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

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Joined: 29 Jun 2017
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Re: If x is positive, which of the following could be correct ordering of  [#permalink]

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09 Apr 2019, 08:40
vbetanabhatla wrote:
Copied from an other forum. Thought it might help someone. This is a great explanation...

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Each one of these gives you two inequalities. You know that x is positive, so you don't need to worry about the sign changing direction.

(1) x^2<2x<1/x

This means that x^2<2x so divide by x to get x<2. The second one tells you that 2x<1/x which simplifies to x < 1/sqrt(2). These can obviously both be satisfied at the same time, so (1) works.

(2) x^2<1/x<2x

This means that x^2<1/x which gives x^3<1, or x<1. The second half gives you 1/x<2x or 1<2(x^2) or x>1/sqrt(2). So any number that satisfies 1/sqrt(2)<x<1 will work.

(3) 2x<x^2<1/x. The first part gives 2x<x^2 or x>2. The second half gives x^2<1/x or x^3<1 or x<1. Since the regions x>2 and x<1 do not overlap, (3) can not be satisfied.

The Answer choice is (4), 1 and 2 only.

above explanation is correct because x is positive. if x is any number, the problem is much more complex
Re: If x is positive, which of the following could be correct ordering of   [#permalink] 09 Apr 2019, 08:40

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