a+b = 0 and ab =0 if and only if both a and b are = 0. That does not say anything about the choices.
The question probably has a typo.
Mantha is correct. I am disappointed that everyone else was so quick to give up. This problem is very easy to analyze using simple logic.
We are given: If ab = 0 then ab=a+b-ab which means that 0 = a+b - 0
or simply: a+b=0.
Well if ab = 0, then either a or b must be zero, hence if a+b=0, then both
a and b must be zero or else the sum cannot be zero.
Consequently, b cannot be anything but zero so the answer choices do not make sense.
However, if the condition was ab<>0, then the answer choice is obvious. b cannot possibly be zero because if it was, ab = 0. But is a trivial result so I suspect the typo may be elsewhere.
The GMAT does not test difficult math. In order to keep it difficult, it asks somewhat confusing questions that can be solved often using simple logic once one makes the effort. I have taken the test 3 times and have seen literally 1000s of practice questions. Each of those 3 times I have seen at least one question that I have never seen before.
If you fall into the habit of giving up too easily, you will always
panic whenever you see a strangely worded question. If you develop the habit of taking up the challenge, you will gain confidence over time and will actually want to see these types of questions (they will separate you from the pack).
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993