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Manager  Joined: 02 Dec 2012
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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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11 00:00

Difficulty:   5% (low)

Question Stats: 93% (00:40) correct 7% (01:12) wrong based on 1667 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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3
1
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

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

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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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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

GMAT assassins aren't born, they're made,
Rich
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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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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

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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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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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Manager  S
Joined: 03 Jan 2017
Posts: 132
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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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
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4226
If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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Top Contributor
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

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Originally posted by GMATPrepNow on 30 Aug 2017, 14:32.
Last edited by GMATPrepNow on 19 Jan 2020, 13:47, edited 1 time in total.
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GMAT 1: 690 Q50 V34 Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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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

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
Intern  B
Joined: 01 Sep 2011
Posts: 12
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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While squaring both sides why we did not consider the negative value of r?
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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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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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3230
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?  [#permalink]

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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.

_________________ 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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