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If x is positive, which of the following could be the

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Manager
Joined: 27 Mar 2008
Posts: 63
If x is positive, which of the following could be the [#permalink]

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Updated on: 30 Jul 2012, 11:39
1
00:00

Difficulty:

85% (hard)

Question Stats:

34% (01:32) correct 66% (01:19) wrong based on 62 sessions

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If x is positive, which of the following could be the correct ordering of 1/x, 2x and x^2 ?

I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x

(A) None
(B) I only
(C) III only
(D) I and II only
(E) I II and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-is-posit ... 71070.html AND HERE: http://gmatclub.com/forum/if-x-is-posit ... 04082.html

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Originally posted by dishant007 on 09 Aug 2008, 18:53.
Last edited by Bunuel on 30 Jul 2012, 11:39, edited 1 time in total.
Edited the question and added the OA.
Director
Joined: 10 Sep 2007
Posts: 914

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09 Aug 2008, 21:15
3
First of all we need to see whether the possibilities are there for positive x and if they do then in what range. So below is list of possible scenarions discussed in question and the possible values for x in given inequality.

x^2 > 2x
=> x^2 - 2x > 0
=> x(x-2)>0
=> x > 2

x^2 x^2 - 2x x(x-2) x x^3 x x^2 > 1/2
=> x > 1/Sqrt(2)

1/x > 2x
=> x^2 x 2x > x^2 (possible for all x less than 1)
2) 2x > 1/x > x^2 (possible for all 1 > x > 1/Sqrt(2))
3) 1/x > x^2 > 2x (Not possible because x^2 to be greater than 2x x needs to be greater than 2 and 1/x to be greater than x^2, x should be less than 1 so contradicting values)

--== 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: Another PS   [#permalink] 09 Aug 2008, 21:15
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