At a two-day seminar, 90 percent of those registered attended the seminar on the first day. What percent of those registered did not attend the seminar on either day?

(1) A total of 1,000 people registered for the two-day seminar

(2) Of those registered, 80 percent attended the seminar on the second day.



Circle #1 is first day attendants, circle #2 is second day attendants, the overlap is attendants for both days, and Neither is the space outside the diagram.

The information from the original problem plus statement (1) give you the first circle (900). Insufficient to solve for Neither.
The information from the original problem plus statement (2) give you the second circle (800). Also Insufficient to solve for Neither.

Together, you still have no idea how many individuals addended Both days. Since the proper formula for such a situation is
Total = Group 1 + Group 2 - Both + Neither, in our case we have
1000 = 900 + 800 - Both + Neither.
Since we are still left with two variables (B and N), the correct answer is E.