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

(2) \(m^2=9\). Either \(m=3=\text{positive}\) or \(m=-3=\text{negative}\). Not sufficient.

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

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

(2) \(m^2=9\). Either \(m=3=\text{positive}\) or \(m=-3=\text{negative}\). Not sufficient.

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

Answer: C

But 0 is neither +ve nor -ve. So why is it -m>=0 and not -m>0??

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

(2) \(m^2=9\). Either \(m=3=\text{positive}\) or \(m=-3=\text{negative}\). Not sufficient.

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

Answer: C

But 0 is neither +ve nor -ve. So why is it -m>=0 and not -m>0??

Because \(-m=|-m|\) holds for 0 too: -0 = 0 = |-0|.
_________________

I think this question is good and helpful. Had a different take. If an integer is prefixed by the - (neg) sign, it cannot be zero by definition. Hence 1 should be sufficient to answer this. Can you clarify my thought process.

I think this question is good and helpful. Had a different take. If an integer is prefixed by the - (neg) sign, it cannot be zero by definition. Hence 1 should be sufficient to answer this. Can you clarify my thought process.

That's not correct at all. There is nothing wrong in writing -0=|-0|.
_________________

I think this question is good and helpful. Had a different take. If an integer is prefixed by the - (neg) sign, it cannot be zero by definition. Hence 1 should be sufficient to answer this. Can you clarify my thought process.

That's not correct at all. There is nothing wrong in writing -0=|-0|.

Hi Bunuel, there still seems to be some confusion in my head. The article on Wikipedia on 'Sign in Mathematics' made me more confused.

Hope such ambiguous/debatable concepts are not tested in the GMAT.

I think this question is good and helpful. Had a different take. If an integer is prefixed by the - (neg) sign, it cannot be zero by definition. Hence 1 should be sufficient to answer this. Can you clarify my thought process.

That's not correct at all. There is nothing wrong in writing -0=|-0|.

Hi Bunuel, there still seems to be some confusion in my head. The article on Wikipedia on 'Sign in Mathematics' made me more confused.

Hope such ambiguous/debatable concepts are not tested in the GMAT.

You have to be a little bit careful about the logic you're following on this question.

From the outset, the only trustworthy information you have is that m is a real number and you're asked to determine if it's less than 0. The logical path you started going down is the false belief that, because of statement (1), m has to be either a negative or positive real number. This is incorrect. What Statement 1 is really saying is, "If you multiply m by -1 it will equal the absolute value of the m multiplied by -1." Which, as Bunuel said, holds true for 0 as well as any negative real number.

Hope this helps you. This is not an ambiguous/debatable concept and I strongly recommend practicing similar questions types as you will likely see multiple on a GMAT exam.

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

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.

Please let me know the gaps in my understanding. Thanks in advance Bunuel.
_________________

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- When nothing seem to help, I would go and look at a Stonecutter hammering away at his rock perhaps a hundred time without as much as a crack showing in it. Yet at the hundred and first blow it would split in two. And I knew it was not that blow that did it, But all that had gone Before.