Question

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?

Sunday

Monday

Wednesday

Friday

Saturday

Answer: B

Concepts:triangular number modular arithmetic

Difficulty rating: 1020

Solution:

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 Problem 4

Answer: B

Difficulty rating: 1020

Solution:

Problem 4 in Other Years