Easy to make the assumption that since the question is seeking an integer value that the individual values must also be integers, but that is not stated as a limitation.

So the goal is to maximize both X and Y to maximize their sum.

Clearly each can be >9 and every amount below 10 that Y is must be added to 9 to create X and to create an integer result, as follows:

a=10-Y and Y=10-a
X=9+a

So X+Y = 10-a+9+a = 19,D