AMC10 2006 A

AMC10 2006 A · Q4

AMC10 2006 A · Q4. It mainly tests Rounding & estimation, Money / coins.

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

一个数字手表显示小时和分钟，并带有AM和PM标识。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

(E) The largest possible sum of the two digits representing the minutes is 5+9 = 14, occurring at 59 minutes past each hour. The largest possible single digit that can represent the hour is 9. This exceeds the largest possible sum of two digits that can represent the hour, which is 1 + 2 = 3. Therefore, the largest possible sum of all the digits is 14 + 9 = 23, occurring at 9:59.

（E）表示分钟的两位数字之和最大为$5+9=14$，出现在每小时的$59$分。表示小时的最大一位数字是$9$。这大于表示小时的两位数字之和的最大值，即$1+2=3$。因此，所有数字之和的最大值为$14+9=23$，发生在$9:59$。

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