If you solve the original equation for x you get
x = (-b)/a
When would x be positive? Basically, as long as a and b are different signs.
If b is negative and a is positive, we'd have (-)(-)/+, which is +/+ which is +.
If b is positive and a is negative, we'd have (-)(+)/(-), which is -/-, which is +.
So we rephrase the question: Do A and B have opposite signs?
(We should also keep our eyes open for the possibility that it comes out to zero, as that would also be sufficient to say no, but in this case that's not really super relevant. It might have been in another problem though.)
From
statement (1) all we learn is that at least one of A or B, or both, is/are positive. It's possible that they're both positive (which would mean a "no" answer) and it's possible that one is positive and one is negative (which would mean a "yes" answer).
Insufficient.
From
statement (2) all we learn is that A is greater than B. They could be both positive or both negative, or it could be that A is positive and B is negative. That's a potential "yes" and a potential "no."
Insufficient.
Together, basically, either they're both positive, or A is positive and B is negative. That's still a potential yes and a potential no.
Insufficient even together. Choice E.
By the way, these translations make good flashcard fodder.
a - b> 0 --> a > b
a + b > 0 --> at least one of a or b (or both) is positive.
Edited to add: I think you must have typed the response above while I was typing this one up. Picking numbers has a way of making you feel out of control, doesn't it? It's a nice backup plan, though, as it did get you the right answer. However, if you learn the translations just above, you'll be more confident next time you see a question like this one.
BTW, I find this question EXTREMELY testlike. So many questions posted on this forum don't look anything like real GMAT questions. This one is super authentic.
