2022 AMC 10B 第 4 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

4.

一头驴突然打嗝,第一次打嗝发生在某天下午 4:004:00。假设它每隔 55 秒规律地打一次嗝。它第 700700 次打嗝发生在什么时间?

A donkey suffers an attack of hiccups and the first hiccup happens at 4:004:00 one afternoon. Suppose that the donkey hiccups regularly every 55 seconds. At what time does the donkey’s 700700th hiccup occur?

4:584:58 后 1515 秒

1515 seconds after 4:584:58

4:584:58 后 2020 秒

2020 seconds after 4:584:58

4:584:58 后 2525 秒

2525 seconds after 4:584:58

4:584:58 后 3030 秒

3030 seconds after 4:584:58

4:584:58 后 3535 秒

3535 seconds after 4:584:58

答案:A
知识点:等差数列单位换算
难度评级:870
小提示:

将 4:004{:}00 之后经过的秒数换算成分钟和秒

Convert the elapsed seconds past 4:004{:}00 into minutes and seconds

大提示:

数出 4:004{:}00 之后经过的五秒间隔数

Count the number of five-second intervals after 4:004{:}00

解答:

要求第 700700 次打嗝,就要看它比第一次晚了 699699 个间隔。

这相当于 699⋅5=3495699\cdot 5 = 3495 秒。注意 3495=60⋅58+153495 = 60\cdot 58+15,所以这个时刻在第一次打嗝之后 5858 分 1515 秒。因此它是 4:584:58 再过 1515 秒。

所以答案是 A。

Since we want to look at the 700700th hiccup, we need to look at time that is 699699 hiccups after the first one.

This would be 699⋅5=3495699\cdot 5 = 3495 seconds. Note that 3495=60⋅58+15,3495 = 60\cdot 58+15, so the time would be 5858 minutes and 1515 seconds after the first hiccup. This would therefore be 4:584:58 and 1515 seconds.

Thus, the answer is A .

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