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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: 64

Kudos [?]: 10 [6], given: 0

If x is positive, which of the following could be the [#permalink]

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09 Aug 2008, 18:53
6
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2
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Difficulty:

85% (hard)

Question Stats:

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

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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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: if-x-is-positive-which-of-the-following-could-be-correct-71070.html AND HERE: if-x-is-positive-which-of-the-following-could-be-the-104082.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jul 2012, 11:39, edited 1 time in total.
Edited the question and added the OA.

Kudos [?]: 10 [6], given: 0

Director
Joined: 10 Sep 2007
Posts: 934

Kudos [?]: 338 [8], given: 0

Re: Another PS [#permalink]

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09 Aug 2008, 21:15
8
KUDOS
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 < 2x
=> x^2 - 2x < 0
=> x(x-2)<0
=> x < 2

x^2 < 1/x
=> x^3 < 1
=> x < 1

1/x < 2x
=> x^2 > 1/2
=> x > 1/Sqrt(2)

1/x > 2x
=> x^2 < 1/2
=> x < 1/Sqrt(2)

1) 1/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)

Kudos [?]: 338 [8], given: 0

Re: Another PS   [#permalink] 09 Aug 2008, 21:15
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# If x is positive, which of the following could be the

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