Martin pretended to be asleep whenever she came
into the room.
(A) whenever she came
(B) at the time she comes
(C) although she came
(D) since she came
(E) by the time she came

I would have to say that A makes the most sense. You are correct in your thinking. If you put b, c, d, and e at the end of asleep then these options don't really make sense. Hopefully this helps.

If you are looking for the best ending then I would go for "A" :)