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A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi

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Bunuel
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A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   30 Jan 2015, 07:29
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A bookshelf contains 40 books, 30 of which are hardcover and 20 of which are fiction. What is the maximum number of books that are both hardcover and fiction?

A. 10
B. 15
C. 20
D. 25
E. 30


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C
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   30 Jan 2015, 09:46
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Hello Bunuel, I gave it a try:

This problem can be solved in the most simple way with the aid of a table (Hard cover / not hard cover in verticals for example and Fiction / other books in horizontal)

The table would help us visualize that there is a max of 20 books to be both fiction and hardcover so CORRECT ANSWER C. 20

Bunuel wrote:
A bookshelf contains 40 books, 30 of which are hardcover and 20 of which are fiction. What is the maximum number of books that are both hardcover and fiction?

A. 10
B. 15
C. 20
D. 25
E. 30


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The OA will be revealed on Sunday
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   30 Jan 2015, 10:02
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ans C... fiction book can be subset of hardcover books so 20
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   30 Jan 2015, 10:35
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As the number of fiction is 20 so maximum number of both hardcover & fiction CANNOT be MORE THAN 20 !! so we can rule out options D & E immediately.

FOR get the maximum result, we assume that ALL the 20 fiction are hardcover too . SO the maximum number of fiction books which are hardcover is 20


Answer c..... :P :P :P
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   30 Jan 2015, 12:04
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Another way to solve:

Total = Group1 + Group2 - Both + Neither

Group1 = Books that are hardcover
Group2 = Books that are fiction

40 = 30 + 20 - Both + Neither

Both + 40 = 50 + Neither

Both = 10 + Neither

We know that the highest value for "Neither" is 10, since it is given that 30 of the 40 books are hardcover.

Both = 10 + 10 = 20.

C
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   31 Jan 2015, 00:33
Bunuel wrote:
A bookshelf contains 40 books, 30 of which are hardcover and 20 of which are fiction. What is the maximum number of books that are both hardcover and fiction?

A. 10
B. 15
C. 20
D. 25
E. 30


Kudos for a correct solution.

The OA will be revealed on Sunday


The maximum number of Hardcover and Fiction books - 20 (c)
I solved it using a table.
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   02 Feb 2015, 04:31
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Bunuel wrote:
A bookshelf contains 40 books, 30 of which are hardcover and 20 of which are fiction. What is the maximum number of books that are both hardcover and fiction?

A. 10
B. 15
C. 20
D. 25
E. 30


Kudos for a correct solution.

The OA will be revealed on Sunday


VERITAS PREP OFFICIAL SOLUTION:

The fact that there are 40 total books but that the two subcategories (hardcover and fiction) add to 50 should tell you that you're looking at Overlapping Sets. Some books need to be both hardcover and fiction. Here is where a lesser-known fact about Venn Diagrams comes in handy: the overlapping portion can only be as large as the smaller of the two circles. Here only 20 total books are fiction, so it cannot be that more than 20 books are both fiction and something else. Accordingly, the correct answer is C.
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   16 Apr 2016, 03:45
Can anyone tell me why it is not 10?

If you have 40 books, of which are 30 hardcover and 20 are fiction... if you have 20 fiction and hardcover, it does not add up to 40. You'll have 10 hardcover and 20 hardcover + fiction? Or are you supposed to think that there are also softcover books?
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   05 Sep 2016, 11:18
so, we don't assume that neither = 0 unless explicitly told so, or implied (ie. boys and girls), right? Please confirm, still trying to wrap my head around this. Thanks!!
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A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   05 Sep 2016, 12:10
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Bunuel wrote:
A bookshelf contains 40 books, 30 of which are hardcover and 20 of which are fiction. What is the maximum number of books that are both hardcover and fiction?

A. 10
B. 15
C. 20
D. 25
E. 30


Kudos for a correct solution.

The OA will be revealed on Sunday


Total Books = 40
Hard Cover = 30
Non hardcover = 10

Fiction = 20
Non-Fiction = 20

Quote:
What is the maximum number of books that are both hardcover and fiction?


Maximum no of Hardcover & fiction will be 20 ( Assuming All the Fiction Books are Hard Cover )

Hence correct answer will be (C)
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A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   24 Oct 2016, 08:21
If you set this problem up as an overlapping set (i.e. using the grid), you'll find that fiction is 20 and hardcover is 30 --> Therefore, the max we can get for this cross section is 20 because we cannot exceed number of fiction books they've established in the problem.

Fict Non-Fict
Hard ---- ------ 30
Soft ---- ------ 10
-----20 ---- 20 40 (total)
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink] New post   10 Feb 2022, 13:50
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Re: A bookshelf contains 40 books, 30 of which are hardcover and 20 of whi [#permalink]
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