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# If Z is a factor of Y , XZ even? (1) The multiple of any two

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Manager
Joined: 14 May 2009
Posts: 189
If Z is a factor of Y , XZ even? (1) The multiple of any two [#permalink]

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03 Jun 2009, 00:32
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If $$Z$$ is a factor of $$Y$$, $$XZ$$ even?

(1) The multiple of any two factors of $$X$$ or $$Y$$ is odd.

(2) $$\frac{XY}{Z}$$ is odd.
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Senior Manager
Joined: 15 Jan 2008
Posts: 269

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03 Jun 2009, 01:24

1, insufficient.. doesnt say anthing abt Z, just says taht X and Y are odd numbers..
2, insuffficient..

XY is even and Z is odd... XZ depends on X .. can be odd or even..
XY is odd and Z is is odd.. XZ is odd ..

Combined..

X and Y are odd numbers... and Z is odd number.. hence XZ is odd..
SVP
Joined: 28 Dec 2005
Posts: 1500

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03 Jun 2009, 08:20
Really ? I got C as well

With statement 2, Y/Z perfectly divide each other, and for the result when multiplied by X to be odd, X must be odd as well. But I dont know anything about Z ... Y/Z is odd and that could happen if Z is even (i.e. 6/2 = 3, or if Z is odd 9/3=3)

From statement 1, we can conclude that X and Y are odd, but nothing about Z

Together, X is odd, Y is odd, and since Y/Z=odd (from statement 2), I concluded that Z is odd as well. Hmmm....
Manager
Joined: 14 May 2009
Posts: 189

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03 Jun 2009, 16:05
If $$Z$$ is a factor of $$Y$$, $$XZ$$ even?

(1) The multiple of any two factors of $$X$$ or $$Y$$ is odd.

(2) $$\frac{XY}{Z}$$ is odd.

Question:$$(XZ$$ even?$$)$$

(1) The multiple of any two factors of $$X$$ or $$Y$$ is odd.

$$\longrightarrow$$ X & Y are odd

$$Y$$ odd $$\longrightarrow Z$$ odd

$$XZ = ODD*ODD = ODD$$

$$\longrightarrow$$ SUFFICIENT

(2) $$\frac{XY}{Z}$$

$$\longrightarrow X$$ odd & $$\frac{Y}{Z}$$ odd

But $$Y=MZ$$ where $$M$$ is any integer

So $$\frac{Y}{Z}$$ odd $$\longrightarrow$$ $$\frac{MZ}{Z}$$ odd

$$\longrightarrow M$$ odd

And doesn't tell you anything about $$Z$$, hence $$Z$$ can be ODD or EVEN.

Insufficient.

Final Answer, $$A$$.
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Senior Manager
Joined: 15 Jan 2008
Posts: 269

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03 Jun 2009, 22:58

I missed out on a simple statement that..

when X is a factor of Y, and when Y is odd, then X must be ODD...

good one..
Re: Tough DS 7   [#permalink] 03 Jun 2009, 22:58
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