BTGmoderatorDC wrote: ↑

Thu Mar 10, 2022 7:42 pm

The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?

A. 1/4
B. 5/14
C. 5/9
D. 9/14
E. 5/6

OA D

Source: e-GMAT

Let's choose values that satisfy the given information...

The library has 2/3 as many shelves on its 2nd floor as it does on its 1st.
So, let's say there are 3 shelves on the 1st floor, which means there are 2 shelves on the 2nd floor

The second floor has 5/6 as many books per shelf as the first floor
So, let's say there are 6 books per shelf on the first floor, which means there are 5 books per shelf on the second floor.

The total number of books on the first floor = (3)(6) = 18 books
The total number of books on the second floor = (2)(5) = 10 books
The TOTAL number of books in the library = 18 + 10 = 28

What fraction of the library's books are on the first floor?
Of the library's 28 books, 18 are on the first floor.
Answer: 18/28 = 9/14

Answer: D