Question

A ferry boat shuttles tourists to an island every hour starting at $10$ am until its last trip, which starts at $3$ pm. One day the boat captain notes that on the $10$ am trip there were $100$ tourists on the ferry boat, and that on each successive trip, the number of tourists was $1$ fewer than on the previous trip. How many tourists did the ferry take to the island that day?

$585$

$594$

$672$

$679$

$694$

Answer: A

Concepts:arithmetic sequence summation

Difficulty rating: 970

Solution:

The ferry makes $6$ trips: at $10,$ $11,$ $12,$ $1,$ $2,$ and $3.$

The numbers of tourists are $100,99,98,97,96,95,$ so the total is $\begin{gathered} 6\cdot100-(1+2+3+4+5) \\ =600-15 \\ =585. \end{gathered}$

Thus, A is the correct answer.

2010 AMC 12A Problem 2

Answer: A

Difficulty rating: 970

Solution:

Problem 2 in Other Years