Quote:
Susan has a 5-foot long bookshelf that she wants to fill with 22 books of differing sizes. Each book can fit on the shelf, but they cannot all fit on the shelf. In order to fit all of her books on the same shelf, she would need a 5.5-foot long bookshelf. What is the maximum number of books she can fit on her shelf?
(1) The 8 thinnest books each have a thickness of 2 inches.
(2) The 2 thickest books each have a thickness of 5 inches.
KAPLAN OFFICIAL EXPLANATIONAnalyze the question stem
This Value question asks whether there is enough information to determine the maximum number of books that can fit on Susan's shelf. Susan's books are of various widths.
Susan's shelf is 5 feet, or 60 inches long. Her 22 books need 5.5 feet, or 66 inches. Thus, Susan needs to eliminate 6 inches' worth of books. To get the maximum number of books on her shelf, Susan wants to leave out as few books as possible. This will probably mean leaving out one or more of the thickest books, since more than one thin book might be able to fit in the same space as one thick book. Specific information about the thickness of the books is required for sufficiency, but keep in mind the general strategy of getting rid of thick books first.
Evaluate the statements
Statement (1) only gives information about some of the thinnest books. Since those books are 2 inches wide each, Susan could just leave out three of those thinnest books (for a total of 6 inches) and fit everything else on the shelf. That would be 22 – 3 = 19 books. The problem is that statement (1) says nothing about the thickest books. If the thickest book is 6 inches wide or wider, for example, then Susan could just leave that one out and fit the other 21 on the shelf. But if the three thickest books are each
2
1
3
inches wide, Susan would still have to leave out three books in order to cut out at least 6 inches. How many books she has to leave out cannot be determined from statement (1), which is therefore insufficient. Eliminate (A) and (D).
Statement (2) deals with the thickest books (which are giant tomes! Susan must be studying for the GMAT!), which was determined in the initial analysis to be the crucial information. Susan could leave out one of these thickest books and be just 1 inch over. She could leave out one more book (either another of the thickest books or any other book that is at least 1 inch wide) and fit everything else on the shelf. That would be 20 books. Statement (2) is sufficient, so the correct answer is (B).
TAKEAWAY: Paying attention to the right detail can boil down lengthy word problems to their essentials. Here, the word "maximum" in the question was a clue to eliminate as few books as possible, which in turn was a clue to look for information about the thickest books.