Is integer x odd?

[Gmat_mission]

Is integer x odd?

(1) 2x + 1 is odd

(2) \(\frac{x}{2}\) is even

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT

[Vincen]

Hi Gmat_mission.

The question we need to answer is if x is odd or not.

Statement 1:

(1) 2x + 1 is odd

This doesn't tell us anything. Since 2x+1 is odd for all integers x. No matter if x is even or odd. So, NOT SUFFICIENT.

Statement 2:

(2) \(\frac{x}{2}\) is even

Here we have that \(\frac{x}{2} = 2k\) for some integer \(k\). Then \(x = 2\cdot (2k)\) and so, x is even. Hence, the answer to the initial question is NO.

Therefore, this statement is SUFFICIENT.

Therefore, the correct answer is the option _B_.

I hope it helps you. <i class="em em-wink"></i>

[Brent@GMATPrepNow]

Is integer x odd?

(1) 2x + 1 is odd

(2) \(\frac{x}{2}\) is even

Target question: Is integer x odd?

Statement 1: 2x + 1 is odd
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 1. Notice that 2x + 1 = 2(1) + 1 = 3, which is odd. In this case, the answer to the target question is YES, x IS odd
Case b: x = 2. Notice that 2x + 1 = 2(2) + 1 = 5, which is odd. In this case, the answer to the target question is NO, x is NOT odd
ASIDE: The fact of the matter is that 2x+1 is odd for ALL integer values of x.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x/2 is even
If a number is even, we can rewrite that number as 2k, where k is some integer.
So, for this statement, we can write: x/2 = 2k for some integer k
Multiply both sides by 2 to get: x = 4k
Since k is an integer, x MUST be EVEN
So, the answer to the target question is NO, x is definitely NOT odd
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent