GMAT Prep 1: PS Q22 : PS Archive
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# GMAT Prep 1: PS Q22

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Manager
Joined: 30 Aug 2007
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GMAT Prep 1: PS Q22 [#permalink]

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06 Oct 2007, 17:16
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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
VP
Joined: 10 Jun 2007
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Re: GMAT Prep 1: PS Q22 [#permalink]

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06 Oct 2007, 17:29
avenger wrote:
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

D.
Try x=1/2 for I
Try x=3/4 for II
For III, nothing will work because x^2 > 2x when x is some number greater 1. This means 1/x will be a fraction. This means it won't be greater than 2x.
VP
Joined: 10 Jun 2007
Posts: 1459
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07 Oct 2007, 08:00
A little logic for this problem.
If you know graphs well, you can easily find out the answer for this one.

Three graphs are being tested here:
y=2x
y=x^2
y=1/x

It is hard to imagine y=2x, so for the sake of it, replace y=2x with y=x. Having all these graphs, you know that all these graphs intersect at (1,1)

Therefore, the values you want to consider for x must be:
0<x<1
and
x>1

When 0<x<1, you know that 1/x > x > x^2
When x>1, you know that x^2 > x > 1/x

This hints that when x is close to 1, 2x must be greater than x^2 because of steeper slope.

This is just a good way to know which point to pick when you want to test these conditions.

Cheers.
Manager
Joined: 30 Jan 2006
Posts: 62
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07 Oct 2007, 15:24
avenger wrote:
OA is D.

Thanks

A.

The condition fails when x = 1...So i think the answer should be A (None)
07 Oct 2007, 15:24
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