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If r and s are positive integers, is (r/s) an integer?

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Senior Manager
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Joined: 10 Mar 2008
Posts: 333
If r and s are positive integers, is (r/s) an integer? [#permalink]

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New post 22 Sep 2008, 12:03
00:00
A
B
C
D
E

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Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

Please show your workings

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
VP
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Joined: 17 Jun 2008
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Re: DS [#permalink]

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New post 22 Sep 2008, 12:54
what the question is asking is whether 0<xy<1

From stmt1: x^2 = 3/14, hence x = sqrt(3/14), -sqrt(3/14).

From stmt2: y = 1, -1

Combining stmt1 and 2, xy = sqrt(3/14), -sqrt(3/14). Hence, not sufficient.

Hence, E.
Senior Manager
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Re: DS [#permalink]

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New post 23 Sep 2008, 10:39
I was able to successfully solve this problem by plugging numbers. But, I'm looking to learn faster ways of solving such problems.

Could you please explain as to how you came to the conclusion that the question is essentially asking: 0<xy<1. Thanks
Intern
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Schools: Chicago Booth, Wharton, MIT, Haas
Re: DS [#permalink]

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New post 23 Sep 2008, 16:06
The inequality reduces to :
x^2y^2 - xy < 0
or xy(xy-1) < 0

This implies 0<xy<1
But instead of trying to derive this for the GMAT, you should probably remember that x^2<x implies 0<x<1
SVP
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Re: DS [#permalink]

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New post 23 Sep 2008, 18:20
icandy wrote:
Please underline SC questions.

Please Do not post OA along with the Q.

Give and take Kudos.





in addition to that, most importattly, mention the source of the question.
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Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


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VP
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Re: DS [#permalink]

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New post 23 Sep 2008, 19:48
GMAT TIGER wrote:
icandy wrote:
Please underline SC questions.

Please Do not post OA along with the Q.

Give and take Kudos.





in addition to that, most importattly, mention the source of the question.



If you were just making a point, thats fine. if you were thinking that I posted the Q, that was not me. I was annoyed with people posting OA along with Q and not underlining the SC Q. Thats how it came out.
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Re: DS [#permalink]

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New post 23 Sep 2008, 22:19
icandy wrote:
GMAT TIGER wrote:
icandy wrote:
Please underline SC questions.

Please Do not post OA along with the Q.

Give and take Kudos.





in addition to that, most importattly, mention the source of the question.



If you were just making a point, thats fine. if you were thinking that I posted the Q, that was not me. I was annoyed with people posting OA along with Q and not underlining the SC Q. Thats how it came out.


all your signature lines make sense. if you add "Always mention the source of the question" in your signature line, your signature lines would be a summary of gmat club forum etiquette. :lol:
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

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Re: DS [#permalink]

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New post 26 Sep 2008, 12:03
If we combine the 2 statements we have to prove that xy > 3/14.

Possible values of x are +/- (3/14)^1/2 and that of y are +/- 1

For all combinations of xy we get xy < 3/14

The ans is therefore C

Please correct me if I am wrong

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS   [#permalink] 26 Sep 2008, 12:03
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If r and s are positive integers, is (r/s) an integer?

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