AMC12 2010 B
AMC12 2010 B · Q4
AMC12 2010 B · Q4. It mainly tests Patterns & sequences (misc).
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?
一个有 $31$ 天的月份，星期一和星期三的数量相同。这个月的第一天可能是星期中的哪几天？
(A)
2
2
(B)
3
3
(C)
4
4
(D)
5
5
(E)
6
6
Answer
Correct choice: (B)
正确答案：（B）
Solution
$31 \equiv 3 \pmod {7}$ so the week cannot start with Saturday, Sunday, Tuesday or Wednesday as that would result in an unequal number of Mondays and Wednesdays. Therefore, Monday, Thursday, and Friday are valid so the answer is $\boxed{B}$.
$31 \equiv 3 \pmod {7}$，因此这一周不可能从星期六、星期日、星期二或星期三开始，否则星期一和星期三的数量将不相等。因此，星期一、星期四和星期五都可行，所以答案是 $\boxed{B}$。
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