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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] New post 07 Jul 2013, 23:54
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Re: Is M<0? (1) -M = |-M| (2) M^2 = 9 [#permalink] New post 08 Jul 2013, 15:34
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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

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Re: Is M<0? (1) -M = |-M| (2) M^2 = 9 [#permalink] New post 25 Jul 2014, 04:15
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] 25 Jul 2014, 04:15
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