2006 AMC 10A Problem 4

Below is the professionally curated solution for Problem 4 of the 2006 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 10A solutions, or check the answer key.

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Concepts:clockdigitsoptimization

Difficulty rating: 1030

4.

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

1717

1919

2121

2222

2323

Solution:

The minutes run from 0000 to 59,59, so the largest digit sum for the minutes is 5+9=14,5 + 9 = 14, at 5959 minutes.

For the hour, the single digit 99 beats 1+2=31 + 2 = 3 from 12.12. The largest total is 9+14=23,9 + 14 = 23, occurring at 9 ⁣: ⁣59.9\!:\!59.

Thus, the correct answer is E.

Problem 4 in Other Years