BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:13 am
What is the value of m?
(1) |m| = −36/m
(2) 2m+2|m| = 0
Answer:
A
Source: Economist GMAT
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
Answer: A
