Hint for process of elimination: Draw a fast picture of the rooms and try to distribute the books in a way that gives you a total of 400, 500, and 600 books. You may quickly realize that there cannot be a total 600 books in these classrooms, and you may also gain enough intuition about this situation to solve the problem.
Read on for a full solution.
Solution: The count of textbooks in classrooms 6 through 10 is contained in both the counts of textbooks in classrooms 1 through 10 and classrooms 5 through 15. The greatest possible textbook count in rooms 6 through 10 is 250. In this case, there are no textbooks in classrooms 1 through 5, and 50 textbooks in classrooms 11 through 15, for a total of 300 textbooks. Similarly, the least possible textbook count in rooms 6 through 10 is 0. In this case, there are 250 textbooks in classrooms 1 through 5, and 300 textbooks in classrooms 11 through 15, for a total of 550 textbooks. Options I and II fall in between 300 and 550, but option III does not.