Bunuel wrote:
Is z an even integer?
(1) z/2 is an even integer.
(2) 3z is an even integer.
Kudos for a correct solution.
MANHATTAN GMAT OFFICIAL SOLUTION:The wording of this question has a tendency to bias people towards integers. After all, the “opposite” of even is odd, and odd numbers are integers, too. However, the question does not state that z must be an integer in the first place, so
do not assume that it is.
(1) SUFFICIENT: The fact that z/2 is an even integer implies that z = 2 × (an even integer), which much be an even integer. (In fact, according to statement (1), z must be divisible by 4).
(2) INSUFFICENT: The fact that 3z is an even integer implies that z = (an even integer)/3, which might not be an integer at all. For example, z could equal 2/3.
One way to avoid assuming is to invoke Principle #3: Work from Facts to Question. Statement (2) tells us that 3z = even integer = –2, 0, 2, 4, 6, 8, 10, etc. No even integers have been skipped over, nor have we allowed the question to suggest z values. That is how assumptions sneak in.
Next, we divide 3z by 3 to get z, so we divide the numbers on our list by 3: z = –2/3, 0, 2/3, 4/3, 2, 8/3, 10/3, etc. Only then do we check this list against our question and see that the answer is Maybe.
The correct answer is A. !

If we had assumed that z must be an integer, we might have evaluated statement (2) with two cases: 3 × even = even, so z could be even. 3 × odd = odd, so z is definitely not odd. We would have incorrectly concluded that Statement (2) was sufficient and therefore incorrectly selected answer (D). 
Another common assumption is that a variable must be positive. Do not assume that any unknown is positive
unless it is stated as such in the information given (or if the unknown counts physical things or measures some other positiveonly quantity).
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