Last visit was: 08 Jul 2025, 02:09 It is currently 08 Jul 2025, 02:09
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
505-555 Level|   Overlapping Sets|                        
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 8 July 2025
Posts: 102,580
Own Kudos:
Given Kudos: 97,342
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,580
Kudos: 739,328
 [82]
8
Kudos
Add Kudos
73
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Divyadisha
User avatar
Current Student
Joined: 18 Oct 2014
Last visit: 01 Jun 2018
Posts: 667
Own Kudos:
1,890
 [12]
Given Kudos: 69
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT 1: 660 Q49 V31
Posts: 667
Kudos: 1,890
 [12]
10
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
SchruteDwight
Joined: 03 Sep 2018
Last visit: 30 Mar 2023
Posts: 167
Own Kudos:
106
 [10]
Given Kudos: 923
Location: Netherlands
GPA: 4
Products:
Posts: 167
Kudos: 106
 [10]
8
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
avatar
flsh
Joined: 03 Jun 2015
Last visit: 25 Jun 2025
Posts: 2
Own Kudos:
52
 [9]
Given Kudos: 2
Posts: 2
Kudos: 52
 [9]
6
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Bunuel
George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

(1) 40 of the B books are fiction and the rest are nonfiction
(2) 60 of the B books are hardcovers and the rest are paperbacks

Stem
FI | NF |
---------------
25 | ?? | HC
---------------
?? | ?? | PB
---------------

1)
FI | NF |
---------------
25 | ?? | HC
---------------
15 | ?? | PB
---------------
^
||
Total = 40
Insufficient

2)
FI | NF |
---------------
25 | 35 | HC <= Total = 60
---------------
?? | ?? | PB
---------------
Insufficient

Both
FI | NF |
---------------
25 | 35 | HC
---------------
15 | ?? | PB
---------------
Insufficient

E is the answer.
avatar
GMATAcademy
Joined: 25 Jun 2016
Last visit: 03 Mar 2020
Posts: 58
Own Kudos:
614
 [1]
Given Kudos: 4
GMAT 1: 780 Q51 V46
GMAT 1: 780 Q51 V46
Posts: 58
Kudos: 614
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A couple of ways to solve this question:

Venn Diagram Method: https://youtu.be/5G5IwHoHjgk
Chart Method: https://www.youtube.com/watch?v=DCn-r_4rNFI
avatar
manlog
Joined: 08 Jan 2015
Last visit: 20 Aug 2018
Posts: 48
Own Kudos:
60
 [1]
Given Kudos: 53
Posts: 48
Kudos: 60
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
In this kind of DS questions are fiction/non-fiction and hardcover/paperback options exhaustive? If there is no note that he has only these kinds of books, we can't assume it, right?
User avatar
abhimahna
User avatar
Board of Directors
Joined: 18 Jul 2015
Last visit: 06 Jul 2024
Posts: 3,520
Own Kudos:
5,694
 [1]
Given Kudos: 346
Status:Emory Goizueta Alum
Products:
Expert
Expert reply
Posts: 3,520
Kudos: 5,694
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
manlog
In this kind of DS questions are fiction/non-fiction and hardcover/paperback options exhaustive? If there is no note that he has only these kinds of books, we can't assume it, right?

We cannot assume that because each of the statements clearly stated " and the rest ", implying other options could not be assumed.
User avatar
reynaldreni
Joined: 07 May 2015
Last visit: 02 Nov 2022
Posts: 76
Own Kudos:
138
 [7]
Given Kudos: 152
Location: India
Schools: Darden '21
GPA: 4
Schools: Darden '21
Posts: 76
Kudos: 138
 [7]
6
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
There are 4 categories of Books
P = Fiction & Hardcover
Q = Fiction & Paperback
R = Non-Fiction & Hardcover
S = Non-Fiction & Paperback

P+Q+R+S = B (given)
P = 25
Find Value of B

STMT 01: P+Q = 40
P=25 => Q = 15
P+Q+R+S = B
40+R+S = B
Since values of R & S are unknown. This stmt is insufficient.

STMT 02: P + R = 60
P=25 => R = 35
Q+S+60 = S
Since values of Q & S are unknow. This stmt is insufficient

STMT 01 & 02:
P=25 ; Q=15 ; R = 35 ; S = ?
P+Q+R+S = B
75+S = B
Still value of S is unknown. Hence E.
User avatar
JeffYin
User avatar
Tutor
Joined: 28 Apr 2016
Last visit: 16 Jul 2020
Posts: 40
Own Kudos:
148
 [3]
Given Kudos: 9
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Expert
Expert reply
GMAT 1: 780 Q51 V47
Posts: 40
Kudos: 148
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
I completely agree that this question can be answered efficiently using a matrix box approach, also known as the double matrix. The one thing I want to add to this discussion is to answer the question: How do we know that we can use a matrix box on this question?

Whenever we see that a group can be divided into 2 parts in 2 different ways, we can use a matrix box. In this case, George's books can be divided into fiction and nonfiction (1st way) and hardcover and paperback (2nd way). This tells us that we can use a matrix box.

I hope that this helps others to more quickly recognize that a matrix box or double matrix will be useful on questions like these.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 8 July 2025
Posts: 102,580
Own Kudos:
739,328
 [2]
Given Kudos: 97,342
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,580
Kudos: 739,328
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ghnlrug
How do I immediately see that the following matrix is not sufficient? I though I had enough equations to solve for B Bunuel?

Plug some numbers there: if x = 0, then B = 75 but if x = 10, then B = 85.
User avatar
Shekhar89
Joined: 14 Feb 2012
Last visit: 21 Mar 2021
Posts: 7
Own Kudos:
Given Kudos: 1
Location: India
Concentration: General Management, Social Entrepreneurship
GMAT Date: 05-25-2012
GPA: 3.9
WE:Engineering (Computer Software)
Posts: 7
Kudos: 6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
254. George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B ?
(1) 40 of the B books are fiction and the rest are nonfiction.
(2) 60 of the B books are hardcovers and the rest are paperbacks.

This question from OG'18 has been solved using Venn Diagram in the OG, whereas the CrackVerbal Quant course says you can't solve for mutually exclusive categories with Venn Diagram. Is that a matter of choice or a rule? I know they have tried and pick non-exclusive categories to represent a Venn Diagram but is that even suggested?
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 07 Jul 2025
Posts: 4,847
Own Kudos:
8,619
 [1]
Given Kudos: 225
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,847
Kudos: 8,619
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hello Shekhar,

For data that is mutually exclusive, drawing a table is the most optimal way of solving the problem. Drawing a Venn diagram for mutually exclusive events is pointless; the whole idea of drawing a Venn diagram is to work with the common regions. If data is mutually exclusive, you will not have any overlap of the circles and hence the advice to draw a table. However, it’s not a mandate. You can still draw a Venn diagram and answer the question.
I shall demonstrate both the approaches for you.

Using the table method, we can draw up a table like the ones below:

From statement I alone, we do not know the number of non-fiction books. Hence, insufficient.

Attachment:
25th Feb 2020 - Reply 1 - 2.jpg
25th Feb 2020 - Reply 1 - 2.jpg [ 36.56 KiB | Viewed 14703 times ]

From statement II alone, we do not know the split of the paperbacks. Insufficient.

Attachment:
25th Feb 2020 - Reply 1 - 3.jpg
25th Feb 2020 - Reply 1 - 3.jpg [ 36.68 KiB | Viewed 14699 times ]

The individual statements are insufficient since they do not provide us with enough information to fill up all the cells in the table and hence insufficient to find a value for B.

When we combine the statements also, you can see that we are unable to fill all the cells and there is still information needed about the Non-fiction paperback books to be able to find the value of B.

Attachment:
25th Feb 2020 - Reply 1 - 4.jpg
25th Feb 2020 - Reply 1 - 4.jpg [ 40.16 KiB | Viewed 14636 times ]

The combination of statements is also insufficient.

As you can see, the Venn diagrams approach is cumbersome because you need to draw multiple diagrams while testing the individual statements. We can draw the following Venn diagrams:

Attachment:
25th Feb 2020 - Reply 1 - 5.jpg
25th Feb 2020 - Reply 1 - 5.jpg [ 48.81 KiB | Viewed 14648 times ]

Using statement I alone, we see that we do not have information about the non-fiction books.

Attachment:
25th Feb 2020 - Reply 1 - 6.jpg
25th Feb 2020 - Reply 1 - 6.jpg [ 53.62 KiB | Viewed 14667 times ]

Using statement II alone, we see that we do not have information about the paperbacks.

Attachment:
25th Feb 2020 - Reply 1 - 7.jpg
25th Feb 2020 - Reply 1 - 7.jpg [ 52.8 KiB | Viewed 14625 times ]

Combining both statements, we see that we don’t have information about the Non-fiction paperbacks.

Attachment:
25th Feb 2020 - Reply 1 - 8.jpg
25th Feb 2020 - Reply 1 - 8.jpg [ 67.59 KiB | Viewed 14622 times ]

Since the combination of statements is insufficient to answer the question, the correct answer option is E

As I mentioned earlier, you CAN draw Venn diagrams to solve questions related to mutually exclusive data. But, its probably not the most optimal method in terms of time and effort, that is why we recommend drawing up a table.

Hope that helps!
User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 06 Jul 2025
Posts: 1,294
Own Kudos:
1,888
 [4]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
GMAT 3: 770 Q50 V45
Posts: 1,294
Kudos: 1,888
 [4]
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 07 Jul 2025
Posts: 6,369
Own Kudos:
15,557
 [2]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,369
Kudos: 15,557
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

(1) 40 of the B books are fiction and the rest are nonfiction
(2) 60 of the B books are hardcovers and the rest are paperbacks

Answer: Option E

Video solution by GMATinsight

User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 07 Jul 2025
Posts: 6,369
Own Kudos:
15,557
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,369
Kudos: 15,557
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

(1) 40 of the B books are fiction and the rest are nonfiction
(2) 60 of the B books are hardcovers and the rest are paperbacks

Answer: Option E

Video solution by GMATinsight

User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 07 Jul 2025
Posts: 21,052
Own Kudos:
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,052
Kudos: 26,099
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

(1) 40 of the B books are fiction and the rest are nonfiction
(2) 60 of the B books are hardcovers and the rest are paperbacks
Solution:

Question Stem Analysis:

We need to determine the value of B, the number of books in George’s library. (Note: Here we are assuming all the books in George are either fiction or nonfiction, and either hardcover or paperback.)

Statement One Alone:

Since 40 books are fiction books and 25 are hardcover fiction books, 40 - 25 = 15 books are paperback fiction books. However, we can’t determine the value of B, the number of books in George’s library. Statement one alone is not sufficient.

Statement Two Alone:

Since 60 books are hardcovers and 25 are hardcover fiction books, 60 - 25 = 35 books are hardcover nonfiction books. However, we can’t determine the value of B, the number of books in George’s library. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we can see that there are 25 hardcover fiction books, 15 paperback fiction books, and 35 hardcover nonfiction books. However, since we still don’t know the number of paperback nonfiction books, we can’t determine the value of B, the number of books in George’s library. Both statements together are still not sufficient.

Answer: E
User avatar
SillyCat
Joined: 12 May 2025
Last visit: 07 Jul 2025
Posts: 6
Own Kudos:
Given Kudos: 15
Products:
Posts: 6
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What if there are only three groups? Fiction (Hardcover and Paper) and Non Fiction (Only HardCover), then we would have an answer, right?
abhimahna
manlog
In this kind of DS questions are fiction/non-fiction and hardcover/paperback options exhaustive? If there is no note that he has only these kinds of books, we can't assume it, right?

We cannot assume that because each of the statements clearly stated " and the rest ", implying other options could not be assumed.
Moderator:
Math Expert
102580 posts