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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

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.

The answer is A 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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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.

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.

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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