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Please help with a DS Question

by smodak » Tue Jun 07, 2011 2:56 pm
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.

Offical Answer: B
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by cans » Tue Jun 07, 2011 5:12 pm
22books
1 foot = 12 inches
we need extra .5 foot or 6 inches space.
a)8 books have 2 inches thickness.
so we can remove 3 of them and place 19 books
but what if thickest book has 10 inches thickness? then removing that will make 21 books
insufficient
b)2 thickest books have 5 inches.
remove i thickest book. still we are short 1 inch space. remove other thickest book.
thus 20
IMO B
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by phanideepak » Tue Jun 07, 2011 7:47 pm
Rephrasing the question:

How many books can fit in a shelf of width 60 Inches. All books can fit the shelf if the width of the shelf were to be 66 inches.

a. This choice talks about min size but we know nothing about the max size for example the remaining space in the shelf will be 60 - 8x2 = 44. So here we can consider the remaining 14 books to have various sizes > = 2 for eg we can consider 13 books to have the width 3 inches and the remaining book to have the width 11 inches we can consider infinite possibilities such as this.

b. This talks about the max width of the books so every book should be smaller than the two books. and given that all the books fit in 66 inches and by removing two books with the maximum width that is 5 inches we can see that rest of the books fit into the 60 inch cupboard. So this is sufficient.

IMO B
Last edited by phanideepak on Tue Jun 07, 2011 8:38 pm, edited 1 time in total.
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by krishnasty » Tue Jun 07, 2011 8:32 pm
phanideepak wrote:Rephrasing the question:

How many books can fit in a shelf of width 60 Inches. All books can fit the shelf if the width fo the shelf were to be 65 inches.

a. This choice talks about min size but we know nothing about the max size for example the remaining space in the shelf will be 60 - 8x2 = 44. So here we can consider the remaining 14 books to have various sizes > = 2 for eg we can consider 13 books to have the width 3 inches and the remaining book to have the width 10 inches we can consider infinite possibilities such as this.

b. This talks about the max width of the books so every book should be smaller than the two books. and given that all the books fit in 65 inches and by removing one book with the maximum width that is 5 inches we can see that rest of the books fit into the 60 inch cupboard. So this is sufficient.

IMO B
Nice explaination. A little typo..it would be 66 inches and not 65. As cans pointed out, 1foot = 12 inches. hence, 0.5 foot = 6 inches.

Not that it makes any difference in the ans ;)
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by phanideepak » Tue Jun 07, 2011 8:39 pm
krishnasty wrote:
phanideepak wrote:Rephrasing the question:

How many books can fit in a shelf of width 60 Inches. All books can fit the shelf if the width fo the shelf were to be 65 inches.

a. This choice talks about min size but we know nothing about the max size for example the remaining space in the shelf will be 60 - 8x2 = 44. So here we can consider the remaining 14 books to have various sizes > = 2 for eg we can consider 13 books to have the width 3 inches and the remaining book to have the width 10 inches we can consider infinite possibilities such as this.

b. This talks about the max width of the books so every book should be smaller than the two books. and given that all the books fit in 65 inches and by removing one book with the maximum width that is 5 inches we can see that rest of the books fit into the 60 inch cupboard. So this is sufficient.

IMO B
Nice explaination. A little typo..it would be 66 inches and not 65. As cans pointed out, 1foot = 12 inches. hence, 0.5 foot = 6 inches.

Not that it makes any difference in the ans ;)
Thank you krish I have edited my post now :)
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by vikram4689 » Tue Jun 07, 2011 9:03 pm
somehow muddles up with this ques.. i thought "fit the shelf" means completely fit i.e. use 60 inch of space and chose E after wasting so much time.. Did not any of you feel that "fit the shelf" means that way
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