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# If x is not equal to zero is xy > 0 ?

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If x is not equal to zero is xy > 0 ? [#permalink]  24 Sep 2012, 22:06
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35% (medium)

Question Stats:

60% (01:54) correct 40% (00:37) wrong based on 105 sessions
If x is not equal to zero is xy > 0 ?

(1) x >0

(2) 1/x < y
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Sep 2012, 00:22, edited 1 time in total.
Edited the question.
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Re: If x is not equal to zero is xy > 0 ? [#permalink]  24 Sep 2012, 23:04
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harikris wrote:

If x is not equal to zero is xy > 0 ?

1) x >0

2) 1/x < y

xy will be positive if x and y have the same sign. Statement 1 gives no information about y, and from Statement 2, it is possible that x and y are both positive or both negative, or that x is negative and y is positive.

Using both statements, we know x is positive, so 1/x is positive. From Statement 2, if y > 1/x, then y is greater than something positive, so y is also positive, and xy is positive, so the answer is C.
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Re: If x is not equal to zero is xy > 0 ? [#permalink]  25 Sep 2012, 00:28
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Expert's post
If x is not equal to zero is xy > 0 ?

xy will be positive if x and y have the same sign, when both are negative or both are positive.

(1) x > 0. No info about $$y$$. Not sufficient.

(2) 1/x < y. If $$x=-1$$ and $$y=1$$ then the answer is NO but if $$x=2$$ and $$y=1$$ then the answer is YES. Not sufficient.

(1)+(2) Since from (1) $$x>0$$, then $$\frac{1}{x}>0$$, hence from (2) we have that $$0<\frac{1}{x}<y$$ --> $$y>0$$. Thus both $$x$$ and $$y$$ are positive. Sufficient.

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Re: If x is not equal to zero is xy > 0 ? [#permalink]  27 Sep 2012, 11:53
Sorry but I don't understand why the answer can not be B.

B) 1/x < y This can be transformed in xy > 1. So if xy>1 it should be also true xy > 0.

Please could you tell me where I am wrong?

Thank you
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Re: If x is not equal to zero is xy > 0 ? [#permalink]  27 Sep 2012, 12:01
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Expert's post
Marcyfal wrote:
Sorry but I don't understand why the answer can not be B.

B) 1/x < y This can be transformed in xy > 1. So if xy>1 it should be also true xy > 0.

Please could you tell me where I am wrong?

Thank you

Never multiply an inequality by variable (or expression with variable) unless you know the sign of variable (or expression with variable). Because if $$x>0$$ you should write $$xy>1$$ BUT if $$x<0$$, you should write $$xy<1$$ (flip the sign when multiplying by negative expression).

Hope it helps.
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Re: If x is not equal to zero is xy > 0 ? [#permalink]  27 Sep 2012, 12:31
All right, Thank you very much. By the way I follow all your answers. You are great!
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Re: If x is not equal to zero is xy > 0 ? [#permalink]  05 Sep 2013, 23:28
Expert's post
Bumping for review and further discussion.
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Re: If x is not equal to zero is xy > 0 ?   [#permalink] 05 Sep 2013, 23:28
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