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

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Joined: 12 Jul 2012
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If x is not equal to zero is xy > 0 ?  [#permalink]

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Updated on: 25 Sep 2012, 01:22
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Difficulty:

35% (medium)

Question Stats:

63% (00:54) correct 37% (00:42) wrong based on 263 sessions

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

(1) x >0

(2) 1/x < y

Originally posted by harikris on 24 Sep 2012, 23:06.
Last edited by Bunuel on 25 Sep 2012, 01:22, edited 1 time in total.
Edited the question.
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Re: If x is not equal to zero is xy > 0 ?  [#permalink]

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25 Sep 2012, 00:04
1
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]

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25 Sep 2012, 01:28
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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.

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Re: If x is not equal to zero is xy > 0 ?  [#permalink]

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27 Sep 2012, 12:53
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]

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27 Sep 2012, 13:01
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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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Re: If x is not equal to zero is xy > 0 ?  [#permalink]

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27 Sep 2012, 13:31
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]

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19 Jan 2016, 06:36
1
harikris wrote:
If x is not equal to zero is xy > 0 ?

(1) x >0

(2) 1/x < y

Question : Is xy > 0?

Statement 1: x>0
i.e. x is positive but we have no information about y being positive or Negtive, Hence
NOT SUFFICIENT

Statement 2: 1/x<y
This relation will be true for x=-1 and y=2 i.e. xy<0
or x= 1 and y = 2 i.e. xy>0
NOT SUFFICIENT

Combining the two statements
x is positive and y>1/x i.e. y too is positive
hence, xy>0
SUFFICIENT

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Re: If x is not equal to zero is xy > 0 ?  [#permalink]

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20 Jan 2016, 10:37
hi bunuel,

Cant we write the option B as y>1/x= (x-y)/x>0 and if you put both the statements together and try few values as mentioned below it is satisfying for neg/pos value of Y.

X=10 Y=8 and X=10 and Y=-8 in both cases above equation holds.

Kindly explain!! Thanks
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Re: If x is not equal to zero is xy > 0 ?  [#permalink]

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20 Jan 2016, 10:44
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rocky1988 wrote:
hi bunuel,

Cant we write the option B as y>1/x= (x-y)/x>0 and if you put both the statements together and try few values as mentioned below it is satisfying for neg/pos value of Y.

X=10 Y=8 and X=10 and Y=-8in both cases above equation holds.

Kindly explain!! Thanks

y is NOT greater than 1/x as per highlighted set of values so they can't be taken as they violate the information os Second statement.

I hope this helps
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Re: If x is not equal to zero is xy > 0 ?  [#permalink]

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20 Jan 2016, 11:02
rocky1988 wrote:
hi bunuel,

Cant we write the option B as y>1/x= (x-y)/x>0and if you put both the statements together and try few values as mentioned below it is satisfying for neg/pos value of Y.

X=10 Y=8 and X=10 and Y=-8 in both cases above equation holds.

Kindly explain!! Thanks

You can not perform the calculations you have mentioned above.

y>1/x $$\neq$$ (x-y)/x>0

You can although, rewrite statement 2 as y-1/x > 0 --->(xy-1)/x>0 and as x>0 ---> for this fraction to be >0 --> xy-1>0 ---> xy>1 . Again, 2 cases possible, x>0 and y>0 and x<0 and y<0. Thus this statement is NOT sufficient.
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Re: If x is not equal to zero is xy > 0 ?  [#permalink]

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03 Oct 2017, 04:46
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