1951 AMC 12 Problem 12

Attempt Problem 12 of the 1951 AMC 12 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 1951 AMC 12 solutions, or check the answer key.

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

12.

2{:}15

o’clock, the hour and minute hands of a clock form an angle of:

30^\circ

5^\circ

22\dfrac12^\circ

7\dfrac12^\circ

28^\circ

2{:}15

the minute hand is at

90^\circ

from

12

The hour hand moves

0.5^\circ

per minute in addition to its position at

2{:}00

2{:}15

the minute hand is

90^\circ

from

12.

The hour hand is

2\cdot30^\circ+15\cdot0.5^\circ=67.5^\circ

from

12.

Their angle is

90^\circ-67.5^\circ=22.5^\circ=22\dfrac12^\circ.

Thus, the correct answer is C.

Problem 12 in other years