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# Is rst = 1 ? (1) r p t = s p t s (2) prt t = p t st

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Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139595 [0], given: 12794

Is rst = 1 ? (1) r p t = s p t s (2) prt t = p t st [#permalink]

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31 Dec 2017, 11:10
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Difficulty:

35% (medium)

Question Stats:

82% (00:32) correct 18% (01:35) wrong based on 11 sessions

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Is rst = 1 ?

(1) $$r\sqrt{t} =\frac{s\sqrt{t}}{s}$$

(2) $$\frac{rt}{\sqrt{t}}=\frac{\sqrt{t}}{st}$$
[Reveal] Spoiler: OA

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Kudos [?]: 139595 [0], given: 12794

examPAL Representative
Joined: 07 Dec 2017
Posts: 117

Kudos [?]: 21 [0], given: 3

Re: Is rst = 1 ? (1) r p t = s p t s (2) prt t = p t st [#permalink]

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31 Dec 2017, 13:23
Bunuel wrote:
Is rst = 1 ?

(1) $$r\sqrt{t} =\frac{s\sqrt{t}}{s}$$

(2) $$\frac{rt}{\sqrt{t}}=\frac{\sqrt{t}}{st}$$

As this looks to be a very technical question (with many equations), we'll just solve it.
This is a Precise approach.

(1) We can cancel out $$s$$ from the right-hand side giving $$r\sqrt{t} =\sqrt{t}$$
As we don't know if $$t = 0$$ or not, we can't cancel it out but we can rewrite as $$r\sqrt{t} -\sqrt{t}=0$$
This simplifies to $$\sqrt{t}(r-1)=0$$ meaning that $$t = 0$$ or $$r = 1$$.
Insufficient!

(2) Since both $$s$$ and $$t$$ are in the denominator, they can't be equal to 0 so we can multiply by them.
Multiplying by $$s$$ and by $$\sqrt{t}$$ gives $$rst = \frac{t}{t}=1$$
Sufficient!

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David
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Kudos [?]: 21 [0], given: 3

Re: Is rst = 1 ? (1) r p t = s p t s (2) prt t = p t st   [#permalink] 31 Dec 2017, 13:23
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