I think that the question is supposed to end as "when S is divided by T?"
I would solve it this way:
Let's say the remainder = R.
This means that R/T must equal .12 because that is the very definition of a remainder.
Then you substitute in each of the answers for R until you get a value of T that is an integer.
Because the question asks "which of the following COULD be the remainder...", it is pretty much saying that only one of them could possibly be a remainder and that would be the one where the solved-for value of T is an integer.
The only remainder in the choices given that yields T as an integer is 45.
I don't know how the OG11
solved it because I don't have a copy of it. I'm taking my GMAT in July and I just ordered my copy of it. I'm curious as to how they solve it. Do you mind posting their solution?