2022 AMC 10B Problem 4

Problem 4 of 25EasierAlgebra

A donkey suffers an attack of hiccups and the first hiccup happens at

4:00

one afternoon. Suppose that the donkey hiccups regularly every

5

seconds. At what time does the donkey’s

700

th hiccup occur?

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Solution

Since we want to look at the

700

th hiccup, we need to look at time that is

699

hiccups after the first one. This would be

699\cdot 5 = 3495

seconds. Note that

3495 = 60\cdot 58+15,

so the time would be

58

minutes and

15

seconds after the first hiccup. This would therefore be

4:58

and

15

seconds. Thus, the answer is A .