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16 Sep 2014, 00:15
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16 Sep 2014, 00:15
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Official Solution:
Is \(m \lt 0\)?
(1) \(-m=|-m|\).
Firstly, \(|-m|=|m|\), (for example: \(|-3|=|3|=3\)), so we can rewrite the statement as \(-m=|m|\). Since \(|x| = -x\) when \(x \leq 0\), then \(-m=|m|\) implies \(m \leq 0\). Therefore, \(m\) could be either negative, giving a YES answer to the question, or zero, giving a NO answer to the question. This statement is not sufficient.
(2) \(m^2=9\).
The above implies that either \(m=3\) (positive) or \(m=-3\) (negative). This information alone is not sufficient to answer the question.
(1)+(2) We know from (1) that \(m \leq 0\), and from (2) we have two possibilities: \(m=3\) or \(m=-3\). Since \(m \leq 0\), we can eliminate \(m=3\), leaving us with \(m=-3\), which is negative. Thus, the answer to the question "is \(m \lt 0\)" is YES. Sufficient.
Answer: C
Is \(m \lt 0\)?
(1) \(-m=|-m|\).
Firstly, \(|-m|=|m|\), (for example: \(|-3|=|3|=3\)), so we can rewrite the statement as \(-m=|m|\). Since \(|x| = -x\) when \(x \leq 0\), then \(-m=|m|\) implies \(m \leq 0\). Therefore, \(m\) could be either negative, giving a YES answer to the question, or zero, giving a NO answer to the question. This statement is not sufficient.
(2) \(m^2=9\).
The above implies that either \(m=3\) (positive) or \(m=-3\) (negative). This information alone is not sufficient to answer the question.
(1)+(2) We know from (1) that \(m \leq 0\), and from (2) we have two possibilities: \(m=3\) or \(m=-3\). Since \(m \leq 0\), we can eliminate \(m=3\), leaving us with \(m=-3\), which is negative. Thus, the answer to the question "is \(m \lt 0\)" is YES. Sufficient.
Answer: C
11 May 2017, 16:10
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Bunuel
Too me a long time to understand this. Plugging in values makes it clear. For -m = | -m | we can find:
m = 1
-1 = | -1|
-1 = 1
Doesn't make sense. m cannot be 1.
m = 0
-0 = | -0|
0 = 0.
Make sense.
m = -1
1 = | 1|
1 = 1. Makes sense.
So for statement 1, m can be -1 or 0. Insufficient.
