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Problem 529

AMC 12 late, AIME early

Geometry Difficulty 4.9 Find the answer

The minute hand on a clock points at the 12. The minute hand then rotates $120^{\circ}$ clockwise. Which number will it be pointing at?
(A) 6
(B) 2
(C) 4
(D) 3
(E) 5

Your answer

Official solution

Since there are 12 equally spaced numbers and the total angle in a complete circle is $360^{\circ}$ , then the angle between two consecutive numbers is $360^{\circ} \div 12=30^{\circ}$ .

To rotate $120^{\circ}$ , the minute hand must move by $120^{\circ} \div 30^{\circ}=4$ numbers clockwise from the 12 . Therefore, the hand will be pointing at the 4 .

ANsWER: (C)

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.