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

Question

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

A. 20
B. 23
C. 25
D. 28
E. None of these

Bunuel · Accepted Answer

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

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

The question asks to find the least number of books we should pick to   guarantee   that we have 6 books of one particular type. In such questions we should consider the worst case scenario which could happen. This would be if we pick all 4 drama books, 5 novel books, 5 poetry books, and 5 grammar books, so total of 19 books. In this case we still wouldn't have 6 books of one type. But the next, 20th, book we pick, be it novel, poetry or grammar book, would make 6 books for one of these types.

Answer: A.

Check other  Worst Case Scenario Questions  from our  Special Questions Directory  to understand the concept better.

ashimasood · Answer

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.

kostyan5 · Answer

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

ScottTargetTestPrep · Answer

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

lichting · Answer

I still do not understand. Can anyone please give more explaination on this question?

ZIX · Answer

How would the answer change if it instead asked: What is the least number of books that must be drawn from the shelf in order to get 6 books  of any type ?

Bunuel · Answer

That would mean the saem thing and the answer would be the same. We cannot guarantee getting 6 books of any kind in fewer than 20 picks.

Gorang · Answer

What is the significance of "not at all in the order of their type"?

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

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