seyna wrote:Is n<0?
1) -n = |-n|
2) n² = 16

When we list numbers for statement 1, are we supposed to add zero? Is it valid to write -(-0)=|-0|?

Sure, n = 0 satisfies the equation -n=|-n|

Here's my full solution:

Target question: Is n less than zero?

Statement 1: -n = |-n|
There are several values of n that satisfy this condition. Here are two:
Case a: n = -1, in which case n IS less than 0
Case b: n = 0, in which case n is NOT less than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n² = 16
There are exactly two values of n that satisfy this equation:
Case a: n = -4, in which case n IS less than 0
Case b: n = 4, in which case n is NOT less than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells that n equals EITHER 4 or -4
Of these two possible values of n, only -4 meets the condition in statement 1 (-n = |-n|)
So, n MUST EQUAL -4, in which case n is definitely less than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

seyna wrote:Thank you!

I asked 'is it valid to write -(-0)=|-0|?' because since 0 is neither negative nor positive I was thinking -(-0)=|-0| might not be valid.

That's totally understandable; zero is a strange value in many ways.

Another way to look at a negative sign in front of a variable, is to rewrite it as a product with (-1)
That is, -n is the same as (-1)(n)

So, when we test n = 0, we get: (-1)(0) = |(-1)(0)|
Simplify to get: 0 = 0

Cheers,
Brent