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# If X and Y are positive, is x/y +y/x >2 ? 1. X does not

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If X and Y are positive, is x/y +y/x >2 ? 1. X does not [#permalink]  14 May 2008, 01:06
If X and Y are positive, is x/y +y/x >2 ?

1. X does not equal Y
2.X and Y are integers which do not have common divisors except 1
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Re: M12-16 [#permalink]  14 May 2008, 02:06
farend wrote:
A)

What do you think about B Farend? I think the way B is wording is the same as A!
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Re: M12-16 [#permalink]  14 May 2008, 02:35
sondenso wrote:
farend wrote:
A)

What do you think about B Farend? I think the way B is wording is the same as A!

sondenso - with B we can still have 1 and 1 for x and y which will not satisfy
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Re: M12-16 [#permalink]  14 May 2008, 02:47
I think "1" is only in common, this make x and y different, do you think so? otherwise, I am wrong!
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Re: M12-16 [#permalink]  14 May 2008, 04:00
I got D.

Statement 2 is the another rendition of statement 1. Essentially, if the two number have no divisors in common except 1, they are two unique numbers (say 2,3 or 2,9).
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Re: M12-16 [#permalink]  14 May 2008, 04:27
D for me as well..

1) x and y are different.. x>0 y>0 sufficient try any number sum>2
2) GCD=1..tells me that x and Y are different either odd or even or different primes...sufficient
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Re: M12-16 [#permalink]  14 May 2008, 07:20
In the question -
Stt2: X and Y are integers which do not have common divisors except 1
Since,
1 and 1 are integers which do not have common divisors except 1
So, this will be insufficient.

IMO - D
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Re: M12-16 [#permalink]  15 May 2008, 20:00
dushver, fresinha12, anirudhoswal, I got D too, I think Statement 2 is the same meaning as statement1.

Unfortunately, OA is A. God! I think there something wrong with OA!
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Re: M12-16 [#permalink]  16 May 2008, 19:16
fresinha12 wrote:
whats the OE?

When X and Y are different, x/y + y/x is always bigger than 2. This is because (x-y)^2 >0 , from where x^2 + y^2 > 2xy . After dividing by XY we get x/y + y/x >2 .

S_2 alone is not sufficient. The answer is NO if X = Y = 1.
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Re: M12-16   [#permalink] 16 May 2008, 19:16
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