Bunuel wrote:
What is the value of m?
(1) |m| = −36/m
(2) 2m+2|m| = 0
Project DS Butler Data Sufficiency (DS3)
For DS butler Questions Click Here Target question: What is the value of m? Statement 1: |m| = −36/m Key property: If |something| = k (where k is positive), then something = k or something = -kWhen we apply the property we get: m = -36/m or m = 36/m
Let's solve each equation separately...
Take: m = -36/m
Multiply both sides of the equation by m to get: m² = -36
Since the square of a number (e.g., m²) is always greater than or equal to 0, there are no real solutions to the equation m² = -36
Take: m = 36/m
Multiply both sides of the equation by m to get: m² = 36
So, either m = 6 or m = -6
IMPORTANT: Before we conclude that statement 1 is not sufficient, we must test each possible solution by plugging it into the original equation Let's first test m = 6.
We get |6| = -36/6, which simplifies to be |6| = -6
NOT TRUE.
So, m = 6 is an extraneous root that we must ignore.
Now we will test m = -6.
We get |-6| = -36/-6, which simplifies to be |-6| = 6
WORKS
So,
m = -6 is the only solution
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: 2m+2|m| = 0Subtract 2m from both sides of the equation to get: 2|m| = -2m
Divide both sides of the equation by 2 to get: |m| = -m
Applying the above property we get two equations: m = -m and m = m
Once again, we'll solve each equation separately.
Take: m = -m
Add m to both sides to get: 2m = 0
Solve:
m = 0Let's make sure this is an actual solution by plugging m = 0 into the original equation to get: 2(0)+2|0| = 0...WORKS!
Take: m = m
We can see right away that all values of m will satisfy the equation m = m
So, one possible value is
m = -1Let's make sure this is an actual solution by plugging m = -1 into the original equation to get: 2(-1)+2|-1| = 0...WORKS!
Since we've already identified the two possible values of m (
m = 0 and
m = -1), we know that statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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