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# If x > o and the quantities

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If x > o and the quantities [#permalink]  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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Director
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Re: If x > o and the quantities [#permalink]  24 Sep 2017, 09:09
Any help on this one?
Director
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Re: If x > o and the quantities [#permalink]  24 Sep 2017, 10:34
1
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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]  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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