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A school library contains 200 hardcover and 300 paperback books. 30%

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A school library contains 200 hardcover and 300 paperback books. 30%  [#permalink]

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New post 13 May 2017, 14:34
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A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%

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Re: A school library contains 200 hardcover and 300 paperback books. 30%  [#permalink]

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New post 13 May 2017, 20:13
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Bunuel wrote:
A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%


\(30\%\) of the hardcover books or \(30\% \times 200 = 60\) hardcover books are fiction.

Hence, from 500 books at the library, there are \(300 + 60 = 360\) books that are either paperback or fiction.

The probability is \(\frac{360}{500}=\frac{36}{50}=\frac{72}{100}=72\%\)

The answer is A.
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Re: A school library contains 200 hardcover and 300 paperback books. 30%  [#permalink]

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New post 13 May 2017, 21:11
Bunuel wrote:
A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%


Hard cover Fiction = 30% of 200 = 60
Paperback Fiction = 70% of 300 = 210
Remaining Paper back = 300-210 = 90

Total Favourable Books = 60+210+90 = 360

Probability = 360/500 = 18/25 = 72%

Answer: Option A
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Re: A school library contains 200 hardcover and 300 paperback books. 30%  [#permalink]

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New post 14 May 2017, 17:27
First, the probability of PP is 300/500 and since this probability is already takes care of fiction books that are pps, we only need to get the percentage of fiction books from the HC books to reach to our probabilities. Therefore,

\(\frac{300}{500} +\frac{3}{10}*\frac{200}{500}= (\frac{3}{5} + \frac{6}{50})*100=72\)

The correct option is: A
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Re: A school library contains 200 hardcover and 300 paperback books. 30%  [#permalink]

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New post 09 Oct 2018, 09:56
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Top Contributor
Bunuel wrote:
A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%


Another approach is to use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).

Here, we have a population of books, and the two characteristics are:
- hardcover or paperback
- fiction or nonfiction

With the given information, we can complete our matrix as follows (I've skipped a few steps. So, if you're unfamiliar with this approach, watch the video (below) to see how to set things up).
Image

We want, P(selected book is either paperback or fiction)
The boxes representing books that are either paperback or fiction are shaded below.
Image
So, the number of books that satisfy this condition = 60 + 210 + 140 = 360
Total number of books = 500

So, P(selected book is either paperback or fiction) = 360/500
= 72%

Answer: A
This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:

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Re: A school library contains 200 hardcover and 300 paperback books. 30%  [#permalink]

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New post 12 Oct 2018, 07:56
Bunuel wrote:
A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%



We are given that 30% of the 200 hardcover books are fiction, and thus 200 x 0.3 = 60 hardcover books are fiction. We are also given that 70% of the 300 paperback books are fiction, and thus 0.7 x 300 = 210 paperback books are fiction. We see that there are a total of 60 + 210 = 270 fiction books.

Recall that P(A or B) = P(A) + P(B) - P(A and B). If we let B be paperback and F be fiction, we have:

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

P(B or F) = 300/500 + 270/500 - 210/500

P(B or F) = 360/500 = 72/100 = 72%

Alternate Solution:

The group of books referred to as “either paperback or fiction” consists of all of the paperback books plus the hardcover books that are fiction. Since there are 300 paperback books and 200 x 0.3 = 60 hardcover fiction books, there are 300 + 60 = 360 books that are either paperback or fiction, out of a total of 500. Thus, the probability is 360/500 = 72/100 = 72%.

Answer: A
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Re: A school library contains 200 hardcover and 300 paperback books. 30% &nbs [#permalink] 12 Oct 2018, 07:56
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