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
