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# If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?

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If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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12 Dec 2012, 08:32
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If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s
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Posts: 59095
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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12 Dec 2012, 08:33
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Walkabout wrote:
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

$$\sqrt{\frac{r}{s}}=s$$ --> $$\frac{r}{s}=s^2$$ --> $$r=s^3$$.

Answer: D.
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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24 Jan 2015, 19:05
Hi All,

This question can be solved by TESTing VALUES. The key is to keep the values relatively small and think about how the square root sign impacts the math:

We're told that S > 0 and (r/s)^1/2=s

We're asked for the value of R.

IF....
R = 8
S = 2
\sqrt{4} = 2

So we're looking for an answer that = 8 when S = 2....

Answer A: 1/2 NOT a match
Answer B: \sqrt{2} NOT a match
Answer C: 2\sqrt{2} NOT a match
Answer D: 2^3 = 8 This IS a MATCH
Answer E: 2^2 - 2 = 2 NOT a match

Final Answer:

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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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11 Jun 2016, 06:41
Walkabout wrote:
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

To solve, we need to simplify the equation √(r/s) = s.

We first want to eliminate the square root, so we square both sides, obtaining:

(√(r/s))^2 = s^2

r/s = s^2

To isolate r, we multiply the entire equation by s and we get:

r = s^3

The answer is D.
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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12 Jun 2016, 05:10
Walkabout wrote:
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

An alternate method will be testing the options , except (D) none follows -

$$\sqrt{\frac{s^3}{s}}=\sqrt{s^2}$$ = $$s$$
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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25 Mar 2017, 11:49
let's pick smart numbers and solve: let s be 3, then r is 27
if we test the answers D is the only that works
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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30 Aug 2017, 14:32
Top Contributor
Walkabout wrote:
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

Let's test some values that satisfy the given equation √(r/s) = s

For example, r = 125 and s = 5 satisfies the equation √(r/s) = s

What is r in terms of s ?
Check the answer choices to see which one yields 125 when s = 5

(A) 1/5125 ELIMINATE
(B) √5125 ELIMINATE
(C) 55125 ELIMINATE
(D) 5^3 = 125 KEEP!!
(E) 5^2 - 5125 ELIMINATE

Answer:

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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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15 Sep 2019, 00:23
Walkabout wrote:
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

Given: s > 0 and $$\sqrt{\frac{r}{s}}=s$$

Asked: What is r in terms of s ?

$$\sqrt{\frac{r}{s}}=s$$
Squaring both sides
r/s = s^2
r = s^3

IMO D
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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15 Oct 2019, 23:16
While squaring both sides why we did not consider the negative value of r?
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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15 Oct 2019, 23:24
1
chayon222 wrote:
While squaring both sides why we did not consider the negative value of r?

What do you mean by that? How do you think that should have been considered?

Anyway, since s is positive and r/s is under the square root, then r must also be positive, because if r is negative, then r/s would also be negative and even roots (such as the square root) from negative numbers are not defined on the GMAT. All numbers on the GMAT are real numbers by default.
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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22 Oct 2019, 22:10
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?   [#permalink] 22 Oct 2019, 22:10
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# If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?

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