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# On a certain bookshelf with 500 books, all books are either hardcover

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Math Expert
Joined: 02 Sep 2009
Posts: 51100
On a certain bookshelf with 500 books, all books are either hardcover  [#permalink]

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01 Dec 2016, 06:20
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:19) correct 11% (01:40) wrong based on 83 sessions

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On a certain bookshelf with 500 books, all books are either hardcover or have more than three hundred pages. If 300 of the books are hardcover and 350 have more than three hundred pages, then how many books are both hardcover and have more than three hundred pages?

A. 250
B. 200
C. 150
D. 100
E. 50

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Re: On a certain bookshelf with 500 books, all books are either hardcover  [#permalink]

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01 Dec 2016, 06:31
Bunuel wrote:
On a certain bookshelf with 500 books, all books are either hardcover or have more than three hundred pages. If 300 of the books are hardcover and 350 have more than three hundred pages, then how many books are both hardcover and have more than three hundred pages?

A. 250
B. 200
C. 150
D. 100
E. 50

IMO : C

all books are either hardcover or have more than three hundred pages Neither = 0.

Total = hardcover + more than 300 - both

500 = 300 +350 - B

500 = 650 - B

B =150
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Re: On a certain bookshelf with 500 books, all books are either hardcover  [#permalink]

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01 Dec 2016, 08:15
Bunuel wrote:
On a certain bookshelf with 500 books, all books are either hardcover or have more than three hundred pages. If 300 of the books are hardcover and 350 have more than three hundred pages, then how many books are both hardcover and have more than three hundred pages?

A. 250
B. 200
C. 150
D. 100
E. 50

Quote:
500 Books = Hardcover + More than three hundred pages - ( Hard Cover & > 300 Pages )

500 = 300 + 350 - ( Hard Cover & > 300 Pages )

So, ( Hard Cover & > 300 Pages ) = 150

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Joined: 02 Nov 2013
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Re: On a certain bookshelf with 500 books, all books are either hardcover  [#permalink]

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01 Dec 2016, 08:29
I will vote C.
Neither hard cover nor books more than three hundred pages = 0.
Total - 0 = hardcover books + book with pages more than 300 - both. Let say it is x.
500 - 0 = 300 +350 - x
X=150. Hence C.
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Re: On a certain bookshelf with 500 books, all books are either hardcover  [#permalink]

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22 Mar 2017, 15:07
Bunuel wrote:
On a certain bookshelf with 500 books, all books are either hardcover or have more than three hundred pages. If 300 of the books are hardcover and 350 have more than three hundred pages, then how many books are both hardcover and have more than three hundred pages?

A. 250
B. 200
C. 150
D. 100
E. 50

It's C- but shouldn't the question read "On a certain bookshelf with 500 books, all books are either hardcover, more than three hundred pages or both." Doesn't all and either imply that there cannot be a category of both- maybe I'm wrong- I know it does imply that there cannot be a group of books that have neither.
Re: On a certain bookshelf with 500 books, all books are either hardcover &nbs [#permalink] 22 Mar 2017, 15:07
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