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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]

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Is M<0?

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

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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Sep 2012, 06:16, edited 1 time in total.
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Re: Is [m]M<0[/m]? [#permalink]

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seekmba wrote:
Is \(M<0\)?

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

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.
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Re: Is [m]M<0[/m]? [#permalink]

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New post 28 Aug 2010, 07:24
Thanks so much Bunuel.

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

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Re: Is [m]M<0[/m]? [#permalink]

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New post 28 Aug 2010, 13:45
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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Re: Is [m]M<0[/m]? [#permalink]

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New post 28 Aug 2010, 13:49
amlandutta007 wrote:
Bunuel ,i love youuuuuuuuuuuuuuuuuuuu!!!!!!!


It is not an uncommon reply to Bunuels posts :lol:

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

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I love the 'follow' feature. :cool

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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Re: Is [m]M<0[/m]? [#permalink]

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New post 06 Sep 2010, 20:34
Almost missed that M could be also 0 in S 1
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Re: Is [m]M<0[/m]? [#permalink]

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New post 07 Sep 2010, 03:09
Good work Bunuel. I missed the zero consideration too!

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Re: Is [m]M<0[/m]? [#permalink]

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New post 07 Sep 2010, 04:48
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-

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Re: Is [m]M<0[/m]? [#permalink]

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New post 07 Sep 2010, 05:08
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

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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Re: Is [m]M<0[/m]? [#permalink]

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New post 25 Sep 2011, 04:33
The answer is C but I also missed the Zero part.
As Bunuel says ZIP code

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Re: Is [m]M<0[/m]? [#permalink]

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New post 26 Sep 2011, 05:33
yeah..I also committed the classic error - missed the zero....grrrr!!!
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New post 26 Sep 2011, 11:28
GMATmission wrote:
yeah..I also committed the classic error - missed the zero....grrrr!!!



That is the most frequent mistake which we normally commit

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Re: absolute value [#permalink]

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New post 29 Apr 2012, 10:01
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

Last edited by pstrench on 29 Apr 2012, 10:22, edited 1 time in total.

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Re: absolute value [#permalink]

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New post 29 Apr 2012, 10:10
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

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Re: Is [m]M<0[/m]? [#permalink]

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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

2-

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Re: Is [m]M<0[/m]? [#permalink]

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New post 20 Dec 2012, 08:06
samramandy wrote:
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
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Re: Is [m]M<0[/m]? [#permalink]

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eaakbari wrote:
samramandy wrote:
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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Re: Is M<0? (1) -M = |-M| (2) M^2 = 9 [#permalink]

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Re: Is M<0? (1) -M = |-M| (2) M^2 = 9   [#permalink] 08 Jul 2013, 00:54

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