Is z an even integer?
(1) z^2 is an even integer.
(2) y*z is an even integer, where z and y are integers.
The OA is C.
How can I conclude with both statements that z is an even integer?
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Is z an even integer?
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Hi Vincen,
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: C
GMAT assassins aren't born, they're made,
Rich
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: C
GMAT assassins aren't born, they're made,
Rich
