AMC12 2006 A

AMC12 2006 A · Q4

AMC12 2006 A · Q4. It mainly tests Rounding & estimation, Digit properties (sum of digits, divisibility tests).

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

一块电子表以小时和分钟显示时间，并标有AM和PM。显示中各位数字之和的最大可能值是多少？

(A) 17 17

(B) 19 19

(D) 22 22

(E) 23 23

Answer

Correct choice: (E)

正确答案：（E）

Solution

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

由贪心法可得小时部分取$9$，分钟部分取$59$。$9+5+9=\boxed{\textbf{(E) }23}$

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