2003 AMC 8 Problem 20

Attempt Problem 20 of the 2003 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

20.

What is the measure of the acute angle formed by the hands of a clock at 4:204{:}20 a.m.?
0∘0^{\circ}
5∘5^{\circ}
8∘8^{\circ}
10∘10^{\circ}
12∘12^{\circ}
Answer: D
Concepts:clock
Small hint:
At 4:20,4{:}20, the minute hand points at 4.4.
Big hint:
The hour hand has moved one third of the way from 44 to 5.5.
Solution:
At 4:20,4{:}20, the hour hand will be 13\frac{1}{3} of the way between 44 and 5.5.
Each hour represents 360÷12=30∘.360 \div 12 = 30^{\circ}. This means the hour hand will be 30÷3=10∘30 \div 3 = 10^{\circ} past 4.4.
At 2020 minutes, the minute hand points to 4,4, so the acute angle between the hands is 10∘.10^{\circ}.
Thus, D is the correct answer.
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