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

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

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

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New post 08 Jul 2013, 16:34
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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)
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Re: Is M<0? (1) -M = |-M| (2) M^2 = 9 [#permalink]

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New post 25 Jul 2014, 05:15
Hello from the GMAT Club BumpBot!

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

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New post 23 Dec 2015, 08:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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New post 23 Dec 2015, 23:32
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] 23 Dec 2015, 23:32

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