Question

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?

$15 \text{ seconds after } 4:58$

$20 \text{ seconds after } 4:58$

$25 \text{ seconds after } 4:58$

$30 \text{ seconds after } 4:58$

$35 \text{ seconds after } 4:58$

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 .

2022 AMC 10B Problem 4

Solution:

Problem 4 in Other Years