2022 AMC 10B Problems/Problem 4
Contents
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
Video Solution 1
~Education, the Study of Everything
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 |
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