2006 AMC 12A Problem 4

Attempt Problem 4 of the 2006 AMC 12A 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 2006 AMC 12A solutions, or check the answer key.

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

$17$

$19$

$21$

$22$

$23$

Answer: E

Concepts:digits clock

Difficulty rating: 1050

Solution:

The two minutes digits sum to at most $5 + 9 = 14,$ at $59$ minutes past the hour. For the hour, a single digit $9$ gives digit sum $9,$ which beats any two-digit hour $(10, 11, 12$ give at most $1 + 2 = 3).$

The largest total is $14 + 9 = 23,$ occurring at $9\!:\!59.$

Thus, the correct answer is E.

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