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# If x > 0 and y > 0

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Intern
Joined: 22 Aug 2016
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If x > 0 and y > 0 [#permalink]  06 Jan 2017, 08:12
00:00

Question Stats:

85% (00:36) correct 14% (01:41) wrong based on 21 sessions
If $$x >$$ 0 and $$y > 0$$, which of the following os equivalent to $$\frac{x}{y}\sqrt{\frac{y}{x^2}}$$

A. $$1$$

B. $$\frac{\sqrt{x}}{\sqrt{y}}$$

C. $$\sqrt{x}$$

D. $$\frac{1}{\sqrt{x}}$$

E. $$\frac{1}{\sqrt{y}}$$
[Reveal] Spoiler: OA
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1820 [1] , given: 397

Re: If x > 0 and [#permalink]  06 Jan 2017, 16:14
1
KUDOS
Expert's post
Hey,

This question is pretty straight forward.
We have

$$\frac{x}{y}\sqrt{\frac{y}{x^2}}$$

rewritten as

$$\sqrt{\frac{x}{y}} \times \sqrt{\frac{x}{y}} \times \sqrt{\frac{y}{x}}\times\sqrt{\frac{1}{x}}$$

cancelling out $$\sqrt{\frac{x}{y}}$$ and $$\sqrt{\frac{y}{x}}$$

As x > 0 and y > 0 $$\sqrt{x}$$ and $$\sqrt{y}$$ are defined and $$\frac{x}{y}$$ and $$\frac{y}{x}$$ are also defined.

$$\sqrt{\frac{x}{y}} \times \sqrt{\frac{1}{x}}$$

cancelling out $$\sqrt{x}$$

$$\sqrt{\frac{1}{y}}$$

Hence E is the correct answer.
_________________

Sandy
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Re: If x > 0 and [#permalink]  29 Mar 2019, 06:33
1
KUDOS
Expert's post
HarveyKlaus wrote:
I got the answer right but Im not sure regarding the method I used. Any ideas how to solve this?

Thanks

Another approach is to choose some x- and y-vales to evaluate the original expression, and then see which answer choice evaluates to the same value.

For example, if x = 2 and y = 4, then $$\frac{x}{y}\sqrt{\frac{y}{x^2}}=\frac{2}{4}\sqrt{\frac{4}{2^2}}=\frac{1}{2}\sqrt{1}=\frac{1}{2}$$

So, when x = 2 and y = 4, the original expression evaluates to be 1/2
So, the CORRECT answer must also evaluate to be 1/2, when x = 2 and y = 4

Let's take each answer choice and plug in x = 2 and y = 4

A) 1
Doesn't equal 1/2
ELIMINATE

B) (√x)/(√y) = (√2)/(√4) ≈ 1.4/2
Doesn't equal 1/2
ELIMINATE

C) √x = √2 ≈ 1.4
Doesn't equal 1/2
ELIMINATE

D) 1/√x = 1/√2 ≈ 1/1.4
Doesn't equal 1/2
ELIMINATE

E) 1/√y = 1/√4 = 1/2
VOILA!!

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: If x > 0 and   [#permalink] 29 Mar 2019, 06:33
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