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## Is z an even integer?

This topic has 1 expert reply and 0 member replies

### Top Member

Vincen Legendary Member
Joined
07 Sep 2017
Posted:
550 messages
6

#### Is z an even integer?

Fri Sep 22, 2017 9:39 am
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?

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
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Followed by:
472 members
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GMAT Score:
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Sat Sep 23, 2017 10:35 am
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

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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