math for fourth grader

Question

The number of mystery books is 32.

 

The local library is hosting a book fair in Auguest that features the mystery books. All authors discuss the same number of mystery books and each will discuss more than 1 mystery book. How many authors could be featured in the show?

Answer 1

Assuming that each book is unique to an author and there is two books per author, then there would be 16 authors. There cannot be 3 books per author (since each author discusses the same number of books). If each author discusses 4 books, there will be 32/4 = 8 authors. Similarly, if each author discusses 8 books, there will be 4 authors, 16 books per author -> 2 authors. 32 books per author -> 1 author. There could be:

1 author

2 authors

4 authors

8 authors

16 authors

 

*Note: since each author discusses the same number of books, there will only be "factors of 32" authors (i.e. 1,2,4,8,16,32). Since each discusses more than one book, you cannot have 32 authors.

Answer 2

If each author discusses more than 1 book and each author discusses the same number of books, then the least number of books each author discusses is 2.

 

32 / 2 = 16.  So the most number of authors featured is 16.