2010 AMC 10B 第 5 题

Question

某个有

31

天的月份中，星期一和星期三的天数相同。这个月的第一天可能是七天中的多少种？

A month with

31

days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?

2

3

4

5

6

31

天中，有三个星期几会多出现一次。

In

31

days, three weekdays occur one extra time

星期一和星期三必须同时是多出的日子，或同时不是。

Monday and Wednesday must either both be extra days or both not be extra days

注意

31

除以

7

时余数为

3

。

因此，如果这个月从星期六、星期日、星期二或星期三开始，星期一和星期三的天数就不相等。

所以这个月只能从星期一、星期四或星期五开始。

所以正确答案是 B。

Note that

31

days leaves a remainder of

3

when divided by

7.

This means that if the month starts on a Saturday, Sunday, Tuesday, or Wednesday, there will be an uneven number of Mondays and Wednesdays.

Then the month can only start on a Monday, Thursday, or Friday.

Thus, B is the correct answer.

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