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# If p, r, s, and t are nonzero integers, is p/r = s/t ?

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Math Expert
Joined: 02 Sep 2009
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If p, r, s, and t are nonzero integers, is p/r = s/t ?  [#permalink]

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15 Nov 2017, 08:48
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35% (medium)

Question Stats:

89% (01:31) correct 11% (01:39) wrong based on 39 sessions

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If p, r, s, and t are nonzero integers, is p/r = s/t ?

(1) s = 3p and t = 3r.

(2) 3p = 2r and 3s = 2t.

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If p, r, s, and t are nonzero integers, is p/r = s/t ?  [#permalink]

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15 Nov 2017, 09:03
Bunuel wrote:
If p, r, s, and t are nonzero integers, is p/r = s/t ?

(1) s = 3p and t = 3r.

(2) 3p = 2r and 3s = 2t.

Statement 1: $$s=3p$$ and $$t=3r$$. divide both equations to get

$$\frac{s}{t}=\frac{3p}{3r}=\frac{p}{r}$$. Sufficient

Statement 2: $$3p=2r => \frac{p}{r}=\frac{2}{3}$$

$$3s=2t => \frac{s}{t}=\frac{2}{3}$$ so we have $$\frac{p}{r}=\frac{s}{t}=\frac{2}{3}$$. Sufficient

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Re: If p, r, s, and t are nonzero integers, is p/r = s/t ?  [#permalink]

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15 Nov 2017, 09:33
Top Contributor
Bunuel wrote:
If p, r, s, and t are nonzero integers, is p/r = s/t ?

(1) s = 3p and t = 3r.

(2) 3p = 2r and 3s = 2t.

Target question: Is p/r = s/t?

Statement 1: s = 3p and t = 3r
Divide the first equation by the second equation to get: s/t = 3p/3r
Simplify right side to get: s/t = p/r
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3p = 2r and 3s = 2t
Given: 3p = 2r
Divide both sides by r to get: 3p/r = 2
Divide both sides by 3 to get: p/r = 2/3

Given: 3s = 2t
Divide both sides by t to get: 3s/t = 2
Divide both sides by 3 to get: s/t = 2/3

Since p/r and s/t both equal 2/3, we can conclude that p/r = s/t
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

Re: If p, r, s, and t are nonzero integers, is p/r = s/t ? &nbs [#permalink] 15 Nov 2017, 09:33
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