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If x, y, and z are integers, what is the remainder . . .

This topic has 1 expert reply and 0 member replies

Top Member

Vincen Master | Next Rank: 500 Posts
Joined
07 Sep 2017
Posted:
458 messages
6

If x, y, and z are integers, what is the remainder . . .

Thu Sep 14, 2017 2:35 pm
If x, y, and z are integers, what is the remainder when xyz is divided by 2?

(1) 6xy is even.
(2) 9zx is even.

B is the OA?

Why is B the correct choice? Can any expert help me here?

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GMATGuruNY GMAT Instructor
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Thu Sep 14, 2017 6:34 pm
Vincen wrote:
If x, y, and z are integers, what is the remainder when xyz is divided by 2?

(1) 6xy is even.
(2) 9zx is even.
Statement 1:
Let x=1 and y = 1, with the result that 6xy = 6*1*1 = 6.
Case 1: z=2
In this case, (xyz)/2 = (1*1*2)/2 = 1 R0.
Case 2: z=3
In this case, (xyz)/2 = (1*1*3)/2 = 1 R1.
Since the remainder can be different values, INSUFFICIENT.

Statement 2:
9zx will be even only if zx is even.
Implication:
xyz = (y)(zx) = (y)(even) = even.
Since xyz is even, dividing xyz by 2 will yield a remainder of 0.
SUFFICIENT.

The correct answer is B.

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Thanked by: Vincen
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