Question:
Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop?

Option A):
64
Option B):
32
Option C):
16
Option D):
8

Correct Answer is Option A):
64

Explanation:
Work backwards. If one person got off at stop 7, as the bus approached the stop there must have been two people on board. As it approached the previous stop (no. 6) there were four on board. Approaching stop 5, there were 8. Approaching stop 4, there were 16 on board. Approaching stop 3, there were 32. Approaching stop 2, there were 64. As stop 2 was the first stop at which people got off there must have been a total of 64 people who boarded at the first stop. (We are assuming that no people could have been on the bus before the first official stop.)