Susan has a 5-foot long bookshelf that she wants to fill

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Susan has a 5-foot long bookshelf that she wants to fill [#permalink]

07 Jun 2011, 15:46

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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.

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Re: Please help with a DS Question [#permalink]

07 Jun 2011, 20:59

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.

And in 5 ft shelf, only 20 books can fit.

Answer B.

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Re: Please help with a DS Question [#permalink]

07 Jun 2011, 21:23

agdimple333, could you please explain this line ?

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.
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Re: Please help with a DS Question [#permalink]

08 Jun 2011, 07:18

subhashghosh wrote:

agdimple333, could you please explain this line ?

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.

0.5 ft = 6" and it was concluded that approx size of each book is 2.75", so in that extra space of 6" approx we are fitting 2 books.

Its a DS Q, so an estimation is better & saves time than actually deriving the exact #s.

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Re: Please help with a DS Question [#permalink]

08 Jun 2011, 10:02

smodak wrote:

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

Hence 21 books can be accommodated. Sufficient.

Hence B
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Re: Please help with a DS Question [#permalink] 08 Jun 2011, 10:02

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Susan has a 5-foot long bookshelf that she wants to fill

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Susan has a 5-foot long bookshelf that she wants to fill

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