Is \(m<0\)?

(1) \(-m=|-m|\) --> first of all \(|-m|=|m|\), (for example: \(|-3|=|3|=3\)), so we have \(-m=|m|\), as RHS is absolute value which is always non-negative, then LHS, \({-m}\) must also be non-negative --> \(-m\geq{0}\) --> \(m\leq{0}\), so \(m\) could be either negative or zero. Not sufficient.

(2) \(m^2=9\) --> \(m=3=positive\) or \(m=-3=negative\). Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is \(m=-3=negative\), hence answer to the question "is \(m<\)0" is YES. Sufficient.

Answer: C.

Hope it's clear.
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Thanks so much Bunuel.

Bunuel ,i love youuuuuuuuuuuuuuuuuuuu!!!!!!!

very nicely explained by Bunnel.

The tricky part here was the consideration of zero.
While dealing with these type of DS questions always consider scenario of -ve, 0 ,and +ve numbers.
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It is not an uncommon reply to Bunuels posts

You can kindly give Bunuel Kudos (there is a button for that)

P.S. You can also "Follow" bunuel (you will get daily summaries of his posts) so you don't miss any wisdom. There is a follow button next to his name.
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I love the 'follow' feature.

I remember you posted something on the top notification- all know how to lead, can you follow?.

I feel I m actually leading them by following what are they posting, though I m not the leader. A new way to look at the leadership.
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Almost missed that M could be also 0 in S 1

Good work Bunuel. I missed the zero consideration too!

1- Any thing equals to Modlus is always Positive, therefore, -M = must be a Positive number. this can only be possible when M itself is a -ve number.
Therefore Answer should be A

2- Option 2 would have 2 number + & -, therefore not sufficient

2-

Hi, and welcome to Gmat Club.

OA for this questionj is C not A (official answer is given under the spoiler in the first post).

Next, the red part is not correct: absolute value is always non-negative, which means that something equal to absolute value is either positive or zero. See my first post for the full solution of this question.

Hope it helps.
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The answer is C but I also missed the Zero part.
As Bunuel says ZIP code

yeah..I also committed the classic error - missed the zero....grrrr!!!

That is the most frequent mistake which we normally commit

Statement 1: -M = |M|
M can either be any negative number, or Zero. Not Sufficient.

Statement 2: M^2=9
M can either be 3 or -3. Not Sufficient.

Together:
M must be either a negative number or zero AND either 3 or -3. M must be -3. Sufficient. Answer C

edit: swapped positive with negative. Below post is correct

1) Statement 1: -M = |M|

M can be either negative or zero.

as for M>0
-M is not equal to M
when M<0
-M = -(M)

Not sufficient.

2) Statement 2: M^2=9
M = 3 , -3
Not sufficient.

1&2) M= -3
Sufficient

C is the answer

Statement 1 looks confusing indeed. But it's good to get back to the basics. How is an absolute value defined?

|X|= X if X>=0 or -X if x<0. the reason for this definition is that absolute value is defined as being a non-negative value. it can be anything b a negative number.

Now,
|-M| looks strange. but think of -M as X. then |(-M)|= -M if (-M)>=0 or -(-M) if -M<0.
we are told that |-M|=-M. so the first condition applies. -M>=0. The question asks is M<0. -M>=0 is to say M<=0 (sign flipped). so yes, M< 0 but also M=0. So not sufficient.

Statement 2: we know that in this case, m could be +-3. so not sufficient.

taken together, we know from first statement that M is either negative or 0 and from the second statemnent that M is either plus or minus 3. clearly together, M is a negative number. Hence, C.

Bunuel,

Bestow your legendary wisdom upon this mortal, so that he too can know what ZIP code is.

P.S. M assuming Z - zero...whats the rest

ZIP - Zero, Integers, Positive numbers.

GMAT likes to act in -1<=x<=1 range. So:

Don't assume, with no ground for it, that variable cannot be Zero. Check 0!
Don't assume, with no ground for it, that variable is an Integer. Check fractions!
Don't assume, with no ground for it, that variable is Positive. Check negative values!
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