# George has a total of B books in his library, 25 of which are hardcover fiction…

## Solution:

We are given that George has a total of B books in his library, 25 of which are hardcover fiction books. We need to determine the value of B.

Statement One Alone:

40 of the B books are fiction, and the rest are nonfiction.

Using the information in statement one, we know that 40 books are fiction, and B – 40 books are nonfiction. Since there are 25 hardcover fiction books, there are 40 – 25 = 15 paperback fiction books. However, we cannot determine the value of B. Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

60 of the B books are hardcovers, and the rest are paperbacks.

Using the information in statement two, we know that 60 books are hardcovers and B – 60 books are paperbacks. Since there are 25 hardcover fiction books, there are 60 – 25 = 35 hardcover nonfiction books. However, we cannot determine the value of B. Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

From the two statements, we can fill out the following table:

Let’s focus on the “Paperback” row.
If we subtract the number of paperback fiction books from the total number of paperback books, we have:
(B – 60) – 15 = B – 75 (which equals the number of paperback nonfiction books)
Let’s fill this into the empty cell:

Now let’s focus on the “Nonfiction” column. We can create the following equation:
35 + (B – 75) = B – 40
If we simplify the left side of the equation, we have:
B – 40 = B – 40
We still cannot determine a value of B.