Question

一座钟每小时过 $30$ 分钟时敲一次，整点时按小时数敲钟。例如下午一点敲一次，中午和午夜都敲十二次。从二〇〇三年二月二十六日上午十一点十五分开始，第二〇〇三次钟声会发生在哪一天？

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?

三月八日

March 8

三月九日

March 9

三月十日

March 10

三月二十日

March 20

三月二十一日

March 21

答案：B

知识点：日期与时间求和过程模拟

难度评级：1690

解答：

每 $12$ 小时有 $12 + 78 = 90$ 次钟声，所以每天有 $180$ 次钟声。

从二月二十六日上午十一点十五分之后，到当天结束有 $91$ 次钟声。之后每天增加 $180$ 次，到三月八日结束时累计达到 $1891$ 次。

剩余钟声发生在三月九日；第二〇〇三次钟声是当天第 $112$ 次钟声，发生在三月九日下午三点半。

所以正确答案是 B。

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 第 22 题

答案：B

难度评级：1690

解答：

其他年份的第 22 题