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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, 01:48
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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

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

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

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12 Sep 2017, 02:02
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

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--== 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!

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

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