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# George has a total of B books in his library, 25 of which are hardcove

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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
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Bunuel wrote:
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

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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
A couple of ways to solve this question:

Venn Diagram Method: https://youtu.be/5G5IwHoHjgk
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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
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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?
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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
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manlog wrote:
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.
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George has a total of B books in his library, 25 of which are hardcove [#permalink]
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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.
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George has a total of B books in his library, 25 of which are hardcove [#permalink]
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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.
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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
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ghnlrug wrote:
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.
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Venn Diagrams vs Tables to solve [#permalink]
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?
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Venn Diagrams vs Tables to solve [#permalink]
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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 [ 36.56 KiB | Viewed 11035 times ]

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

Attachment:

25th Feb 2020 - Reply 1 - 3.jpg [ 36.68 KiB | Viewed 11032 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 [ 40.16 KiB | Viewed 10971 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 [ 48.81 KiB | Viewed 10992 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 [ 53.62 KiB | Viewed 10995 times ]

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

Attachment:

25th Feb 2020 - Reply 1 - 7.jpg [ 52.8 KiB | Viewed 10980 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 [ 67.59 KiB | Viewed 10969 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!
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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
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Bunuel wrote:
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

Video solution by GMATinsight

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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
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Bunuel wrote:
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

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Re: George has a total of B books in his library, 25 of which are hardcove [#permalink]
Bunuel wrote:
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.