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

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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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76% (00:40) correct 24% (00:37) wrong based on 37 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?

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-and-yar ... 39480.html
[Reveal] Spoiler: OA

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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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30 Sep 2010, 00:57
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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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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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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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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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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

B

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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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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: If x and y are positive, is x/y greater than 1? [#permalink]

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28 Apr 2012, 21:46
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If x and y are positive, is x/y greater than 1?

(1) xy > 1
(2) x-y > 1
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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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28 Apr 2012, 22:04
1. xy=1 says nothing about which is greater, x or y.
So insufficient.
2. x-y>O i.e. X>Y
So if x and y are integars
so x/y >1 but if x is negative or y is negative.? It can be less than 1 also. So
Insufficient.
1+2
X and y are of same sign by xy>1 and x>y so sufficient.

C is right.

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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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29 Apr 2012, 05:09
If x and y are positive, is x/Y greater than 1 ?
(1) xy > 1
(2) x – y > 0

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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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29 Apr 2012, 05:15
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Expert's post
monir6000 wrote:
If x and y are integers, is x/y greater than 1 ?

(1) xy > 1
(2) x – y > 0

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

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.

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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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21 Dec 2012, 19:54
Bunuel wrote:
monir6000 wrote:
If x and y are integers, is x/y greater than 1 ?

(1) xy > 1
(2) x – y > 0

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

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.

Slight correction, even though your answer and your reasoning are correct, is that your reasoning for 2 does not address the question mentioned -- again, it's still correct, but want to make sure it talks about the question. It should be $$x-y>0$$ not $$x-y>1$$
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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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22 Dec 2012, 05:29
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Expert's post
megafan wrote:
Bunuel wrote:
monir6000 wrote:
If x and y are integers, is x/y greater than 1 ?

(1) xy > 1
(2) x – y > 0

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

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.

Slight correction, even though your answer and your reasoning are correct, is that your reasoning for 2 does not address the question mentioned -- again, it's still correct, but want to make sure it talks about the question. It should be $$x-y>0$$ not $$x-y>1$$

The question posted by monir6000 has typos. Again:

If x and y are positive, is x/y greater than 1?
(1) xy>1
(2) x-y>1
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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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17 Aug 2014, 21:14
Referring to the same question.
1) The statement is insufficient without a doubt
2) x-y>0, in case x is 7 and y is 3. But if y is -3, then the solution will be 7-(-3)=10 which is greater than 10.

But in case y is negative, then x/y, will not be greater than 1.

Need some help here - Am i missing something?

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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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18 Aug 2014, 02:58
omerqureshi wrote:
Referring to the same question.
1) The statement is insufficient without a doubt
2) x-y>0, in case x is 7 and y is 3. But if y is -3, then the solution will be 7-(-3)=10 which is greater than 10.

But in case y is negative, then x/y, will not be greater than 1.

Need some help here - Am i missing something?

The stem says: if x and y are positive...
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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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Re: If x and y are positive, is x/y greater than 1? [#permalink]

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15 Aug 2017, 09:43
If x and yare positive, is x/y greater than 1 ?

Is $$\frac{x}{y}>1$$? --> as given that $$y$$ is positive we can safely multiply both parts of the 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 > 0. Directly answers the questions. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-and-yar ... 39480.html
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Re: If x and y are positive, is x/y greater than 1?   [#permalink] 15 Aug 2017, 09:43
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