2014-11-10 09:00:04

A bus is driving through Smithtown. At the bus stop on A Street, half the passengers get off and 5 get on. At the bus stop on B Street, half get off, and 4 get on. At the final stop, on C Street, all of the remaining 12 passengers get off. How many people were on the bus before it stopped at A Street?

(A) 8
(B) 13
(C) 16
(D) 22
(E) 24

The correct answer is D
Explanation: Work backwards from the most specific information in the passage: the number of people who exited the bus at C Street. There were 12 people on the bus at that time, and that includes the 4 who got on at B Street. Thus, there were 8 passengers on the bus after half the bus exited at B Street, meaning that there were 16 passengers on the bus before it stopped at B Street. That includes the 5 who got on at A Street, meaning there were 11 people who did not exit the bus at B Street. As 11 people is half the passengers on the bus at A street, there must have been 22 people on the bus at that time.

This can be expressed in a table too:

Before A Street: 22 passengers
At A Street: 11 get off, 5 get on

Before B Street: 16 passengers
At B Street: 8 get off, 4 get on.

At C Street: all 12 passengers get off.

Thus, the bus had 22 passengers before it got to A Street, so choice D is correct.