It mostly filters for people who spend a lot of time preparing for interviews, practicing that problem or similar ones, from books of problems known to be asked by interviewers. In a more general sense it filters for people who want a job badly enough to do the goofy dance that many companies expect of candidates, and are savvy enough to know the dance exists.

“Write a function that finds the longest positive-sum subsequence in an int array and runs in O(n) time.”

That's a horrible interview question. If you know the trick (saw the question before), it's easy. If you don't know the trick, it isn't reasonable to expect someone to figure it out in 5-15 minutes.

That's a brainteaser question disguised as an algorithms question.

But there isn't really a "trick" here, though. The point of these questions is to figure out if the candidate has enough CS fundamentals to construct a reasonable solution to a problem that they've never seen before.

There is a trick. Loop over the array, remembering the maximum and minimum. If you've seen it before, the question is MUCH easier, making it a bad question.

Problems like that are the distilled versions of problems you'll often see at places like TopCoder where you have an hour and a half to solve 3 of them. They're looking for skilled TopCoder competitors, basically.