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# If x and y are positive, is x/y greater than 1?

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Manager
Status: GMAT Preperation
Joined: 04 Feb 2010
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If x and y are positive, is x/y greater than 1? [#permalink]

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30 Sep 2010, 00:49
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Difficulty:

35% (medium)

Question Stats:

75% (01:31) correct 25% (00:56) wrong based on 20 sessions

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If x and y are positive, is x/y greater than 1?

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

My question if x and y are both positive, shouldnt x/y always be positive?
[Reveal] Spoiler: OA
Ms. Big Fat Panda
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30 Sep 2010, 00:57
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Expert's post
vanidhar wrote:
If x and y are positive, is x/y greater than 1?

1)xy > 1
2)x-y > 1

My question if x and y are both positive, shouldnt x/y always be positive?

To answer your question: Yes. $$\frac{x}{y}$$ will always be positive. But being positive could also mean numbers between 0 and 1.

Statement 1 says xy>1. NO information about $$\frac{x}{y}$$. Insufficient.

Statement 2:

x - y > 1

Divide by y on both sides

$$\frac{x}{y}$$ - 1 > $$\frac{1}{y}$$

$$\frac{x}{y}$$ > 1 + $$\frac{1}{y}$$

But. y is a positive integer so $$\frac{1}{y}$$ > 0 which means that $$\frac{x}{y}$$ > 1.

B.
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30 Sep 2010, 01:15
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Expert's post
vanidhar wrote:
If x and y are positive, is x/y greater than 1?

1)xy > 1
2)x-y > 1

My question if x and y are both positive, shouldnt x/y always be positive?

Is $$\frac{x}{y}>1$$? --> as given that $$y$$ is positive we can safely multiply boith parts of inequality by it --> so the question becomes "is $$x>y$$?" OR: is $$x-y>0$$?

(1) $$xy>1$$ --> product of two numbers is more than one we can't say which one is greater. Not sufficient.

(2) $$x-y>1$$ --> $$x>y+1$$ --> as $$x$$ is more than $$y$$ plus 1 then it's obviously more than just $$y$$ alone: $$x>y$$. Sufficient.
Or: as $$x-y>1$$ then $$x-y$$ is obviously more than zero --> $$x-y>1>0$$. Sufficient.

As for your question: yes, if $$x$$ and $$y$$ are both positive (or both negative) then $$\frac{x}{y}>0$$.

Hope it helps.
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30 Sep 2010, 10:14
[quote="vanidhar"]If x and y are positive, is x/y greater than 1?

1)xy > 1
2)x-y > 1

x,y +ve , is x/y > 1 ie is x>y

from 1

insuff

from 2

suff

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30 Sep 2010, 15:08
Bunuel wrote:

(2) $$x-y>1$$ --> $$x>y+1$$ --> as $$x$$ is more than $$y$$ plus 1 then it's obviously more than just $$y$$ alone: $$x>y$$. Sufficient.

Hope it helps.

Nice approach, I didn't went with this approach, but good to know.
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Re: DS question   [#permalink] 30 Sep 2010, 15:08
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