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

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Intern
Joined: 16 Oct 2017
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If r, s, and t are all positive, what is the ratio of r to s to t?  [#permalink]

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Updated on: 27 Mar 2018, 10:32
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25% (medium)

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83% (01:51) correct 17% (01:11) wrong based on 34 sessions

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If r, s, and t are all positive, what is the ratio of r to s to t?
(1) r – s = 2s and (t – 2s)^2 = 0
(2) r = 6 and t = 8s^-1

I don't understand how to manipulate statement #2 to make it not sufficient...

Originally posted by OCDianaOC on 27 Mar 2018, 10:23.
Last edited by OCDianaOC on 27 Mar 2018, 10:32, edited 2 times in total.
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Re: If r, s, and t are all positive, what is the ratio of r to s to t?  [#permalink]

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27 Mar 2018, 10:28
OCDianaOC wrote:
If r, s, and t are all positive, what is the ratio of r to s to t?
(1) r – s = 2s and (t – 2s)2 = 0
(2) r = 6 and t = 8s-1

I don't understand how to manipulate statement #2 to make it not sufficient...

Statement 1: $$r-s=2s=>r=3s => \frac{r}{s}=\frac{3}{1} =>r:s=3:1$$

$$(t-2s)2=0=>t=2s=>\frac{s}{t}=\frac{1}{2}=>s:t=1:2$$

Therefore $$r:s:t=3:1:2$$. Sufficient

Statement 2: from this we cannot find the values of variable $$t$$ & $$s$$ and hence we cannot calculate the ratio of $$r:s:t$$. Insufficient

Option A
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Re: If r, s, and t are all positive, what is the ratio of r to s to t?  [#permalink]

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27 Mar 2018, 21:31
OCDianaOC wrote:
If r, s, and t are all positive, what is the ratio of r to s to t?
(1) r – s = 2s and (t – 2s)^2 = 0
(2) r = 6 and t = 8s^-1

I don't understand how to manipulate statement #2 to make it not sufficient...

Please refer to the solution above by Niks to understand how statement A is sufficient.

Well, in second statement, we get r=6. And t = 8/s which gives us s*t = 8
So we have value of r, and we just have the product of s & t. This will certainly not be sufficient to get r:s:t. Even if the statement had given us the ratio of s & t (s/t) instead of their product, still we wouldnt have been able to get the desired answer, because we are not given the relation of r to any of s or t. Hence this statement is not sufficient.
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Re: If r, s, and t are all positive, what is the ratio of r to s to t?  [#permalink]

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28 Mar 2018, 10:40
amanvermagmat wrote:
OCDianaOC wrote:
If r, s, and t are all positive, what is the ratio of r to s to t?
(1) r – s = 2s and (t – 2s)^2 = 0
(2) r = 6 and t = 8s^-1

I don't understand how to manipulate statement #2 to make it not sufficient...

Please refer to the solution above by Niks to understand how statement A is sufficient.

Well, in second statement, we get r=6. And t = 8/s which gives us s*t = 8
So we have value of r, and we just have the product of s & t. This will certainly not be sufficient to get r:s:t. Even if the statement had given us the ratio of s & t (s/t) instead of their product, still we wouldnt have been able to get the desired answer, because we are not given the relation of r to any of s or t. Hence this statement is not sufficient.

How do you manipute to get s*t = 8 though? When I move things around, I get t/s = 1/8...
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Posts: 1412
Location: India
Re: If r, s, and t are all positive, what is the ratio of r to s to t?  [#permalink]

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28 Mar 2018, 21:05
1
OCDianaOC wrote:
amanvermagmat wrote:
OCDianaOC wrote:
If r, s, and t are all positive, what is the ratio of r to s to t?
(1) r – s = 2s and (t – 2s)^2 = 0
(2) r = 6 and t = 8s^-1

I don't understand how to manipulate statement #2 to make it not sufficient...

Please refer to the solution above by Niks to understand how statement A is sufficient.

Well, in second statement, we get r=6. And t = 8/s which gives us s*t = 8
So we have value of r, and we just have the product of s & t. This will certainly not be sufficient to get r:s:t. Even if the statement had given us the ratio of s & t (s/t) instead of their product, still we wouldnt have been able to get the desired answer, because we are not given the relation of r to any of s or t. Hence this statement is not sufficient.

How do you manipute to get s*t = 8 though? When I move things around, I get t/s = 1/8...

Hello

We are given t = 8s^-1. It means t = 8 * s^-1 or t = 8 * 1/s
So if we take s to the other side (cross multiply), we get: t*s = 8
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Re: If r, s, and t are all positive, what is the ratio of r to s to t?  [#permalink]

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28 Mar 2018, 22:15
A.

Why not st. 2 - r=6 okay
t= 8/s >> t*s = 8. You need a ratio ie. t/s . Therefore not sufficient

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Intern
Joined: 16 Oct 2017
Posts: 38
If r, s, and t are all positive, what is the ratio of r to s to t?  [#permalink]

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29 Mar 2018, 10:49
amanvermagmat ,

Oh, I get it now... didn't realize that t = 8 *1/s! Thank you for the explanation!
If r, s, and t are all positive, what is the ratio of r to s to t? &nbs [#permalink] 29 Mar 2018, 10:49
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