Is \(z\) an even integer?

[M7MBA]

Is \(z\) an even integer?

(1) \(\dfrac{z}2\) is an even integer.
(2) \(3z\) is an even integer.

Answer: A

Source: Manhattan GMAT

[Brent@GMATPrepNow]

Is \(z\) an even integer?

(1) \(\dfrac{z}2\) is an even integer.
(2) \(3z\) is an even integer.

Answer: A

Source: Manhattan GMAT

Target question: Is z an even integer?

Aside: Integer n is even if we can express n as n = 2k for some integer k

Statement 1: z/2 is an even integer.
This means z/2 =2k for some integer k
Multiply both sides by 2 to get: z = 4k
This tells us that z is a multiple of 4, which means z is definitely even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3z is an even integer.
If we were told that z is an integer, then statement 2 would be sufficient. However, we aren't told that z is an integer.
With this in mind, consider these two possible cases:
Case a: z = 2. Works because 3z = 3(2) = 6, and 6 is even. In this case, the answer to the target question is YES, z is even
Case b: z = 2/3. Works because 3z = 3(2/3) = 2, and 2 is even. In this case, the answer to the target question is NO, z is not even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent