AMC10 2016 B

AMC10 2016 B · Q4

AMC10 2016 B · Q4. It mainly tests Arithmetic sequences basics.

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 15th book?

佐伊一次读一本书，共读了15本。第一本花了她1天读完，第二本花了她2天读完，第三本花了她3天读完，依此类推，每本书比前一本多花1天。佐伊在星期一读完第一本，在星期三读完第二本。她读完第15本是在星期几？

(A) Sunday 星期日

(B) Monday 星期一

(D) Friday 星期五

(E) Saturday 星期六

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): It took Zoey $1+2+3+\cdots+15=\frac{15\cdot16}{2}=120$ days to read the 15 books. Because $120=7\cdot17+1$, it follows that Zoey finished the 15th book on the same day of the week as the first, a Monday.

答案（B）：Zoey读完这15本书共用了 $1+2+3+\cdots+15=\frac{15\cdot16}{2}=120$ 天。因为 $120=7\cdot17+1$，所以Zoey读完第15本书的那一天与读完第1本书的星期几相同，即星期一。

Topics

AR.012 Arithmetic sequences basics