The numbers x and y are three-digit positive integers, and x + y is a four-digit integer.  The tens digit of x equals 7 and the tens digit of y equals 5.  If x < y, which of the following must be true?

I.  The units digit of x + y is greater than the units digit of either x or y.
II.  The tens digit of x + y equals 2.
III.  The hundreds digit of y is at least 5.