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# What is the value of m?

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What is the value of m?  [#permalink]

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06 Dec 2013, 12:04
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What is the value of m?

(1) |m| = −36/m

(2) 2m+2|m| = 0
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Joined: 10 Oct 2012
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Re: What is the value of m?  [#permalink]

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06 Dec 2013, 12:10
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nechets wrote:
What is the value of m?

(1) |m| = −36/m

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

As |m| is a non-negative entity, $$|m|\geq{0}$$

Now, F.S 1 states that $$|m| = \frac{-36}{m}$$. This will be possible only if m<0.

Thus, as |m| = -m (for m<0), we have$$-m = \frac{-36}{m}$$ and $$m^2 = 36 \to m=-6$$.Sufficient.

F.S 2 states that |m| = -m. This is valid for any negative number or for Zero.Insufficient.

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

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22 Jun 2017, 07:27
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nechets wrote:
What is the value of m?

(1) |m| = −36/m

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

Target question: What is the value of m?

Statement 1: |m| = −36/m
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Let's consider the two cases: m = −36/m and m = -(-36/m)
case a: m = −36/m
multiply both sides by m to get: m² = -36
unsolvable

case b: m = -(-36/m)
Simplify: m = 36/m
multiply both sides by m to get: m² = 36
So, EITHER m = 6 OR m = -6

Test each answer choice by plugging it into the original equation

m = 6 . We get: |6| = −36/6
Evaluate: 6 = -6 doesn't work.
So, m = 6 is NOT a solution

m = -6 . We get: |-6| = −36/(-6)
Evaluate: 6 = 6 WORKS
So, m = 6 IS a solution

Since there's only one valid solution, we know that m = -6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2m + 2|m| = 0
Subtract 2m from both sides to get: 2|m| = -2m
Divide both sides by 2 to get: |m| = -m
Upon inspection we might see that there are several possible solutions, including m = 0, m = -1, m = -2 and so on.
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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22 Jun 2017, 07:30
What is the value of m?

(1) |m| = −36/m

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

Solution:

Statement 1: m has to be negative. and only possible value of m is -6. Sufficient.
Statement 2: It says m is negative. But m can take any value. Insufficient.

Therefore the answer is Option A.
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Re: What is the value of m?  [#permalink]

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22 Jun 2017, 11:18
from statement 1 we have |m| = −36/m which implies m*|m|=-36 which is only possible when we have m=-6
From statement 2 we have 2m+2|m| = 0 or m+|m|=0 this can take any value for example m=0, -1, -2,-3 etc
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Re: What is the value of m?  [#permalink]

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06 Aug 2017, 04:28
why m has to be negative??? 1 options leave m as -6 & 6 as answers.. hence not sufficient...
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Re: What is the value of m?  [#permalink]

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06 Aug 2017, 07:38
Ruchita1907 wrote:
why m has to be negative??? 1 options leave m as -6 & 6 as answers.. hence not sufficient...

Did you try to plug 6 into the equation? Does it satisfy it?

What is the value of m?

(1) |m| = −36/m.

The left hand side is an absolute value of a number (|m|), so it's non-negative, thus the right hand side (−36/m) also must be non-negative, which means that m must be negative. Now, if m is negative, then |m| = -m, so we'd have -m = -36/m, which gives m = -6. Sufficient.

(2) 2m+2|m| = 0. This transforms to |m| = -m, which implies only that m is negative or 0. Not sufficient.

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What is the value of m?  [#permalink]

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09 Aug 2017, 05:07
nechets wrote:
What is the value of m?

(1) |m| = −36/m
(2) 2m+2|m| = 0

1) |m| = $$\frac{-36}{m}$$
=> m < 0 (because |m| will always be positive => to make the right hand side positive, we would require m < 0)
=> m = -6
Sufficient.

2) 2m + 2|m| = 0
=> m < 0
BUT, any value of M <= 0 will be sufficient for this equation
=> m =0, -1, -2,....
Insufficient.

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

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05 Feb 2019, 04:30
nechets wrote:
What is the value of m?

(1) |m| = −36/m

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

Great question, m can be anything from integers to fractions

from 1 |m| = −36/m

for LHS = RHS
m = -6

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

m = -1/2 or -1

A
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Re: What is the value of m?   [#permalink] 05 Feb 2019, 04:30
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