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# There are 20 books in a bookcase. If one book is selected at random

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Math Expert
Joined: 02 Sep 2009
Posts: 57297
There are 20 books in a bookcase. If one book is selected at random  [#permalink]

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02 Jun 2018, 13:36
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:28) correct 44% (01:23) wrong based on 104 sessions

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There are 20 books in a bookcase. If one book is selected at random, what is the probability that the book is either a hardback or a novel?

(1) 8 books in the bookcase are novel books and 10 books are hardbacks.
(2) 3 books in the bookcase are hardback novels

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Posts: 57297
Re: There are 20 books in a bookcase. If one book is selected at random  [#permalink]

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02 Jun 2018, 13:42
Naren7 wrote:

Sent from my T1 7.0 using GMAT Club Forum mobile app

The OA will be automatically revealed on Friday 8th of June 2018 01:36:05 PM Pacific Time Zone

Meanwhile you can attempt it and post a solution.
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Re: There are 20 books in a bookcase. If one book is selected at random  [#permalink]

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02 Jun 2018, 13:45
2
Bunuel wrote:
There are 20 books in a bookcase. If one book is selected at random, what is the probability that the book is either a hardback or a novel?

(1) 8 books in the bookcase are novel books and 10 books are hardbacks.
(2) 3 books in the bookcase are hardback novels

We'll use numbers to help us understand the logic behind the question.
This is an Alternative approach.

(1) Say all 8 of the novels are hardbacks. Then 10 of the books are hardbacks or novels and the probability is 10/20. Say none of the novels are hardbacks. Then 18 books are novels or hardbacks and the answer is 18/20.
Insufficient.

(2) We have no information on the number of non-hardback novels and can pick easy numbers such as 0 or to 1. In the first case the probability is 3/20 and in the second 4/20.
Insufficient.

Combined:
So 3 books are hardback novels meaning that 10 - 3 = 7 are hardbacks that aren't novels and 8 - 3 = 5 are novels that aren't hardbacks.
So there are 3 + 7 + 5 = 15 books that are novels or hardbacks and the probability must be 15/20.
Sufficient.

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Re: There are 20 books in a bookcase. If one book is selected at random  [#permalink]

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02 Jun 2018, 13:59

Solution

Given:
• Number of books in the bookcase = 20

To find:
• If one book is selected at random, the probability of it being either hardback or novel

Analysing Statement 1
• As per the information provided in Statement 1, 8 books are novel books and 10 books are hardbacks
o But from this statement, we cannot find out whether there are any books which are novel and have hardcover or vice versa.

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information provided in Statement 2, 3 novels are hardback
o But we don’t know whether there are books which are only novel without hardcover or books with hardcover which are not novel.

Hence, statement 2 is not sufficient to answer

Combining Both Statements
We already know 8 novel books and 10 hardbacks books are there, out of which 3 novels are hardbacks.
• Therefore the probability = $$\frac{(8 + 10 – 3)}{20} = \frac{3}{4}$$

Hence, the correct answer is option C.

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Re: There are 20 books in a bookcase. If one book is selected at random  [#permalink]

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02 Jun 2018, 17:17
Bunuel wrote:
There are 20 books in a bookcase. If one book is selected at random, what is the probability that the book is either a hardback or a novel?

(1) 8 books in the bookcase are novel books and 10 books are hardbacks.
(2) 3 books in the bookcase are hardback novels

When a question asks the probability of an either-or event, then we have a simple formula -

P(A or B) = P(A) + P(B) - P(A and B)

1. From statement 1 we can derive P(A) and P(B), but we can't derive P(A & B) as we don't know the number of novel books with a hardback. So it's insufficient.

2. From statement 2 we can't derive P(A) and P(B), but we know the P(A & B). So it's insufficient.

When we combine both statements, we can have P(A or B).
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Re: There are 20 books in a bookcase. If one book is selected at random  [#permalink]

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03 Aug 2019, 11:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: There are 20 books in a bookcase. If one book is selected at random   [#permalink] 03 Aug 2019, 11:00
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