Art of Problem Solving

2006 AMC 12A Problems/Problem 4: Difference between revisions

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Solution
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== Solution ==
== 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.


== See also ==
== See also ==
* [[2006 AMC 12A Problems]]
* [[2006 AMC 12A Problems]]

Revision as of 21:09, 11 July 2006

Problem

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

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

$\mathrm{(E) \ }  23$

Solution

The sum of digits is largest when the number of hours is $9$ and the number of minutes is $59$. Therefore, the largest possible sum of digits is $9+5+9=23$. The answer is E.

See also