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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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If r and s are positive integers, is (r/s) an integer? [#permalink]  22 Sep 2008, 11:03
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Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

SVP
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Re: DS [#permalink]  22 Sep 2008, 11:54
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.
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Re: DS [#permalink]  23 Sep 2008, 09:39
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
Joined: 17 Sep 2008
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Schools: Chicago Booth, Wharton, MIT, Haas
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Re: DS [#permalink]  23 Sep 2008, 15:06
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
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Re: DS [#permalink]  23 Sep 2008, 17:20
icandy wrote:

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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Re: DS [#permalink]  23 Sep 2008, 18:48
GMAT TIGER wrote:
icandy wrote:

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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Kudos [?]: 576 [0], given: 19

Re: DS [#permalink]  23 Sep 2008, 21:19
icandy wrote:
GMAT TIGER wrote:
icandy wrote:

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.
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Re: DS [#permalink]  26 Sep 2008, 11:03
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
Re: DS   [#permalink] 26 Sep 2008, 11:03
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