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If x, y and z are integers and xy + z is an odd integer, is

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If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 28 Jul 2009, 22:25
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If x, y and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer
(2) y + xz is an odd integer
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Mar 2013, 02:10, edited 1 time in total.
Edited the question and added the OA.
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Re: DS - Is x even? [#permalink] New post 28 Jul 2009, 23:14
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IMO A

1. xy + xz is an even integer - SUFFICIENT
Given:
xy + z is odd ...(i)
xy + xz is even ...(ii)

subtracting (ii) from (i)
we get xz - z, which should be odd (* since odd - even = odd)
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd ...(i)
y + xz is odd ...(ii)

subtracting (ii) from (i)
we get xy + z - y - xz
= (x-1)(y-z) , which should be even
=> either (x-1) is even or (y-z) is even ....insufficient to determine
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Re: DS - Is x even? [#permalink] New post 29 Jul 2009, 04:00
great explanation bigoyal...+1 kudos from my side...:)
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Re: If x,y and z are integers and xy + z is an odd integer, is x [#permalink] New post 06 Mar 2013, 21:55
This question took forever to solve great strategy. Plugging numbers won't work all the time.
Re: If x,y and z are integers and xy + z is an odd integer, is x   [#permalink] 06 Mar 2013, 21:55
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