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

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V
Joined: 02 Sep 2009
Posts: 42579

Kudos [?]: 135467 [0], given: 12695

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

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New post 15 Nov 2017, 07:48
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A
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C
D
E

Difficulty:

  25% (medium)

Question Stats:

93% (01:11) correct 7% (00:44) wrong based on 29 sessions

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Kudos [?]: 135467 [0], given: 12695

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Joined: 25 Feb 2013
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Kudos [?]: 306 [0], given: 39

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

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New post 15 Nov 2017, 08:03
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

Option D

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

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New post 15 Nov 2017, 08:33
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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

Answer: D

Cheers,
Brent
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Brent Hanneson – Founder of gmatprepnow.com

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Kudos [?]: 2741 [0], given: 364

Re: If p, r, s, and t are nonzero integers, is p/r = s/t ?   [#permalink] 15 Nov 2017, 08:33
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