Fast Algorithm to Quickly Find the Range a Number Belongs to in a Set of Ranges?

Question

The Scenario

I have several number ranges. Those ranges are not overlapping - as they are not overlapping, the logical consequence is that no number can be part of

Answer 1

A balanced, sorted tree with ranges on each node seems to be the answer. I can't prove it's optimal, but if I were you I wouldn't look any further.