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Problem 422

Geometry Difficulty 2.1 Find the answer CEMC Cayley

The minute hand on a clock points at the 12. After rotating $120^{\circ}$ clockwise, which number will it point at?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.