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Susan has a 5-foot long bookshelf that she wants to fill [#permalink]
07 Jun 2011, 14:46

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Difficulty:

95% (hard)

Question Stats:

34% (02:31) correct
66% (01:35) wrong based on 134 sessions

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.

Re: Please help with a DS Question [#permalink]
07 Jun 2011, 19:59

st-1 ==> not sufficient, we definitely the size of thickest book(s). Alternatively, we have smallest size book from which we can determine what space of the shelf is utilized. Now for the remaining space, you can assume like the book is 1 ft thick and very few books will be filled or the book is just 2.1 inches thick... so doesnt help much.

St-2 ==> 22 books require 5.5 ft i.e. 65 inches.

2 books utilized 5 inch each. so remaining 20 books are left with 55 inches. or approximately 2.75" each book.

we know that 22 books cannot fit in 5 ft but needs 5.5 ft. so from above we can conclude that (approx.) 2 books are not able to fit and that is why additional 0.5 ft is required.

Re: Please help with a DS Question [#permalink]
08 Jun 2011, 09:02

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This post was BOOKMARKED

smodak wrote:

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.

65 inch can accommodate all the books. But have to find the max number of books that can be accomodated in 5 foot long bookshelf. This could be done by avoiding the thickest books. If you avoid one 5inch thickest book. Number of books = 22-1 = 21 total thickness = 65-5 = 60 = 5 feet

Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]
01 Oct 2014, 23:37

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Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]
06 Dec 2014, 23:09

Sorry but isn't 5.5=66 inches? so from B, if you avoid the thickest book of 5 inches, you will have 61 inches, but the shelf is only 60 inches long...should you drop the second 5" book as well?

I'm very confused...if someone could please help. thanks

Re: Susan has a 5-foot long bookshelf that she wants to fill [#permalink]
07 Dec 2014, 04:47

Expert's post

usre123 wrote:

Sorry but isn't 5.5=66 inches? so from B, if you avoid the thickest book of 5 inches, you will have 61 inches, but the shelf is only 60 inches long...should you drop the second 5" book as well?

I'm very confused...if someone could please help. thanks

Yes, 5.5 feet is 66 inches and the shelf is only 60 inches long. To maximize the number of books on the shelf, Susan should start removing thickest books. If she removes only one 5-inch book, she'd be left with 61 inch long books, thus she must remove both 5-inch books, which means that Susan can fit maximum of 20 books on her 60-inch shelf.

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...