Difference between revisions of "2006 AMC 12A Problems/Problem 4"

Revision as of 12:22, 28 October 2007

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

$\mathrm{(A) \ } 17\qquad \mathrm{(B) \ } 19\qquad \mathrm{(C) \ } 21\qquad \mathrm{(D) \ } 22$

$\mathrm{(E) \ } 23$

From the greedy algorithm, we have 9 in the hours section and 59 in the minutes section. $9+5+9=19 \Rightarrow \mathrm {(E)}$

2006 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

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 == Solution ==
-The sum of digits is largest when the number of hours is <math>9</math> and the number of minutes is <math>59</math>.  Therefore, the largest possible sum of digits is <math>9+5+9=23</math>.  The answer is E.
+From the [[greedy algorithm]], we have 9 in the hours section and 59 in the minutes section. <math>9+5+9=19 \Rightarrow \mathrm {(E)}</math>
 == See also ==