A shelf contains hardcover and paperback books, of either fiction or nonfiction. How many books are on the shelf?
(1) 2/3 of the books are fiction and 1/4 of the books are hardcover
(2) Fewer than 30 books are paperback and more than 10 are nonfiction
Quote:
Statement 1 indicates that the total number of books is a multiple of 12, as the number must be able to be broken into both thirds and fourths. But without any actual numbers, the statement is not sufficient.
Quote:
Similarly statement 2 is not sufficient, as it offers no insight into proportions.
Quote:
But together, the statements guarantee that there are either 24, 36 or 48 total books (multiples of 12 that are in the range of the statement 2 numbers).
48 is out of the question, as if 3/4 of the books are paperback, that would mean that 3/4 of 48 = 36 books are paperback, and statement 2 limits that number to under 30.
And 24 is not enough - 1/3 of the books are nonfiction, meaning that only 8 out of 24 books would be nonfiction, and the statement requires that at least 10 be nonfiction.
With 36 total books: 2/3 are fiction = 24. 1/3 are nonfiction = 12. 1/4 are hardcover = 9, and 3/4 are paperback = 27.