2012-04-03 09:00:47

A certain bookstore sells both hardcover and paperback books, and every book sold is either fiction or nonfiction. On one recent day, 60% of all books sold were fiction, and 30% of the fiction books sold were hardcover. If 100 books were sold, and if paperbacks accounted for 70% of total sales that day, how many books sold were nonfiction paperbacks?

(A) 12
(B) 18
(C) 28
(D) 40
(E) 42

The correct answer is C

Explanation: Make a table that keeps track of paperback, hardcover, and total books on the columns, and nonfiction, fiction, and total books in all the rows. This will allow you to organize the information and keep track of the fact that each book has one binding and one genre. The lower right corner of this table will be the total number of books sold, which in this case is 100, and the sum of each column’s numbers will meet in the Total row for each column, and the same will be true of rows:

                             NONFICTION        FICTION    TOTAL
PAPERBACK
HARDCOVER
TOTAL                                                                               100

Now, fill it in. 60% of total sales is fiction, and 70% is paperback

          N    F    T
P                      70
H
T              60    100

From this, you can deduce that 40% of all books sold (or 40 books) were nonfiction and 30% of all books (or 30 books) were hardcover.

          N    F    T
P                      70
H                      30
T    40    60    100

Now, 30% of all fiction books sold were hardcover, meaning 30% of 60 will be the number of hardcover fiction books sold. 30% of 60 is 18 (from 60 x .3 = 18).

          N    F    T
P                     70
H             18    30
T    40    60    100

From this, you can deduce everything else about the table by simply adding up the rows and columns, giving these results:

         N    F    T
P    28    42    70
H    12    18    30
T    40    60    100

The question asks about paperback nonfiction books, which is 28, or choice C.