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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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Walkabout
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If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   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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D
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   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] New post   24 Jan 2015, 19:05
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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:
Show Spoiler
D


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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   11 Jun 2016, 06:41
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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


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] New post   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] New post   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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BrentGMATPrepNow
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If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   Updated on: 19 Jan 2020, 13:47
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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


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

Answer:
Show Spoiler
D

Originally posted by BrentGMATPrepNow on 30 Aug 2017, 14:32.
Last edited by BrentGMATPrepNow on 19 Jan 2020, 13:47, edited 1 time in total.
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   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] New post   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] New post   15 Oct 2019, 23:24
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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] New post   22 Oct 2019, 22:10
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Solution


Given:
    • s > 0
    • \((\frac{r}{s})^{1/2} = s\)

To find:
    • r in terms of s

Approach and Working Out:
    • \(\frac{r}{s} = s^2\)

Therefore, \(r = s^3\)

Hence, the correct answer is Option D.

Answer: D
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If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   11 Mar 2021, 23:04
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


EducationAisle

we are told that \(s > 0\) but is this information really needed? we are already given that \(\sqrt{\frac{r}{s}}=s\) which means that s is non-zero. Now whether s is -ve or +ve really doesn't matter right
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   11 Mar 2021, 23:21
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Hi Hoozan,

Neither undefined numbers (re: dividing by 0) nor imaginary numbers (re: square-root of a negative number) are subjects that are explicitly 'tested' by the GMAT, so including the information here that S > 0 is essentially 'math legalese' to keep a Test-taker from arguing that this question is unfair because an undefined number or imaginary numbers are possible.

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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink] New post   18 May 2023, 22:32
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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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