Data Sufficiency

Gmat_mission wrote:Is integer x odd?

(1) 2x + 1 is odd $$\left(2\right)\ \ \frac{x}{2}\ is\ even.$$ [spoiler]OA=B[/spoiler].

Target question: Is integer x odd?

Statement 1: 2x + 1 is odd
Since 2x + 1 is ODD for any integer value, this statement doesn't tell us anything.
To understand what I mean, consider these two cases that satisfy statement 1:
Case a: x = 1. Here, 2x + 1 = 2(1) + 1 = 3, which is odd. In this case, x = 1, so the answer to the target question is YES, x IS odd
Case b: x = 2. Here, 2x + 1 = 2(2) + 1 = 5, which is odd. In this case, x = 2, so the answer to the target question is NO, x is NOT odd
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x/2 is even
If x/2 is even, we can write: x/2 = 2k for some integer k.

----ASIDE----------------
That last step applies to ALL even numbers.
For example, we know that 14 is even, because we can write 14 = 2(something), where that something is an integer
Likewise, we know that 16 is even, because we can write 16 = 2(something), where that something is an integer
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If x/2 = 2k for some integer k, we can take x/2 = 2k and multiply both sides by 2 to get: x = 4k (where k is an integer)
This means x must be a multiple 4, which means x is DEFINITELY EVEN
So the answer to the target question is NO, x is NOT odd
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent