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# If x and y are positive, which of the following must be

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Senior Manager
Joined: 05 Aug 2005
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If x and y are positive, which of the following must be [#permalink]  22 Sep 2006, 21:50
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If x and y are positive, which of the following must be greater than 1/√(x+y)?
I. √(x+y)/2x,
II. (√x+√y)/(x+y)
III. (√x-√y)/(x+y)

Senior Manager
Joined: 11 May 2006
Posts: 260
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Re: DS:1/sqrt(x+y) [#permalink]  22 Sep 2006, 22:01
gmacvik wrote:
If x and y are positive, which of the following must be greater than 1/√(x+y)?
I. √(x+y)/2x,
II. (√x+√y)/(x+y)
III. (√x-√y)/(x+y)

I pick II

let x = y then we need to find which ones are greater than 1/√(2x)

now I = 1/√(2x)

II = 2√x/2x = 1/√x

III = 0
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