Question

Zoey 一本一本地读了 $15$ 本书。第一本书花了她 $1$ 天，第二本花了 $2$ 天，第三本花了 $3$ 天，依此类推，每一本都比前一本多花 $1$ 天。Zoey 在星期一读完第一本书，在星期三读完第二本书。她会在星期几读完第 $15$ 本书？

Zoey read $15$ books, one at a time. The first book took her $1$ day to read, the second book took her $2$ days to read, the third book took her $3$ days to read, and so on, with each book taking her $1$ more day to read than the previous book. Zoey finished the first book on a Monday, and the second on a Wednesday. On what day of the week did she finish her $15$ th book?

星期日

Sunday

星期一

Monday

星期三

Wednesday

星期五

Friday

星期六

Saturday

答案：B

知识点：三角形数模运算

难度评级：1020

解答：

读完 $15$ 本书共需要 $\dfrac{ 15\cdot 16}{2} =120$ 天。因此第十五本读完是在第一本读完后的 $120-1=119$ 天。因为这是 $7$ 的倍数，所以第 $15$ 本是在与第 $1$ 本相同的星期几读完的，也就是星期一。

所以正确答案是 B。

The number of days it takes to read $15$ books is $\dfrac{ 15\cdot 16}{2} =120.$ Therefore, it is $120-1=119$ days after the first book is read. This is a multiple of $7,$ so the $15$ th book was finished on the same day as the $1$ st book. Therefore, it was finished on a Monday.

Thus, the correct answer is B .

2016 AMC 10B 第 4 题

答案：B

难度评级：1020

解答：

其他年份的第 4 题