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# Is M < 0? 1) -M = |-M| 2) M^2 = 9

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Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]  25 Feb 2010, 19:49
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Is M < 0?

1) -M = |-M|
2) M^2 = 9.

[Reveal] Spoiler:
I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-m-0-1-m-m-2-m-99913.html
[Reveal] Spoiler: OA

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Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]  25 Feb 2010, 21:32
Is M < 0?

1) -M = |-M|
M<=0 -> any negative value of M, the equation holds good M=-3, RHS = 3 and LHS is 3.
0 coz if M=0, both sides are 0.
Not sufficient
2) M^2 = 9.
M=+3 or -3
Not sufficient

Combining M=-3

C

Barney - yes 0 is neither positive nor negative and you wont get a question asking what is |-0| .. but if a variable is given and the variable is of the kind y=-x, for all x, then for x=0, we say y = 0 --- do you say for x=0, there is no such value as -0 so this is INVALID? No right -- we can substitute 0 in a variable and it the value by chance comes up as -0, the value would be taken as 0.
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Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]  12 Mar 2010, 01:53
BarneyStinson wrote:
Is M < 0?

1) -M = |-M|
2) M^2 = 9.

I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

stmt1: -M = |-M|
there can be two cases
-M = -M or -M = M => 2M = 0 => M= 0
So, M < 0 is not true

stmt2: M^2 = 9 => M = 3, -3 it is not suff not answering the question.
Should not A be the answer of this question?
|x| is actually the amount of x irrespective of its sign. Usually it is used to calculate distances on the coordinates. So, |0| means something with no value right?
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Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]  12 Mar 2010, 15:46
sidhu4u wrote:
BarneyStinson wrote:
Is M < 0?

1) -M = |-M|
2) M^2 = 9.

I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

stmt1: -M = |-M|
there can be two cases
-M = -M or -M = M => 2M = 0 => M= 0
So, M < 0 is not true

stmt2: M^2 = 9 => M = 3, -3 it is not suff not answering the question.
Should not A be the answer of this question?
|x| is actually the amount of x irrespective of its sign. Usually it is used to calculate distances on the coordinates. So, |0| means something with no value right?

value of |0| is 0. inequality questions hinges on the 0 values a lot. so dont ignore those.
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Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]  13 Mar 2010, 17:45
Is M < 0?

1) -M = |-M|
2) M^2 = 9.

1) M is either 0 or negative, insufficient

2) M can be either positive or negative, insufficient

1 and 2, taken together, M is negative, sufficient

Thus, C.
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Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]  09 Sep 2015, 20:08
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Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]  09 Sep 2015, 20:29
Expert's post
BarneyStinson wrote:
Is M < 0?

1) -M = |-M|
2) M^2 = 9.

[Reveal] Spoiler:
I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-m-0-1-m-m-2-m-99913.html
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Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9   [#permalink] 09 Sep 2015, 20:29
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