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

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Joined: 02 Sep 2009
Posts: 47924
If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s  [#permalink]

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New post 12 Oct 2017, 04:15
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

81% (00:35) correct 19% (00:37) wrong based on 75 sessions

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

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New post 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
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Re: If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s  [#permalink]

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

(1) t = 3r – 2s
(2) r = s



(2) r = s

No info about t

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

I considered r = s in examples above.......No clear answer answer

Insufficient

Answer: E
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Re: If rs ≠ 0, is t an integer? (1) t = 3r – 2s (2) r = s  [#permalink]

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New post 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.

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