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# What is the value of m?

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Math Expert
Joined: 02 Sep 2009
Posts: 56266
What is the value of m?  [#permalink]

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19 Sep 2016, 05:44
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Difficulty:

45% (medium)

Question Stats:

60% (01:32) correct 40% (01:33) wrong based on 216 sessions

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What is the value of m?

(1) |m| = −36/m

(2) 2m+2|m| = 0

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Joined: 03 Jul 2016
Posts: 71
Re: What is the value of m?  [#permalink]

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19 Sep 2016, 06:33
Statement 1:

|m| = -36/m

the value of LHS i.e. |m| is always positive, so in order the RHS to be positive m has to -ve. Hence m=-6. SUFFICIENT.

Statement 2:
2m+2|m| = 0 => m is -ve but couldn't find the value of m. NOT SUFFICIENT.

A.
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Joined: 12 Sep 2015
Posts: 3847
Re: What is the value of m?  [#permalink]

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19 Sep 2016, 08:19
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Top Contributor
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Bunuel wrote:
What is the value of m?

(1) |m| = −36/m

(2) 2m+2|m| = 0

When solving questions involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots

Okay, onto the question.....

Target question: What is the value of m?

Statement 1: |m| = -36/m
So, m = −36/m and/or m = −(−36/m)
Now solve each resulting equation:

m = −36/m
Multiply both sides by m to get: m² = −36
No solutions!

m = −(−36/m)
Simplify: m = 36/m
Multiply both sides by m to get: m² = 36
Solve to get: m = -6 or m = 6
Now TEST these two solutions by plugging them into the original equation.

m = −6.
Plug in to get: |-6| = −36/(−6)
Evaluate to get: 6 = 6
So, m = -6 IS a solution....KEEP!

m = 6.
Plug in to get: |6| = −36/6
Evaluate to get: 6 = −6
So, m = 6 is NOT a solution....DISCARD

So, we can be certain that m = -6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2m + 2|m| = 0
Rearrange to get: 2|m| = -2m
Divide both sides by 2 to get: |m| = -m
We should be able to quickly see that this equation holds true for ANY non-positive value of m.
For example, if m = 0, then |m| = -m becomes |0| = -0 WORKS!
Likewise, if m = -1, then |m| = -m becomes |-1| = -(-1) WORKS!
And if m = -2, then |m| = -m becomes |-2| = -(-2) WORKS!
etc.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Re: What is the value of m?  [#permalink]

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19 Sep 2016, 10:19
Bunuel wrote:
What is the value of m?

(1) |m| = −36/m

(2) 2m+2|m| = 0

(1) Let m >=0
then |m|=m
so, m =-36/m----->m^2=-36......but this is just not possible as square of any number is +ve

Let m<0
then |m|=-m
so, -m=-36/m---------->-m^2=-36------>m^2=36
as we have taken m<0 so m=-6....sufff....

(2) 2m+2|m| = 0
or 2|m| = -2m
taking RHS part -2m>=0-------> m <=0
only conclusion from the above is m<0 and can be any -ve number....not suff...

Ans A
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Re: What is the value of m?  [#permalink]

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14 Aug 2018, 07:33
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: What is the value of m?   [#permalink] 14 Aug 2018, 07:33
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