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# If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s

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Math Expert
Joined: 02 Sep 2009
Posts: 44401
If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s [#permalink]

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12 Oct 2017, 04:15
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Difficulty:

25% (medium)

Question Stats:

81% (00:36) correct 19% (00:39) wrong based on 70 sessions

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If rs ≠ 0, is t an integer?

(1) t = 3r – 2s
(2) r = s
[Reveal] Spoiler: OA

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Joined: 25 Feb 2013
Posts: 1008
Location: India
GPA: 3.82
If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s [#permalink]

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12 Oct 2017, 08:12
Bunuel wrote:
If rs ≠ 0, is t an integer?

(1) t = 3r – 2s
(2) r = s

Statement 1: if $$r$$ & $$s$$ are integers then $$t$$ is integer, if not then $$t$$ may or may not be an integer. hence insufficient

Statement 2: no information about $$t$$. Hence insufficient

Combining 1 & 2 we get $$t=3r-2r=r$$, if $$r$$ is an integer then $$t$$ is an integer if not then $$t$$ is not an integer. Hence insufficient

Option E
SVP
Joined: 26 Mar 2013
Posts: 1522
Re: If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s [#permalink]

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12 Oct 2017, 23:58
Bunuel wrote:
If rs ≠ 0, is t an integer?

(1) t = 3r – 2s
(2) r = s

(2) r = s

Insufficient

(1) t = 3r – 2s

Let r = s = 1....t = 1.............Answer is Yes

Let r = s = 1/2..t = 1/2.............Answer is No

Insufficient

Combine 1 & 2

Insufficient

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2155
Re: If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s [#permalink]

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27 Nov 2017, 19:16
Bunuel wrote:
If rs ≠ 0, is t an integer?

(1) t = 3r – 2s
(2) r = s

Statement One Alone:

t = 3r – 2s

If r = 1 and s = 1, then 3r - 2s = 1 and t is an integer; however, if r = 1/2 and s = 1, then 3r - 2s = -0.5 and t is not an integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

r = s

Since statement two does not provide any information regarding t, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the statements together, we have t = 3r - 2r, or t = r. However, since we do not know whether r is an integer, we cannot determine whether t is an integer.

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Re: If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s   [#permalink] 27 Nov 2017, 19:16
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