Q:

Guess the numbers

One day Bob and Alice walk around they were having the following conversation:

Bob: Alice go ahead and pick any random number.
Alice: Okay, I have one.
Bob: Alice multiply the random number by X and sum every single digit(s) until it's Y digit(s) left.
Alice: Done.
Bob: I would bet that the result is an odd number.
Alice: Well, yeah. It's either odd or even either way. You just got lucky!
Bob: How about I said that it was X?
Alice: How do you know?
Bob: Well, that's simply because <reasoning>

What number are X and Y? Can anyone explain Bob's <reasoning>?

 Fun fact: There is a related thread in Math.SE which explains Bob's reasoning. When the question digits are added it would be X-4.

A:

X is 9 and Y is 1, because whenever you multiply a number by nine, the sum of its digits is either nine or a multiple of nine. Nine is the only one digit number that is a multiple of nine.

