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Is x/y>0? 1) x-y>0 2) xy>0

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Math Revolution GMAT Instructor
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Is x/y>0? 1) x-y>0 2) xy>0 [#permalink]

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New post 13 Sep 2017, 00:16
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[GMAT math practice question]

Is \(\frac{x}{y}>0\)?

1) \(x-y>0\)
2) \(xy>0\)

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Re: Is x/y>0? 1) x-y>0 2) xy>0 [#permalink]

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New post 13 Sep 2017, 00:52
1
MathRevolution wrote:
[GMAT math practice question]

Is \(\frac{x}{y}>0\)?

1) \(x-y>0\)
2) \(xy>0\)


1) \(x-y>0\) -> x>y, but y may be negative, so it could be the case that \(\frac{x}{y}<0\).
2) \(xy>0\) -> both are larger than 0, therefore their division would be larger than 0. Sufficient.

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Re: Is x/y>0? 1) x-y>0 2) xy>0 [#permalink]

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New post 13 Sep 2017, 01:23
1
MathRevolution wrote:
[GMAT math practice question]

Is \(\frac{x}{y}>0\)?

1) \(x-y>0\)
2) \(xy>0\)



Case 1: Take y=-4 , x=0
While x-y >0 but the x/y =0
So not sufficient

Case 2: Since xy>0
So , x and y should be either both positive or both negative
this gives a definite ans to the question , that is , x/y is always positive
Hence Sufficient

Ans :B
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Re: Is x/y>0? 1) x-y>0 2) xy>0 [#permalink]

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New post 13 Sep 2017, 04:14
MathRevolution wrote:
[GMAT math practice question]

Is \(\frac{x}{y}>0\)?

1) \(x-y>0\)
2) \(xy>0\)



Hi...

x/y>0 will be ONLY when both x and y are of same sign otherwise it is NO..

1) x-y>0..
both POSITIVE 3-2>0..... Ans YES
y NEGATIVE but x POSITIVE..y=-2, x=2.... Ans NO
Insufficient
2) xy>0..
Possible only when both x and y are of same sign..
Always YES
Sufficient

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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Re: Is x/y>0? 1) x-y>0 2) xy>0 [#permalink]

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New post 15 Sep 2017, 01:58
=>

The question x/y>0 is equivalent to xy > 0 after multiplying both sides of the inequality by y^2. It is equivalent to the condition 2).

Ans: B
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Re: Is x/y>0? 1) x-y>0 2) xy>0   [#permalink] 15 Sep 2017, 01:58
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