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There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar

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There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar [#permalink]

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New post 28 Oct 2011, 23:07
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Difficulty:

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Question Stats:

59% (01:11) correct 41% (01:27) wrong based on 148 sessions

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There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar books in my bookshelf. The books are randomly arranged in the shelf and not at all in the order of their type. What is the least number of books that must be drawn from the shelf in order to get 6 books of a particular type?

a) 20
b) 23
c) 25
d) 28
e) None of these
[Reveal] Spoiler: OA

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Kudos [?]: 60 [2], given: 9

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Re: There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar [#permalink]

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New post 29 Oct 2011, 06:14
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Is the ans a ?

Suppose we need to draw 20 books.
Considering the worst case, If we remove all drama books that is 4 of them are gone out of 20 left with 16. Now suppose 5 of each novel, poetry and drama are drawn out from the shelf, that is 15 more books gone, so total 19 are taken out from the shelf and left with 1. Now the next 1 book which is pulled can be any of the three categories but it would definitely complete a set of 6 for one of the them.

Best case would be the first 6 we draw are of the same category. But if we pull 20 out atleast 1 of them would complete a set of 6.

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Re: There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar [#permalink]

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New post 01 Nov 2011, 14:53
Agreed.

This is a problem where you need to consider worst case:

1. Take out 4 Dramas.
2. Take 5 of each of the other 3, total of 15.
3. Next book you take will complete a set of 6.

Total is 4+15+1 = 20.

A

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Re: There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar [#permalink]

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Re: There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar [#permalink]

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New post 24 Oct 2017, 06:43
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aselfmademan wrote:
There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar books in my bookshelf. The books are randomly arranged in the shelf and not at all in the order of their type. What is the least number of books that must be drawn from the shelf in order to get 6 books of a particular type?

a) 20
b) 23
c) 25
d) 28
e) None of these


Let’s assume the worst case scenario. Let’s say we have drawn 5 novels, all 4 drama books, 5 poetry books, and 5 grammar books; we would have a total of 19 books drawn but still not have 6 books of one type. However, if we draw just one more book (which must be a novel, poetry, or a grammar book), we would have 6 books of one particular type. Thus, the least number of books that must be drawn is 20.

Answer: A
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Re: There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar   [#permalink] 24 Oct 2017, 06:43
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