How many of the books on the shelf have blue covers?

Question

(1) Of the books on the shelf, 15 percent have leather covers and 40 percent of the leather-covered books are novels.
(2) There are 36 blue leather-covered books on the shelf.

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paragw · Answer

Statement (1) 
15 percent of all books have leather covers.
40 percent of leather-covered books are novels.
This information tells us about the proportion of leather and novels but provides no information about the number or proportion of books with blue covers. So, statement (1) alone is  insufficient.

Statement (2) 
There are 36 blue leather-covered books.
This statement directly indicates the number of books with both blue covers and leather covers, but it doesn't specify the total number of books with blue covers that might include non-leather-covered books. So, statement (2) alone is  insufficient.

Combining the statements 
From (2), we know there are 36 blue leather-covered books.
From (1), we know 15 percent of all books are leather-covered, and 40 percent of those leather-covered books are novels—nothing directly about blue covers.
The provided data only confirms 36 blue leather-covered books without addressing the existence or number of non-leather blue-covered books, we cannot determine the total number of blue-covered books with certainty.
 Hence,  E

MaitriD · Answer

(1) Of the books on the shelf, 15 percent have leather covers and 40 percent of the leather-covered books are novels.

Statement 1 does not give us any information about blue cover books.  Insufficient

(2) There are 36 blue leather-covered books on the shelf.

Statement 2 tells us about blue cover leather books but there could also be blue cover books that are non-leather.  Insufficient

Statement 1 and 2 together:
Statement 1 does not provide use any information that can be used with statement 2 to get a clearer number of total blue cover books  Insufficient

Option E

Dereno · Answer

We need to find the number of books which are blue .

Statement 1:

(1) Of the books on the shelf, 15 percent have leather covers and 40 percent of the leather-covered books are novels.

If the number of books on the shelf is 100, then 15 books have leather covers.

Of the 15 leathered covered books, the number of books which are novels = 40%(15) = 6.

So, 6 represents the number of Leather covered novels, while the rest (9) denote the leather covered non-novels.

Hence, there is no mention about blue coloured or any other coloured books.

Thus,  Insufficient.

Statement 2:

(2) There are 36 blue leather-covered books on the shelf.

This statement represents the number of blue covered LEATHER books as 36.

But, there are some non leather blue covered books also, hence without knowing this count, we cannot ascertain a fixed number.

Hence,  Insufficient.

Combining both statements 1 and 2,

We are still not sure about the non leathered books or blue coloured books or non blue coloured books.

Hence,  Insufficient.

Option E

How many of the books on the shelf have blue covers?

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GMAT Data Sufficiency (DS) Questions

How many of the books on the shelf have blue covers?

Prep Toolkit

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