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 $2003$ rd chime occur?

March $8$

March $9$

March $10$

March $20$

March $21$

Answer: B

Concepts:date and time summation process simulation

Difficulty rating: 1690

Small Hint:

In each $12$ -hour period there are $12$ half-hour chimes and $1+2+\cdots+12=78$ hour chimes

Big Hint:

A full day has $180$ chimes; count how many occur after $11{:}15$ AM on Feb $26$ and accumulate by day

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 $2003$ rd 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

Answer: B

Difficulty rating: 1690

Small Hint:

Big Hint:

Solution:

Problem 22 in Other Years