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If x > o and the quantities

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If x > o and the quantities [#permalink] New post 26 Jun 2017, 02:09
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Question Stats:

52% (01:05) correct 47% (02:18) wrong based on 19 sessions


If x > o and the quantities \(\sqrt{x}\) and \(\frac{\sqrt{x}}{x}\) are reciprocals, which of the following could be true?

Indicate all choices that apply.

❑ \(\sqrt{x}\) is greater than \(\frac{\sqrt{x}}{x}\)

❑ \(\sqrt{x}\) is less than \(\frac{\sqrt{x}}{x}\)

❑ \(\sqrt{x}\) is greater than \(x\)


[Reveal] Spoiler: OA
A,B,C
[Reveal] Spoiler: OA

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Re: If x > o and the quantities [#permalink] New post 24 Sep 2017, 09:09
Any help on this one?
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Re: If x > o and the quantities [#permalink] New post 24 Sep 2017, 10:34
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Carcass wrote:
If x > o and the quantities \(\sqrt{x}\) and \(\frac{\sqrt{x}}{x}\) are reciprocals, which of the following could be true?

Indicate all choices that apply.

❑ \(\sqrt{x}\) is greater than \(\frac{\sqrt{x}}{x}\)

❑ \(\sqrt{x}\) is less than \(\frac{\sqrt{x}}{x}\)

❑ \(\sqrt{x}\) is greater than \(x\)


[Reveal] Spoiler: OA
A,B,C



Given x>0 but it has not mentioned x is integer or fraction

Let consider x = 4

now \(\sqrt{4}\) and \(\frac{\sqrt{4}}{4}\)

or 2 > \(\frac{1}{2}\) - This staisfy 1st equation and also they are reciprocal.

Now let conside x = \(\frac{1}{4}\)

Therefore \(\sqrt{x}\) and \(\frac{\sqrt{x}}{x}\)

\(\sqrt{\frac{1}{4}}\) and \(\frac{\sqrt{\frac{1}{4}}}{\frac{1}{4}}\)

= \(\frac{1}{2}\) and \(\frac{1}{2} *4\)

= 1/2 and 2

i.e \(\frac{1}{2}\)< 2 so this satisfy the second equation i.e\(\sqrt{x}\) is less than\(\frac{\sqrt{x}}{x}\)

Now if we consider again x= 1/4

Then \(\sqrt{x}\) and \(x\)

= \(\sqrt{\frac{1}{4}}\) and \(\frac{1}{4}\)

= \(\frac{1}{2}\) > \(\frac{1}{4}\) - This satidfy our third equation.

Hence A,B,C are all correct
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Re: If x > o and the quantities [#permalink] New post 20 Feb 2018, 12:34
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IlCreatore wrote:
Any help on this one?


Do not let square root confuses you.
We are only here to to compare a number x, its reciprocal 1/x and its square x^2.
when x>1, x> 1/x
when x between 0 and 1, x<1/x and x>x^2
Re: If x > o and the quantities   [#permalink] 20 Feb 2018, 12:34
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