What does it mean for the ranges to overlap? It means there exists some number C which is in both ranges, i.e.
x1 <= C <= x2
and
y1 <= C <= y2
To avoid confusion, considering the ranges are:
[x1:x2] and [y1:y2]
Now, if we are allowed to assume that the ranges are well-formed (so that x1 <= x2 and y1 <= y2) then it is sufficient to test
x1 <= y2 && y1 <= x2
OR
(StartA <= EndB) and (EndA >= StartB)