Hi All,

We're asked if Z is an EVEN INTEGER. This is a YES/NO question. We can solve it by TESTing VALUES.

1) Z^2 is an EVEN integer.

IF...

Z^2 = 2, then Z = (root2) and the answer to the question is NO.

Z^2 = 4, then Z = 2 and the answer to the question is YES.

Fact 1 is INSUFFICIENT

2) (Y)(Z) is an EVEN integer and Z and Y are INTEGERS

IF...

Y = 1 and Z = 2, then the answer to the question is YES.

Y = 2 and Z = 1, then the answer to the question is NO.

Fact 2 is INSUFFICIENT

Combined, we know...

Y and Z are INTEGERS

Z^2 is an EVEN integer

The ONLY way to square an INTEGER and end up with an EVEN integer is if you started with an EVEN integer. Fact 2 tells us that Z MUST be an integer, so Z MUST be even and the answer to the question is ALWAYS YES.

Combined, SUFFICIENT

Final Answer:

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Rich

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