At least \(15\) percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was \(20\) percent greater than that for Professor Tyler’s course. If \(120\) students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?

I. \(147\)
II. \(162\)
III. \(185\)

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III

OA E