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# GmatPrep PS Question

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Manager
Joined: 26 Jun 2007
Posts: 104

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02 Feb 2009, 11:46
00:00

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0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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Is there a way to solve it less than 3 minutes?

** My apologies for not typing the question for future searches - don't you just hate all those signs? :wink: **

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SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York

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02 Feb 2009, 12:36
GGUY wrote:
Is there a way to solve it less than 3 minutes?

** My apologies for not typing the question for future searches - don't you just hate all those signs? **

assume x=y=1 you can eliminate option I and III right away.

To find Option III

$$1/sqrt{x+y}=sqrt{x+y}/{x+y}$$
option III = $$sqrt{x}+sqrt{y}/{x+y}$$

Need to find out $$sqrt{x}+sqrt{y} > sqrt{x+y}$$

-- > square on both sides
--> $$x+y+2*sqrt{xy} > x+y$$
this is always true
so Square root of these also true

Fortunately I could solve within 3 minutes.. but will see if this answer match with OA or not.

C
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Intern
Joined: 25 Jan 2009
Posts: 3

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02 Feb 2009, 12:49
(1) rewrite $$\frac{1}{sqrt{x+y}}$$ = $$\frac{1}{sqrt{x+y}}.\frac{sqrt{x+y}}{sqrt{x+y}}$$= $$\frac{sqrt{x+y}}{x+y}$$

(2) You do not know whether $$2x > x + y$$ because $$y$$ could be $$> x$$ , so that leaves with II and III

(3) To test II and III check whether $$sqrt{x}+sqrt{y} > sqrt{x+y}$$

$$sqrt{x}+{sqrt{y} > {sqrt{x+y}$$
$$(sqrt{x}+{sqrt{y})^2 > ({sqrt{x+y})^2$$
$$x+2{sqrt{xy} + y > x+y$$

So the left side is greater than the right side, which makes option II valid only (in option III the left side would be less than the right side)

I think doable in 2min, but hope it's right!

--== 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: GmatPrep PS Question &nbs [#permalink] 02 Feb 2009, 12:49
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