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Max number of books

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Max number of books

by rahulvsd » Sat Oct 29, 2011 5:42 am
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.

OA: B
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Source: — Data Sufficiency |
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by GmatMathPro » Sat Oct 29, 2011 6:49 am
I think statement 2 is the easier one to start with in this case...

Statement 2: We know she can fit all 22 books on a 5.5 foot shelf. If she is trying to maximize the number of books on the five foot shelf, she should start by removing her biggest books. If her two biggest ones are each 5 inches, she could remove one, and still be over her 5 foot space by one inch. Hence, she must remove one more book that is at least one inch thick. We know she has at least one other book that is more than one inch, so she could fit a maximum of 20 books on her 5 foot shelf. SUFFICIENT.

Statement 1: Her 8 thinnest books are 2 inches each, so that's 16 of the available 60 inches, so she has 44 inches left for 14 books that are a total of 50 inches wide. Again, she should start by removing her biggest books. We can use a similar thought process as above, but now that we dont know how thick her thickest books are, there are more possibilities. For example, if her thickest book is 7 inches, then she only would have to leave out 1 book, which would give her a maximum of 21 books on the shelf. If her thickest books are 3 inches, then she would have to leave out at least two books, making her maximum 20. INSUFFICIENT

[spoiler]Ans: B[/spoiler]
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