AMC12 2002 B

AMC12 2002 B · Q8

AMC12 2002 B · Q8. It mainly tests Patterns & sequences (misc).

Suppose July of year $N$ has five Mondays. Which of the following must occur five times in the August of year $N$? (Note: Both months have $31$ days.)

假设 $N$ 年的 7 月有五个星期一。以下哪一项一定在 $N$ 年的 8 月出现五次？（注：两个月都有 $31$ 天。）

(A) Monday 星期一

(B) Tuesday 星期二

(D) Thursday 星期四

(E) Friday 星期五

Answer

Correct choice: (D)

正确答案：（D）

Solution

If there are five Mondays, there are only three possibilities for their dates: $(1,8,15,22,29)$, $(2,9,16,23,30)$, and $(3,10,17,24,31)$. In the first case August starts on a Thursday, and there are five Thursdays, Fridays, and Saturdays in August. In the second case August starts on a Wednesday, and there are five Wednesdays, Thursdays, and Fridays in August. In the third case August starts on a Tuesday, and there are five Tuesdays, Wednesdays, and Thursdays in August. The only day of the week that is guaranteed to appear five times is therefore $\boxed{\textrm{(D)}\ \text{Thursday}}$.

若有五个星期一，则它们的日期只有三种可能：$(1,8,15,22,29)$、$(2,9,16,23,30)$、以及 $(3,10,17,24,31)$。第一种情况下，8 月从星期四开始，8 月有五个星期四、星期五和星期六。第二种情况下，8 月从星期三开始，8 月有五个星期三、星期四和星期五。第三种情况下，8 月从星期二开始，8 月有五个星期二、星期三和星期四。因此唯一保证出现五次的星期几是 $\boxed{\textrm{(D)}\ \text{Thursday}}$。

Topics

LM.002 Patterns & sequences (misc)