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

Question

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.

(1) The 8 thinnest books each have a thickness of 2 inches.

(2) The 2 thickest books each have a thickness of 5 inches.

agdimple333 · Answer

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.

subhashghosh · Answer

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.

agdimple333 · Answer

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.

gurpreetsingh · Answer

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

jegan2388 · Answer

Might be a stupid question, but are we supposed to know these conversions, i.e. foot to inch, et al. ?

Bunuel · Answer

No. The question itself will supply the relative conversions. Though you should have a few basic ones memorized: 1 hour = 60 minutes, ...

Check other  Conversion problems  to practice in  Special Questions Directory .

TARGET730 · Answer

5.5 foot is 66 inches right? not sure why everyone is referring to 65?

usre123 · Answer

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

Bunuel · Answer

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.

usre123 · Answer

yes, it's clear, thank you!

srija9999 · Answer

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.

(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.

gmat1393 · Answer

KAPLAN OFFICIAL EXPLANATION

Analyze 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.

sreddy07 · Answer

I think it should be clarified that fitting maximum number of books means 'no overhang'. Since this wasn't mentioned, I thought Susan could fit either 20 books (no overhang) or 21 books (last 5 inch book overhangs 1" but still fits since 4" are still on the shelf). Thats the only reason I wasn't 100% convinced with B.

bumpbot · Answer

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

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