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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] New post 24 Sep 2012, 22:06
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A
B
C
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60% (01:53) correct 40% (00:39) wrong based on 109 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] New post 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] New post 25 Sep 2012, 00:28
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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.

Answer: C.
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Re: If x is not equal to zero is xy > 0 ? [#permalink] New post 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] New post 27 Sep 2012, 12:01
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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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COLLECTION OF QUESTIONS:
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Re: If x is not equal to zero is xy > 0 ? [#permalink] New post 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] New post 05 Sep 2013, 23:28
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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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