Question

Hui is an avid reader. She bought a copy of the bestseller Math is Beautiful. On the first day, Hui read $1 / 5$ of the pages plus $12$ more, and on the second day she read $1 / 4$ of the remaining pages plus $15$ pages. On the third day she read $1 / 3$ of the remaining pages plus $18$ pages. She then realized that there were only $62$ pages left to read, which she read the next day. How many pages are in this book?

$\ 120$

$\ 180$

$\ 240$

$\ 300$

$\ 360$

Solution:

The pages left after the third day is $62.$ Before reading the last $18$ pages, she had $80$ pages left. This is $\dfrac 23$ of the pages remaining, so she had $120$ pages left before the third day.

Before reading the $15$ pages, she had $120+15=135$ pages left. This is $\dfrac 34$ of the pages remaining, so she had $180$ pages left before the second day.

Before reading the $12$ pages, she had $180+12=192$ pages left. This is $\dfrac 45$ of the pages remaining, so she had $240$ pages left before the first day, making the book $240$ pages.

Thus, the answer is C .

2010 AMC 8 Problem 21

Solution:

Problem 21 in Other Years