BTGModeratorVI wrote: ↑Mon Jun 22, 2020 6:14 am
What is the value of m?
(1) |m| = −36/m
(2) 2m + 2|m| = 0
Answer:
A
Source: Economist GMAT
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
Answer: A
