Difference between revisions of "2003 AMC 8 Problems/Problem 20"
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| + | ==Problem== | ||
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| + | What is the measure of the acute angle formed by the hands of the clock at 4:20 PM? | ||
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| + | <math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 8 \qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}</math> | ||
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==Solution== | ==Solution== | ||
| − | Imagine the clock as a circle. By <math>4:20</math>, the hour hand would have moved <math>\frac{1}{3}</math> way towards the five since <math>\frac{20}{60}</math> is reducible to <math>\frac{1}{3}</math>. The central angle formed between <math>4</math> and <math>5</math> would be <math>30</math> degrees since the angle between <math>12</math> and <math>6</math> is <math>180</math> degrees and <math>\frac{180}{6} = 30</math> Since the central angle formed from <math>4:20</math> is a third of the central angle formed between <math>4</math> and <math>5</math>, <math>30</math> degrees, the answer is <math>\boxed{\textbf{(D)}\ 10}</math> | + | Imagine the clock as a circle. By <math>4:20</math>, the hour hand would have moved <math>\frac{1}{3}</math> way towards the five since <math>\frac{20}{60}</math> is reducible to <math>\frac{1}{3}</math>. The central angle formed between <math>4</math> and <math>5</math> would be <math>30</math> degrees since the angle between <math>12</math> and <math>6</math> is <math>180</math> degrees and <math>\frac{180}{6} = 30</math> Since the central angle formed from <math>4:20</math> is a third of the central angle formed between <math>4</math> and <math>5</math>, <math>30</math> degrees, the answer is <math>\boxed{\textbf{(D)}\ 10}</math>. |
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| + | ==See Also== | ||
{{AMC8 box|year=2003|num-b=19|num-a=21}} | {{AMC8 box|year=2003|num-b=19|num-a=21}} | ||
Revision as of 04:09, 24 December 2012
Problem
What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?
Solution
Imagine the clock as a circle. By 
, the hour hand would have moved 
way towards the five since 
is reducible to . The central angle formed between 
and 
would be 
degrees since the angle between 
and 
is 
degrees and 
Since the central angle formed from is a third of the central angle formed between and , degrees, the answer is 
.
See Also
| 2003 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
