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If x > o and the quantities
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26 Jun 2017, 02:09

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Question Stats:

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 \(x\)

Re: If x > o and the quantities
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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 \(x\)

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 \(x\)

Show: :: 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

Re: If x > o and the quantities
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20 Feb 2018, 12:34

1

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]
14 Dec 2018, 19:04

1

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 \(x\)

Show: :: OA

A,B,C

Aren't sqrt(x) and sqrt(x)/x naturally reciprocals, is that information just to throw you off? So confused.

The reciprocal of sqrt(x)/x is x/sqrt(x), which, when rationalized by multiplying by sqrt(x)/sqrt(x) is equal to sqrt(x). What is the purpose of that information being given? I suspect there is no purpose but to throw you off.

If x > o and the quantities
[#permalink]
20 Aug 2021, 08:23

By choosing x=1, I am not violating any of the conditions i.e:

x > 0

and the reciprocity.

Then all the options given do not hold since 1 = 1 for all cases?

So, how can we conclude that the answers are A,B,C?

x > 0

and the reciprocity.

Then all the options given do not hold since 1 = 1 for all cases?

So, how can we conclude that the answers are A,B,C?

Re: If x > o and the quantities
[#permalink]
20 Aug 2021, 08:58

1

Hey,

You are right but read the stem again. If \(x > 0\) ... which of the following could be true?

Every possible option will be an answer.

You are right but read the stem again. If \(x > 0\) ... which of the following could be true?

Every possible option will be an answer.

saeedrashid00 wrote:

By choosing x=1, I am not violating any of the conditions i.e:

x > 0

and the reciprocity.

Then all the options given do not hold since 1 = 1 for all cases?

So, how can we conclude that the answers are A,B,C?

x > 0

and the reciprocity.

Then all the options given do not hold since 1 = 1 for all cases?

So, how can we conclude that the answers are A,B,C?

Re: If x > o and the quantities
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28 Jul 2024, 04:37

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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Re: If x > o and the quantities [#permalink]

28 Jul 2024, 04:37
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