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How many books are on the shelf?

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by himu » Mon Apr 08, 2013 4:52 am
A shelf contains hardcover and paperback books, of either fiction or nonfiction.How many books are on the shelf?

2/3 of the books are fiction and 1/4 of the books are hardcover
Fewer than 30 books are paperback and more than 10 are nonfiction
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Source: — Data Sufficiency |

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by Anju@Gurome » Mon Apr 08, 2013 5:07 am
himu wrote:A shelf contains hardcover and paperback books, of either fiction or nonfiction.How many books are on the shelf?
(1) 2/3 of the books are fiction and 1/4 of the books are hardcover
(2) Fewer than 30 books are paperback and more than 10 are nonfiction
Let us assume there are n books on the shelf.
We need to determine n.

Now, it is obvious that none of the statements are individually sufficient.

1 & 2 Together:
Form statement 1:
  • Number of non-fictions = (1 - 2/3)*n = n/3
    Number of paperbacks = (1 - 1/4)*n = 3n/4
Form statement 2:
  • Number of non-fictions > 10
    Number of paperbacks < 30
So, n/3 > 10 and 3n/4 < 30
--> n > 30 and n < 40

Now, n must be multiple of 3 and 4 as number of books must be integer.
Therefore, n is multiple of 12 and 30 < n < 40.
Hence, n = 36

Sufficient

The correct answer is C.
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by himu » Mon Apr 08, 2013 7:08 am
An excellent explanation to a fantastic question :)
thanks so much !
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by GMATGuruNY » Mon Apr 08, 2013 7:45 am
himu wrote:A shelf contains hardcover and paperback books, of either fiction or nonfiction.How many books are on the shelf?

2/3 of the books are fiction and 1/4 of the books are hardcover
Fewer than 30 books are paperback and more than 10 are nonfiction
This is an EITHER/OR group question.
Every book is EITHER hardcover OR paperback.
Every book is EITHER fiction OR nonfiction.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

There are two fractions in statement 1: 2/3 and 1/4.
Since the product of the denominators = 4*3 = 12, let the TOTAL = 12x.
Here's the grid:
_______________F______NF_______Total

H:

P:

Total:___________________________12x
Values in the grid have to add up horizontally and vertically.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

Statement 1; 2/3 of the books are fiction and 1/4 of the books are hardcover.
Thus, total fiction = (2/3)12x = 8x, and total hardcover = (1/4)12x = 3x.
The result is the following grid:
________________F______NF______Total

H:_______________________________3x

P:________________________________9x

Total:___________8x______4x______12x
No way to determine the value of 12x.
INSUFFICIENT.

Statement 2: Fewer than 30 books are paperback and more than 10 are nonfiction.
No way to determine the total number of books.
INSUFFICIENT.

Statements combined:
The grid indicates that total P = 9x and total NF = 4x.
Thus:
9x < 30, implying that x < 10/3.
4x > 10, implying that x > 5/2.
Thus, x = 3, implying that the total number of books = 12x = 12*3 = 36.
SUFFICIENT.

The correct answer is C.
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