2022 AMC 10B Problems/Problem 4
Problem
A donkey suffers an attack of hiccups and the first hiccup happens at 
one afternoon. Suppose that
the donkey hiccups regularly every 
seconds. At what time does the donkey’s 
th hiccup occur?
Troll Solution
Obviously, the donkey will have its th hiccup 
seconds after the moment it started. This is 
.
This is not correct, though. Hiccup number 
occurred at 
, so actually the time of hiccup 
is 
.
Solution 1
Since the donkey hiccupped the 1st hiccup at , he hiccupped for 
seconds, which is 
minutes and 
seconds, so the answer is 
.
~MrThinker
Solution 2 (Faster)
We see that the minute has already been determined.
The donkey hiccups once every 5 seconds, or 12 times a minute. 
(mod 12), so the 700th hiccup happened on the same second as the 4th, which occurred on the 
th second. .
~not_slay
See Also
| 2022 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2022 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
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