|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
21 Mar 2017, 05:14
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:09) correct
37%
(02:26)
wrong
based on 356
sessions
History
Date
Time
Result
Not Attempted Yet
In her extensive library, Christie has 42 fantasy books, 35 science fiction books, 32 historical fiction books, and 28 nonfiction books. If she removes books at random, how many must she remove to guarantee that she has removed at least 35 books of the same type?
A. 77
B. 105
C. 128
D. 129
E. 144
A. 77
B. 105
C. 128
D. 129
E. 144
21 Mar 2017, 08:37
Kudos
Bookmarks
Bunuel
To answer this question, let's first determine the MAXIMUM number of books that can be removed WITHOUT having 35 books of the same type.
To start, we can remove all 32 historical fiction books, and 28 nonfiction books WITHOUT having 35 books of the same type.
From there, we can remove 34 fantasy books and 34 science fiction books WITHOUT having 35 books of the same type.
So far we have removed 128 books (32 + 28 + 34 + 34 = 128) and we do not have 35 books of the same type.
At this point, all that remains are 8 fantasy books, 1 science fiction book.
So, once we choose the next book, we will be GUARANTEED to have at least 35 books of the same type.
128 + 1 = 129
So, once we select 129 books, we will be GUARANTEED to have at least 35 books of the same type.
Answer: D
Cheers,
Brent
General Discussion
21 Mar 2017, 10:06
Kudos
Bookmarks
Bunuel
A good question. :D
- • To ensure that she removes 35 books of the same type, we must consider the worst-case scenario.
• At present we have
- o Fantasy books - 42
o Science Fiction - 35
o Historical Fiction - 32
o Non - fiction - 28
• Therefore,
- o Fantasy books - 34
o Science Fiction - 34
o Historical Fiction - 32
o Non - fiction - 28
o Total books taken out so far = 34 + 34 + 32 + 28 = 128
• Now observe, the even after we have taken 128 books, we still don't have 35 books of one type with us.
- o But now when we take out the 129th book, it is guaranteed that either it will the 35th Fantasy book or the 35th Science, ensuring that we get 35 books of one type.
Thus the correct answer is 129, Option D
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
