If we just take the largest number from each set, we have -1 from set A and 1 from set B. Add those together and you've got 0. That's the LARGEST sum you can get. So all the others must be either zero or negative, also. They are all zero or negative...every one of them!
Answer choice A.
Rant on
A really common mistake many test-takers make is applying math concepts that they learn in school when there's no need to do so. A question like this isn't on the GMAT in order to for business schools to find out whether you know the intricacies of permutations, combinations, or set theory. It's on there to test HOW YOU THINK. Business (school) isn't about showing the world how smart you are because you know math; it's about solving problems and doing things better than they've been done before. Can you come up with a way to get the right answer faster and with a decreased probability of making a mistake? Sure, there are times when you do need to know how to do the math, but if you make your GMAT studying all about mastering math and don't spend a good deal of time learning to THINK through questions without diving into the math, you're missing a huge opportunity to improve your problem solving speed and to make fewer mistakes, which means you're missing a huge opportunity to GET A BETTER SCORE. I see a ton of students who think doing the hard math somehow shows that they're smarter. Nope. Getting the right answer faster and more easily is smarter. Doing things the harder way is, well, not that smart.
/Rant off