AMC10 2010 B

AMC10 2010 B · Q5

AMC10 2010 B · Q5. 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 天的月份中，周一和周三的数量相同。这个月的第一天可能是星期中的哪几天？

(A) 2 2

(B) 3 3

(D) 5 5

(E) 6 6

Answer

Correct choice: (B)

正确答案：（B）

Solution

A month with 31 days has 3 successive days of the week appearing five times and 4 successive days appearing four times. If Monday and Wednesday appear five times then Monday must be the first day of the month. If Monday and Wednesday appear only four times then either Thursday or Friday must be the first day of the month. Hence there are 3 days of the week that could be the first day of the month.

31 天的一个月中有 3 个连续的星期连续出现 5 次，4 个连续的星期出现 4 次。如果周一和周三都出现 5 次，则第一天必须是周一。如果周一和周三都只出现 4 次，则第一天必须是周四或周五。因此，可能有 3 天可以是这个月的第一天。

Topics

LM.002 Patterns & sequences (misc)