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# If x, y, z are all integers, is xyz odd?

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Intern
Joined: 12 Oct 2017
Posts: 39
If x, y, z are all integers, is xyz odd?  [#permalink]

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22 Oct 2017, 23:56
00:00

Difficulty:

35% (medium)

Question Stats:

61% (01:03) correct 39% (00:45) wrong based on 61 sessions

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If x, y, z are all integers, is xyz odd?

(1) x - 1 is even
(2) (y - z)(x - z) is odd
Intern
Joined: 22 May 2017
Posts: 1
Re: If x, y, z are all integers, is xyz odd?  [#permalink]

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23 Oct 2017, 00:51
1
1. X-1 is even, i.e. x is odd, this is not sufficient as product of three numbers Can be odd only for odd*odd*odd

2. (Y-Z)(X-Z) is odd. Product of 2 numbers can be odd only when both are odd and difference/sum of two numbers is odd when one is even and other odd. Using this logic, there are two Cases from statement's 2:
Case 1: x odd, y odd, z even, it gives product as even
Case 2: x even, y even, z odd, it gives product as even

Therefore, statement 2 is sufficient and xyz is even

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Re: If x, y, z are all integers, is xyz odd? &nbs [#permalink] 23 Oct 2017, 00:51
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