2006 AMC 10A Problem 4

Question

A digital watch displays hours and minutes with am and pm. What is the largest possible sum of the digits in the display?

17

19

21

22

23

The display uses a

12

-hour clock, so the hour is

1

through

12

Maximize the minutes’ digit sum and the hour’s digit sum separately

The minutes run from

00

to

59,

so the largest digit sum for the minutes is

5 + 9 = 14,

at

59

minutes.

For the hour, the single digit

9

beats

1 + 2 = 3

from

12.

The largest total is

9 + 14 = 23,

occurring at

9\!:\!59.

Thus, the correct answer is E.

Problem 4 in other years