One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of books, and the two characteristics are:
- a fiction or nonfiction
- politics or not politics

Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method allows us to visualize the information easier (IMO).

So we can set up our Matrix as follows:

Since our goal is to find a certain FRACTION let's assign a nice value to the total population of books. We'll say there are 100 books in total.

If 60% of Ana’s books are fiction, then there are 60 fiction books, and the remaining 40 books are nonfiction to get:


We're told that 30% of the nonfiction books are about politics. 30% of 40 = 12, so we have the following:


Finally, since the bottom two boxes must add to 40, the bottom right-hand box must equal 28


So, there are 28 nonfiction books that are NOT about politics.

The FRACTION of al book that are NOT about politics = 28/100 = 7/25

Answer: B