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.