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# If xy > 0, is xyz < 0?

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Re: If xy > 0, is xyz < 0? [#permalink]

Quote:
If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

Is it appropriate to combine two statements
as:
xy $$z^2$$ > 0

I incorrectly chose (C) here

Even if you combine the two statements you cannot arrive at xyz<0.

It is given that xy>0, so you simply need to know whether z<0 and on combining you will not get this information

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Re: If xy > 0, is xyz < 0? [#permalink]

Quote:
If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

Is it appropriate to combine two statements
as:
xy $$z^2$$ > 0

I incorrectly chose (C) here

So when you get xyz^2>0, it just tells you xy>0..
But if all three are negative..xyz^2 will be >0 but xyz<0..
However if all three are positive..xyz^2 will be >0 and xyz>0
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Re: If xy > 0, is xyz < 0? [#permalink]
Bunuel wrote:
If xy > 0, is xyz < 0?

(1) xz > 0
(2) yz > 0

xy > 0 -> x and y have same signs

(1) xz > 0 -> x and z have same signs -> x, y, z have same signs. If all 3 variables are negative -> Yes. If all 3 variables are positive -> No. --> Not sufficient.
(2) yz > 0 -> y and z have same signs -> x, y, z have same signs. If all 3 variables are negative -> Yes. If all 3 variables are positive -> No. --> Not sufficient.
(1)+(2) x, y, z have same signs -> Not sufficient.

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Re: If xy > 0, is xyz < 0? [#permalink]
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Re: If xy > 0, is xyz < 0? [#permalink]
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