Hi, there. I'm happy to help with this.
Prompt:
What is the value of a+b+c?
Statement #1: (a+b+c)^2=0
The only way you can square something and get zero is if the thing you squared is zero.
(a+b+c)^2=0 --> a+b+c = 0
Statement #1, by itself, is
sufficient.
Statement #2: |a|+|b|+|c|=0
The absolute value of any number is greater than or equal to zero. It's greater than zero for any non-zero input, and equal to zero only when the input is zero. Since absolute value can never have a negative output, we know that:
|a|+|b|+|c|=0 --> |a| = 0 AND |b| = 0 AND |c| = 0 ---> a = 0 AND b = 0 AND c = 0
That, in turn, leads to the conclusion that a+b+c = 0. Statement #2, by itself, is
sufficient.
Answer =
D
Does that make sense? Here's a tricky DS about absolute values.
https://gmat.magoosh.com/questions/964
When you submit your answer choice, the following page has the full video explanation.
Let me know if you have any questions about this.
Mike
