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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  [#permalink]

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New post 07 Jun 2011, 15:46
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38% (02:07) correct 63% (02:22) wrong based on 322 sessions

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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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New post 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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New post 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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New post 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]

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New post 08 Jun 2011, 10:02
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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

Hence 21 books can be accommodated. Sufficient.

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

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New post 28 Oct 2014, 03:13
Might be a stupid question, but are we supposed to know these conversions, i.e. foot to inch, et al. ?
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New post 28 Oct 2014, 03:35
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New post 23 Nov 2014, 22:36
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5.5 foot is 66 inches right? not sure why everyone is referring to 65?
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Re: Susan has a 5-foot long bookshelf that she wants to fill  [#permalink]

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New post 07 Dec 2014, 00:09
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
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Re: Susan has a 5-foot long bookshelf that she wants to fill  [#permalink]

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New post 07 Dec 2014, 05:47
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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.

Hope it's clear.
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Re: Susan has a 5-foot long bookshelf that she wants to fill  [#permalink]

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New post 07 Dec 2014, 11:23
yes, it's clear, thank you!
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Re: Susan has a 5-foot long bookshelf that she wants to fill  [#permalink]

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New post 03 Feb 2018, 03:08
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.


1foot= 12 inches;

The length of bookshelf needed to fit all 22 books=65 inches
The length bookshelf Susan has=60 inches
--> Her book shelf falls short by five inches ---> She has to drop x number of books that will take 5 inches of space.

Since we need the maximum book she can fit in the shelf (i.e 22-x), X should be as small as possible--> the thickness of book should be as large as possible(Thickest book).

Statement1: If we know the thickness of the thinnest book, we cannot obtain the maximum number of book that can be kept because of the above reason so not sufficient.

Statement2:
Since we know the thickness of the thickest book i.e. 5 inches exactly , if we drop one of the thickest book we can fit 21 books.
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Re: Susan has a 5-foot long bookshelf that she wants to fill   [#permalink] 03 Feb 2018, 03:08
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