Difference between revisions of "2006 AMC 12A Problems/Problem 4"
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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? | A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display? | ||
| − | <math> \mathrm{(A) \ | + | <math>\mathrm{(A)}\ 17\qquad\mathrm{(B)}\ 19\qquad\mathrm{(C)}\ 21\qquad\mathrm{(D)}\ 22\mathrm{(E)}\ 23</math> |
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== Solution == | == Solution == | ||
| − | + | From the [[greedy algorithm]], we have <math>9</math> in the hours section and <math>59</math> in the minutes section. <math>9+5+9=23\Rightarrow\mathrm{(E)}</math> | |
| − | From the [[greedy algorithm]], we have 9 in the hours section and 59 in the minutes section. <math>9+5+9=23 \Rightarrow \mathrm {(E)}</math> | ||
== See also == | == See also == | ||
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{{AMC12 box|year=2006|ab=A|num-b=3|num-a=5}} | {{AMC12 box|year=2006|ab=A|num-b=3|num-a=5}} | ||
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] | ||
Revision as of 23:33, 27 April 2008
Problem
A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display?
Solution
From the greedy algorithm, we have 
in the hours section and 
in the minutes section. 
See also
| 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 | |
