Creeper300 wrote:

a^2+b^2=6, a+b=?

1. b-a=2

2. a=-b

What is the source of this question? The question is certainly not GMAT specific.

From statement II, you get a = -b, so a + b = 0

While from statement I, you get \((a + b) = \sqrt{8} or -\sqrt{8}\)

Both statements need to give at least one same value of a + b. It isn't possible that (a + b) is both 0 and \(\sqrt{8} or -\sqrt{8}\)

Data Sufficiency questions are like puzzles.

I have an equation on a paper and I ask you, what is the sum of a and b? (Question Stem)

You say that you do not know.

I give you a hint - b - a = 2. (Statement I)

You analyze the hint and say a + b is either root 8 or - root 8.

I decide to give you another hint to solve the puzzle. b - a = 0. (Statement II)

This is incorrect, isn't it? It is the same equation I am asking about. How can a + b be both 0 and either root 8 or - root 8.

Since it is the same puzzle, my hints (i.e. the two statements) cannot contradict each other.

I never thought about that when I was preparing for GMAT. So you are saying that ultimately the answer to the question (a+b) =? should have the same answer from the 2 hints and if the 2 hints give different answers then it doesn't make sense.