. If a cannot be 0, the only way to satisfy the first statement is if a = 5 and b = 0. Because we can derive a unique value for 'a' together the statements are sufficient. The answer is C