Ask HN: What's your speciality, and what's your "FizzBuzz" equivalent?
I was a mathematician, and now work in finance (systematic trading). I've found a reasonable negative filter is  A jar has 1000 coins, of which 999 are fair and 1 is double
  headed. Pick a coin at random, and toss it 10 times. Given
  that you see 10 heads, what is the probability that the next
  toss of that coin is also a head?

That tests their ability to turn a problem into mathematics, and some very basic conditional probability. Another common question (that I don't use myself) is to ask what happens to bond prices if interest rates go up.