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
--------------------------
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
