The answer is yes, and no. I'll explain why.
(This is a very VERY poorly written problem.)
The elevator cable snaps, and you and the elevator go into free fall.
As you and the elevator fall, the elevator will fall
FASTER than you do, because it weighs
MORE than you do. Because the elevator falls faster, there is the possiblity that it looses contact with your feet.
case (1): The elevator separates from you before reaching terminal velocity. Here, you can jump *BEFORE* you separate from the floor. But if you dont, there's still hope!
The elevator will reach a faster terminal velocity than you do because it weighs more, as already mentioned. BUT, as the elevator nears the bottom, it is going to compress the column of air that was below the elevator. This net
pressure force will retard the motion of the elevator.
IF it can slow the elevator down fast enough, you
might be able to catch back up and remake contact with the floor (But perhaps a few split seconds before impact

).
But then again, if the elevator is high enough, it could maintain its higher terminal velocity for a long enough duration that the distance between you and the elevator becomes so great that the dampening caused by the cushion of air below the elevator occurs before you ever catch back up.
case (2): another possible case is that you never separate before reaching reaching terminal velocity with the elevator. This occurs if the elevator falls at a rate that is
negligible as compared to your rate of descent. You can jump from the floor at *ANY* point along your fall.