If r, s, and t are all positive, what is the ratio of r to s to t?

Question

(1)  r – s = 2s  and  (t – 2s)^2 = 0 
(2)  r = 6  and  t = 8s^{-1}

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$!vakumar.m · Answer

If r, s, and t are all positive, what is the ratio of r to s to t?
we are required to find r:s:t =?
(1) r–s=2s 
=> r = 3s or r:s = 3:1
and (t–2s)^2=0
=> t - 2s = 0 
=> t = 2s
or s:t =1:2
therefore, r:s:t = 3:1:2
Statement 1 is Sufficient

(2) r=6 and 
t=8s^(−1) = 8/s 
or st = 8
from this we cannot determine the ratio r:s:t 
Statement 2 is Not sufficient
Answer A

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are asked the value of  r:s:t  
 We know that r, s, and t are all positive

Statement 1:    r – s = 2s  and  (t – 2s)^2 = 0 
  Firstly,  r – s = 2s  or  r=3s  
 Secondly,  (t – 2s)^2 = 0 
 ⇒t-2s=0 
 ⇒t=2s  
 So, the value of  r:s:t=3s:s:2s=3:1:2  
 Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2:    r = 6  and  t = 8s^{-1} 
  We are given  t = 8s^{-1} 
 ⇒t=\frac{8}{s} 
 ⇒ts=8  
 If  t=8  and  s=1 
  the value of  r:s:t=6:1:8    
 If  t=2  and  s=4 
  the value of  r:s:t=6:4:2=3:2:1    
 Thus,  statement 2 alone is not sufficient

Hence the right answer is    Option A

If r, s, and t are all positive, what is the ratio of r to s to t?

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