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I got very confused with option 1 and took lot of time with this question. Can someone help me unedstand how I can solve such questions quickly.

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.

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

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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

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.

I got very confused with option 1 and took lot of time with this question. Can someone help me unedstand how I can solve such questions quickly.

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.

How do you get -m >= 0 => m <=0 ??? i dont understand

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.

harishsharma81 wrote:

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

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

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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