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Is q negative?

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Math Expert
Joined: 02 Sep 2009
Posts: 60687

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21 Feb 2016, 13:46
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Difficulty:

5% (low)

Question Stats:

96% (00:47) correct 4% (01:05) wrong based on 48 sessions

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Is q negative?

(1) rs > 0 and qs < 0
(2) r > 0

Kudos for correct solution.

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Intern
Joined: 10 Nov 2014
Posts: 8

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21 Feb 2016, 14:32
2
Bunuel wrote:
Is q negative?

(1) rs > 0 and qs < 0
(2) r > 0

Kudos for correct solution.

I would say C, although C feels a bit like a trap answer.

(1) $$rs > 0$$ tells us that both r and s are either positive or negative. $$qs < 0$$ indicates that q and s are different signs. Given that s could be positive or negative, based on the first inequality, we do not know whether q is negative. Insufficient

(2) We have no way to relate r to q using just this statement and the question stem. Insufficient

(Both) Now that we know that r is positive, s has to be positive (given $$rs > 0$$), which indicates that q is negative (given $$qs < 0$$). Sufficient
SVP
Joined: 06 Nov 2014
Posts: 1868

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22 Feb 2016, 21:13
1
Bunuel wrote:
Is q negative?

(1) rs > 0 and qs < 0
(2) r > 0

Kudos for correct solution.

Statement 1:
rs > 0 and qs < 0

rs can be positive if both r and s have same signs.
Case1: r > 0
therefore s > 0

Now we are given that qs < 0
Hence q < 0

Case 2:
r < 0
Therefore s < 0

Now we are given that qs < 0
Hence q >0

Insufficient

Statement 2: r >0
Clearly insufficient as there is no information about q

Combining 1 and 2:
We come to the case 2 of statement 1.
Hence we can say that q < 0

Sufficient
Option C
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11 Dec 2019, 18:00
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Re: Is q negative?   [#permalink] 11 Dec 2019, 18:00
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