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

Revision as of 00:04, 28 April 2008

The following problem is from both the 2006 AMC 12A #4 and 2008 AMC 10A #4, so both problems redirect to this page.

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

$\mathrm{(A)}\ 17\qquad\mathrm{(B)}\ 19\qquad\mathrm{(C)}\ 21\qquad\mathrm{(D)}\ 22\qquad\mathrm{(E)}\ 23$

From the greedy algorithm, we have $9$ in the hours section and $59$ in the minutes section. $9+5+9=23\Rightarrow\mathrm{(E)}$

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

2006 AMC 10A (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 10 Problems and Solutions

@@ Line 1: / Line 1: @@
+{{duplicate|[[2006 AMC 12A Problems|2006 AMC 12A #4]] and [[2006 AMC 10A Problems/Problem 4|2008 AMC 10A #4]]}}
 == Problem ==
 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)}\ 17\qquad\mathrm{(B)}\ 19\qquad\mathrm{(C)}\ 21\qquad\mathrm{(D)}\ 22\mathrm{(E)}\  23</math>
+<math>\mathrm{(A)}\ 17\qquad\mathrm{(B)}\ 19\qquad\mathrm{(C)}\ 21\qquad\mathrm{(D)}\ 22\qquad\mathrm{(E)}\  23</math>
 == Solution ==
@@ Line 10: / Line 10: @@
 == See also ==
 {{AMC12 box|year=2006|ab=A|num-b=3|num-a=5}}
+{{AMC10 box|year=2006|ab=A|num-b=3|num-a=5}}
 [[Category:Introductory Number Theory Problems]]