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# M23-31

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Math Expert
Joined: 02 Sep 2009
Posts: 44586

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16 Sep 2014, 01:19
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Difficulty:

25% (medium)

Question Stats:

78% (00:55) correct 22% (01:07) wrong based on 100 sessions

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If $$X$$, $$Y$$, and $$Z$$ are positive integers, is $$X*Y*Z$$ even?

(1) $$X - Y$$ is odd

(2) $$Y*Z + X$$ is odd
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:20
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Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$X$$ and $$Y$$ cannot both be odd or even. One of them must be even and the other must be odd. This information is enough to state that $$X*Y*Z$$ is even.

Statement (2) by itself is sufficient. From S2 it follows that either $$Y*Z$$ or $$X$$ is even. This information is enough to state that $$X*Y*Z$$ is even.

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Joined: 08 Jun 2015
Posts: 469
Location: India
GMAT 1: 640 Q48 V29

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28 Mar 2018, 07:26
+1 for option D.
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Intern
Joined: 02 Jun 2014
Posts: 19

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28 Mar 2018, 09:40
Question is basically asking us X, Y, Z - do we have one variable that is even?

If ANY of these variables are even, then the product of all three numbers are even
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Joined: 04 Jun 2017
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28 Mar 2018, 20:10
To determine whether the product X * Y * Z is even is to specify whether any one of those variables is even

1. X - Y is odd;
(even - odd = odd)
(odd - even = odd)
either X or Y is even --> Sufficient

2. Y * Z + X is odd;
(even + odd = odd)
(odd + even = odd)
either Y * Z or X is even --> Sufficient
Re: M23-31   [#permalink] 28 Mar 2018, 20:10
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# M23-31

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