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Senior Manager  Joined: 13 May 2013
Posts: 396
Re: Is M<0? (1) -M = |-M| (2) M^2 = 9  [#permalink]

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1
Is M<0?

(1) -M = |-M|
-m cannot be negative because it is equal to an absolute value. Therefore:
-M = |-M|
-(-M) = |-M|
M = |-M|
Therefore, M must be negative because -(-M) = M. M is therefore less than or equal to zero, but we don't know if it is LESS than zero.
INSUFFICIENT

(2) M^2 = 9
M^2=9
|M|^2 = 9
|M| = 3
M=3, M=-3
M could be greater than zero or less than zero.
INSUFFICIENT

1+2) In #1 we are told that M is less than or equal to zero. In #2 we are told that M is either -3 or 3. Therefore, the only intersection is that M = -3.
SUFFICIENT

(C)
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is M<0? (1) -M = |-M| (2) M^2 = 9  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is M<0?

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

In the original condition, there is 1 variable(m), which should match with the number equation. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), in order to make -m=|-m|, from -m>=0, m<=0, m=-1 -> yes, m=0 -> no, which is not sufficient. For 2), m=-3 -> yes, m=3 -> no, which is not sufficient. In 1) & 2), m=-3 is yes and sufficient. Therefore, the answer is C.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Is M<0? (1) -M = |-M| (2) M^2 = 9  [#permalink]

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Bunuel,

in statement 1, how can M be zero ? That is the part I am confused about
Math Expert V
Joined: 02 Sep 2009
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Re: Is M<0? (1) -M = |-M| (2) M^2 = 9  [#permalink]

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1
pra1785 wrote:
Bunuel,

in statement 1, how can M be zero ? That is the part I am confused about

-0 = 0 and |-0| = |0| = 0, so if M = 0, then -M = 0 = |-M|.
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Re: Absolute Value: Is M<0?  [#permalink]

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_________________ Re: Absolute Value: Is M<0?   [#permalink] 01 Oct 2019, 07:58

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