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

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harikris
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If x is not equal to zero is xy > 0 ? [#permalink] New post   Updated on: 25 Sep 2012, 01:22
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If x is not equal to zero is xy > 0 ?

(1) x >0

(2) 1/x < y
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C

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] New post   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.

Answer: C.
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Re: If x is not equal to zero is xy > 0 ? [#permalink] New post   25 Sep 2012, 00:04
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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   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] New post   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] New post   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] New post   19 Jan 2016, 06:36
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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

Answer: Option C
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Re: If x is not equal to zero is xy > 0 ? [#permalink] New post   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] New post   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] New post   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] New post   25 Aug 2021, 23:08
chetan2u

From 2 : \(\frac{1}{x}\) < y => \(\frac{1}{x}\)-y < 0 => \(\frac{1-xy}{x}\) < 0 => 1-xy < 0 => 1 < xy

Since xy is greater than 1, it is greater than 0. Hence sufficient,

So why the OA is E.

Kindly Help.
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Re: If x is not equal to zero is xy > 0 ? [#permalink] New post   25 Aug 2021, 23:29
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rocky620 wrote:
chetan2u

From 2 : \(\frac{1}{x}\) < y => \(\frac{1}{x}\)-y < 0 => \(\frac{1-xy}{x}\) < 0 => 1-xy < 0 => 1 < xy

Since xy is greater than 1, it is greater than 0. Hence sufficient,

So why the OA is E.

Kindly Help.



\(\frac{1-xy}{x}<0\)
This means x and 1-xy have opposite sign
If x>0, then 1-xy<0 or xy>1
If x<0, then 1-xy>0 or xy<1
So, you cannot say whether xy>1, unless you know x>0.
This is exactly what statement I tells you.
Hence, both with statements combined, we can tell that xy>1>0.

Ans is C
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Re: If x is not equal to zero is xy > 0 ? [#permalink]
25 Aug 2021, 23:29
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Bunuel
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