I tend to think that this is just not a very good question. D tells us why the symptoms would start showing more than a week after the picnic, but does nothing to address the fact that only 8 people tested positive, or that more than a week = two weeks exactly. So, this isn't a particularly well-written problem/answer choice.

But to your question:

Is it O.K. to eliminate 4 options on solid grounds and select the fifth option even if I am not sure why it is right?

Well, yes. There are certainly times that my fellow instructors and I have told students "look, I agree that it's not a very good answer. But you have to pick one, so pick the least terrible one!" Because CR is more open to interpretation than, say, the quant section, the answers will not always be perfect. Here, we're looking for "best supports," not "100% completely perfectly supports."

Your goal should be to prove answer choices WRONG, not find the right one. If you're doing that well, you'll often find reasons to quibble with all 5! Then just ask yourself - which answer choices do I have the strongest arguments against? If you have more solid logical grounds to eliminate the other 4, pick the 5th one without worrying too much about the fact that it's not perfect.