Difference between revisions of "2022 AMC 10B Problems/Problem 4"
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<math>\textbf{(E) }35 \text{ seconds after } 4:58</math> | <math>\textbf{(E) }35 \text{ seconds after } 4:58</math> | ||
| − | ==Solution== | + | ==Solution 1== |
Since the donkey hiccupped the 1st hiccup at <math>4:00</math>, he hiccupped for <math>5 \cdot (700-1) = 3495</math> seconds, which is <math>58</math> minutes and <math>15</math> seconds, so the answer is <math>\boxed{\textbf{(A) }15 \text{ seconds after } 4:58}</math>. | Since the donkey hiccupped the 1st hiccup at <math>4:00</math>, he hiccupped for <math>5 \cdot (700-1) = 3495</math> seconds, which is <math>58</math> minutes and <math>15</math> seconds, so the answer is <math>\boxed{\textbf{(A) }15 \text{ seconds after } 4:58}</math>. | ||
~MrThinker | ~MrThinker | ||
| + | |||
| + | ==Solution 2== | ||
| + | |||
| + | We see that the minute has already been determined. | ||
| + | The donkey hiccups once every 5 seconds, or 12 times a minute. <math>700\equiv4</math> (mod 12), so the 700th hiccup happened on the same second as the 4th, which occurred on the <math>3(4-1)=15</math>th second. <math>\boxed{\textbf{(A) }15 \text{ seconds after } 4:58}</math>. | ||
== See Also == | == See Also == | ||
Revision as of 22:21, 17 November 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
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. .
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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
