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# If x > 0 and y > 0, which of the following is equivalent to x/y*(y/x)

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Math Expert
Joined: 02 Sep 2009
Posts: 49272
If x > 0 and y > 0, which of the following is equivalent to x/y*(y/x)  [#permalink]

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26 Jun 2018, 05:32
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15% (low)

Question Stats:

81% (00:57) correct 19% (01:07) wrong based on 63 sessions

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If $$x > 0$$ and $$y > 0$$, which of the following is 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) $$\frac{1}{\sqrt{y}}$$

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Posts: 6792
Re: If x > 0 and y > 0, which of the following is equivalent to x/y*(y/x)  [#permalink]

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26 Jun 2018, 05:44
1
Bunuel wrote:
If $$x > 0$$ and $$y > 0$$, which of the following is 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) $$\frac{1}{\sqrt{y}}$$

Two ways..
1) substitute some values..
Take y as a square so let it be 4 and x =5
So $$\frac{x}{y} \sqrt{\frac{y}{x^2}}$$= $$\frac{5}{4} \sqrt{\frac{4}{5^2}}$$=2/4=1/2..
Check the choices which gives you 1/2
Only E
2) algebraic expressions..
$$\frac{X}{y}\sqrt{y/x^2}=X/y * √y/X=\frac{√y}{y}=1/√y$$

E
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Re: If x > 0 and y > 0, which of the following is equivalent to x/y*(y/x)  [#permalink]

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26 Jun 2018, 07:05

Solution

Given:
• x > 0 and y > 0

To find:
• The value of the expression $$\frac{x}{y} \sqrt{\frac{y}{x^2}}$$

Approach and Working:
We can rewrite the expression, in terms of the powers of the variables, as:
• $$\frac{x}{y} \sqrt{\frac{y}{x^2}}$$
= $$x^1 * y^{-1} * y^{0.5} * x^{-2 * 0.5}$$
= $$x^{1-1} * y^{-1+0.5}$$
= $$x^0 * y^{-0.5}$$
= $$\frac{1}{\sqrt{y}}$$

Hence, the correct answer is option E.

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Re: If x > 0 and y > 0, which of the following is equivalent to x/y*(y/x) &nbs [#permalink] 26 Jun 2018, 07:05
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