Rohan271
I saw a question on Instagram on DS:
Question: is m<0?
1)-m=|-m|
2m^2=9
I am not able to understand the first option given here.. can someone help
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.
Hope it's clear.
P.S. Discussed in detail here:
https://gmatclub.com/forum/is-m-0-1-m-m-2-m-99913.html