Problem 4 · 2006 AMC 8
Easy
Fractions, Decimals & Percents
net-rotation
Initially, a spinner points west. Chenille moves it clockwise 214 revolutions and then counterclockwise 334 revolutions. In what direction does the spinner point after the two moves?
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Answer: B — East.
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Hint 1 of 2
Opposite spins partly undo each other — so first combine them into ONE net turn instead of tracking two separate moves.
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Hint 2 of 2
A whole revolution always lands you back where you started, so only the leftover fraction of a turn matters. Throw away whole revolutions.
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Approach: combine into one net turn, then drop whole revolutions
- Counterclockwise wins: 3¾ − 2¼ = 1½ revolutions counterclockwise.
- A full revolution returns the spinner to where it was, so ignore the whole 1 and keep only the ½: a half-turn from west.
- Half a turn is straight across ⇒ west becomes east.
- Why discard whole turns: direction is periodic — it repeats every full revolution. Keeping only the fractional part (the "remainder" after whole turns) is the same idea you use for clock problems and any repeating cycle.
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