1957 AMC 12 Problem 11

Attempt Problem 11 of the 1957 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 1957 AMC 12 solutions, or check the answer key.

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

11.

The angle formed by the hands of a clock at

2:15

is:

30^\circ

27\frac12^\circ

157\frac12^\circ

172\frac12^\circ

none of these

2:15,

the minute hand is at

90^\circ

from twelve

The hour hand has advanced one quarter of the

30^\circ

interval from two to three

The minute hand is

90^\circ

clockwise from twelve. The hour hand is

2(30^\circ)+\frac14(30^\circ)=67.5^\circ

from twelve. Their smaller angle is

90^\circ-67.5^\circ=22.5^\circ,

which is not listed.

Therefore, the correct answer is E.

Problem 11 in other years