1989 AMC 8 Problem 10

Below is the professionally curated solution for Problem 10 of the 1989 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1989 AMC 8 solutions, or check the answer key.

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

Concepts:clock

Difficulty rating: 730

10.

How many degrees are in the smaller angle between the hour hand and the minute hand of a clock that reads seven o'clock?

$50^\circ$

$120^\circ$

$135^\circ$

$150^\circ$

$165^\circ$

The $12$ numbers divide the clock into $12$ equal sections of $\frac{360^\circ}{12} = 30^\circ$ each.

At seven o'clock the hands point to $12$ and $7,$ which are $5$ sections apart the short way, giving $5 \times 30^\circ = 150^\circ.$

Thus, the correct answer is D .