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GMAT Prep even odd

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GMAT Prep even odd [#permalink] New post 01 Jan 2007, 21:20
Could some one explain this please
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Re: GMAT Prep even odd [#permalink] New post 01 Jan 2007, 21:32
jainan24 wrote:
Could some one explain this please


D it is.

Stmt 1) If XZ is even then there are two possibilities EE or EO.
In both cases, for XZ to become even Z must be even.
So sufficient.

Stmt 2) If y is even then Z must be even.
Sufficient.
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 [#permalink] New post 01 Jan 2007, 22:46
thanks, I should have used the factor information in better way
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 [#permalink] New post 02 Jan 2007, 14:44
I go for D

Given, x, y and z are integers such that, x is a factor of y, and y is a factor of z.

This means than x is also a factor of z. Since z contains all factors y.

1. xz is even - If we assume that z is odd, than x has to be odd. since an odd integer cannot have a even divisor. In such case xz will be odd. There for for xz to be even z has to be even.

2. y is even - Since y is a factor of z and an odd integer cannot have an even factor, z has to be even.
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 [#permalink] New post 03 Jan 2007, 14:52
(1) xz even =>
x even & z even
OR
x odd & z even
OR
x even & z odd (impossible; if x even then y and z even).
Therefore: Suff.

(2) y even => z even, right away. Suff.

D.
  [#permalink] 03 Jan 2007, 14:52
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