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Is z an integer?

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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Thu Oct 19, 2017 6:20 am
ardz24 wrote:Is z an integer?

(1) z/3 is an integer.

(2) z/2 is NOT an integer.

Which statement is sufficient? Any experts can explain?
S1: We can set z/3 equal to any integer.
Case 1: z/3 = 1; z = 3. That's an integer, so YES
Case 2: z/3 = 2; z = 6; Again an integer, so YES.
No matter what we pick, we'll get a YES. More abstractly, if z/3 = integer, then z = 3* integer; 3 multiplied by an integer will always yield an integer value. Sufficient.

S2. Set z/2 equal to any non integer.
Case 1: z/2 = 1/2; z = 1;We have an integer. YES
Case 2: z/2 = 1/3; z = 2/3; Not an integer. NO. Because we can get a YES or a NO, this statement alone is not sufficient to answer the question. The answer is A
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