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.
A. II only
B. III only
C. I and II
D. I and III
E. II and III
I. Not true: eg. 5+6 = 11 and 1< 5 or 6
II. Not true: if units digit sum is > 10, then tens digit = 3
III Not true: x+y needs to be greater than 999 and smaller than 1999. If y hundreds unit =5, x will be <5, and only if hundreds units of x is =, then x+ will have four digits. If x=3,2 or 1, then x+y will have three digits.
If III. were "The hundreds digit of x is at least 5" or the stem said "x>y" then III would be true.
Am I getting something wrong here??