Question

A clock chimes once at $30$ minutes past each hour and chimes on the hour according to the hour. For example, at 1 PM there is one chime and at noon and midnight there are twelve chimes. Starting at 11:15 AM on February 26, 2003, on what date will the 2003rd chime occur?

March 8

March 9

March 10

March 20

March 21

Solution:

Each $12$ -hour period has $12 + 78 = 90$ chimes, so each full day has $180.$

After 11:15 AM on February 26, the rest of that day has $91$ chimes. Adding $180$ for each following full day, the count reaches $1891$ by the end of March 8.

The remaining chimes fall on March 9: the 2003rd chime is the $112$ th chime of that day, occurring at 3:30 PM on March 9.

Thus, the correct answer is B.

2003 AMC 10B Problem 22

Solution:

Problem 22 in Other Years