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02 Jun 2018, 13:36
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
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Question Stats:
64% (01:28) correct
36%
(01:29)
wrong
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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
(1) 8 books in the bookcase are novel books and 10 books are hardbacks.
(2) 3 books in the bookcase are hardback novels
02 Jun 2018, 13:45
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Bunuel
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.
(C) is our answer.
02 Jun 2018, 13:59
Kudos
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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.
Answer: C
