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

Question

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 .

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TudorM · Answer

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

chetan2u · Answer

ans C... fiction book can be subset of hardcover books so 20

mehrdadtaheri92 · Answer

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.....

RErules2016 · Answer

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

maxk297 · Answer

The maximum number of Hardcover and Fiction books - 20 (c)
I solved it using a table.

Bunuel · Answer

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.

mathiaskeul · Answer

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?

wmichaelxie · Answer

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!!

Abhishek009 · Answer

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

Fiction = 20
Non-Fiction = 20

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

law258 · Answer

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)

Fict Non-Fict
Hard ---- ------ 30
Soft ---- ------ 10
-----20 ---- 20  40 (total)

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

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