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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display?
Small hint:
Maximize the minutes digits and the hour digits separately
Big hint:
The two minutes digits sum to at most the best hour is the single digit
Solution:
The two minutes digits sum to at most at minutes past the hour. For the hour, a single digit gives digit sum which beats any two-digit hour give at most
The largest total is occurring at
Thus, the correct answer is E.
Problem 4 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
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