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# If x is positive, which of the following could be the correct ordering

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

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12 Sep 2017, 00:48
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If x is positive, which of the following could be the correct ordering of $$\frac{1}{x}, x^{2}, 2x$$

I. $$x^{2}<2x<\frac{1}{x}$$
II. $$x^{2}<\frac{1}{x}<2x$$
III. $$2x<x^{2}<\frac{1}{x}$$

A. None
B. I only
C. III only
D. I and II only
E. I, II and III
[Reveal] Spoiler: OA

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Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com

Kudos [?]: 32 [0], given: 13

Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 73

Kudos [?]: 32 [0], given: 13

GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: If x is positive, which of the following could be the correct ordering [#permalink]

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12 Sep 2017, 01:01
When dealing with all types of real numbers, be cautious of range -1<x<1.
In this case taking x = 3
$$x^{2}$$ = 9
$$\frac{1}{x}$$ = 0.33
$$2x$$ = 6
Thus option A and option C can be eliminated.
Taking x = 0.9
$$x^{2}$$ = 0.81
$$\frac{1}{x}= \frac{10}{9}$$ = 1.11
$$2x$$ = 1.8
Thus option B can be eliminated
Now any other value can not form III true, as squaring any value can be more than 2x only if x >1 (in this case x is positive given) and is x >1 then $$\frac{1}{x}$$ can not be greater than x
Thus option E is eliminated
Thus option D is the answer
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Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com

Kudos [?]: 32 [0], given: 13

Math Expert
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135988 [0], given: 12719

Re: If x is positive, which of the following could be the correct ordering [#permalink]

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12 Sep 2017, 01:02
HolaMaven wrote:
If x is positive, which of the following could be the correct ordering of $$\frac{1}{x}, x^{2}, 2x$$

I. $$x^{2}<2x<\frac{1}{x}$$
II. $$x^{2}<\frac{1}{x}<2x$$
III. $$2x<x^{2}<\frac{1}{x}$$

A. None
B. I only
C. III only
D. I and II only
E. I, II and III

Discussed here: https://gmatclub.com/forum/if-x-is-posi ... 71070.html Please search before posting. Thank you.

Topic is locked and archived.
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Kudos [?]: 135988 [0], given: 12719

Re: If x is positive, which of the following could be the correct ordering   [#permalink] 12 Sep 2017, 01:02
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