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# w, x, y and z are all integers. Is wxyz even?

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Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
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w, x, y and z are all integers. Is wxyz even?  [#permalink]

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05 Jun 2016, 14:23
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Difficulty:

35% (medium)

Question Stats:

69% (01:23) correct 31% (01:46) wrong based on 123 sessions

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w, x, y and z are all integers. Is wxyz even?

(1) wxy is odd.

(2) xy – z is even.
Math Expert
Joined: 02 Sep 2009
Posts: 59725
Re: w, x, y and z are all integers. Is wxyz even?  [#permalink]

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05 Jun 2016, 14:29
w, x, y and z are all integers. Is wxyz even?

(1) wxy is odd. This implies that all of them are odd. If z is even, then wxyz = even but if z is odd, wxyz = odd. Not sufficient.

(2) xy – z is even. All of them can be odd as well as even. Not sufficient.

(1)+(2) We know from (1) that x and y are odd, thus from (2) we have odd - z = even --> z = odd --> wxyz = odd. Sufficient.

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Re: w, x, y and z are all integers. Is wxyz even?   [#permalink] 05 Jun 2016, 14:29
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