Difference between revisions of "2022 AMC 10B Problems/Problem 4"
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We see that the minute has already been determined. | We see that the minute has already been determined. | ||
| − | The donkey hiccups once every 5 seconds, or 12 times a minute. <math>700\ | + | The donkey hiccups once every 5 seconds, or 12 times a minute. <math>700\equiv 4 \pmod{12}</math>, so the 700th hiccup happened on the same second as the 4th, which occurred on the <math>5(4-1)=15</math>th second. <math>\boxed{\textbf{(A) }15 \text{ seconds after } 4:58}</math>. |
~not_slay and HIPHOPFROG1 | ~not_slay and HIPHOPFROG1 | ||
Revision as of 19:34, 7 December 2022
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?
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. 
, so the 700th hiccup happened on the same second as the 4th, which occurred on the 
th second. .
~not_slay and HIPHOPFROG1
Bogus 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 
.
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
