It is currently 19 Oct 2017, 11:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 13 May 2013
Posts: 463

Kudos [?]: 197 [1], given: 134

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

### Show Tags

08 Jul 2013, 16:34
1
KUDOS
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)

Kudos [?]: 197 [1], given: 134

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4133

Kudos [?]: 2891 [0], given: 0

GPA: 3.82
Re: Is M<0? (1) -M = |-M| (2) M^2 = 9 [#permalink]

### Show Tags

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 2891 [0], given: 0

Manager
Joined: 20 Jan 2016
Posts: 197

Kudos [?]: 12 [0], given: 63

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

### Show Tags

29 Sep 2017, 04:38
Bunuel,

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

Kudos [?]: 12 [0], given: 63

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 128889 [1], given: 12183

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

### Show Tags

29 Sep 2017, 04:43
1
KUDOS
Expert's post
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|.
_________________

Kudos [?]: 128889 [1], given: 12183

Re: Is M<0? (1) -M = |-M| (2) M^2 = 9   [#permalink] 29 Sep 2017, 04:43

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by