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

Question

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

Bunuel · Accepted Answer

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

Answer: D.

EMPOWERgmatRichC · Answer

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:  D

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

JeffTargetTestPrep · Answer

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.

Abhishek009 · Answer

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

\sqrt{\frac{s^3}{s}}=\sqrt{s^2}  =  s

SeregaP · Answer

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

BrentGMATPrepNow · Answer

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:  D

Kinshook · Answer

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

chayon222 · Answer

While squaring both sides why we did not consider the negative value of r?

Bunuel · Answer

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.

EgmatQuantExpert · Answer

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

Hoozan · Answer

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

EMPOWERgmatRichC · Answer

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

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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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