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# The public library has exactly 2 floors. It has 2/3 as many shelves on

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Manager
Joined: 20 Nov 2009
Posts: 146
The public library has exactly 2 floors. It has 2/3 as many shelves on  [#permalink]

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22 Jul 2010, 22:19
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Difficulty:

55% (hard)

Question Stats:

61% (01:31) correct 39% (01:57) wrong based on 93 sessions

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The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?

A. 1/4
B. 5/14
C. 5/9
D. 9/14
E. 5/6

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Manager
Joined: 20 Mar 2010
Posts: 80
Re: The public library has exactly 2 floors. It has 2/3 as many shelves on  [#permalink]

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22 Jul 2010, 23:24
Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (2/3)*x
no of books per shelf on 2nd floor = (5/6) * y

So total no books on first floor = xy and total no of books on 2nd floor = (2/3)*x*(5/6)*y = (5/9)*xy

fraction of library books on first floor = (xy)/(xy + (5/9)*xy)
=1 / (1+(5/9))
=9/14
So D
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Joined: 09 Jun 2010
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Concentration: General Management, Nonprofit
Re: The public library has exactly 2 floors. It has 2/3 as many shelves on  [#permalink]

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23 Jul 2010, 06:38
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1
The easiest way to solve this problem would be to imagine a table of sorts.

Attachment:
File comment: Table

c73058.jpg [ 6.14 KiB | Viewed 2002 times ]

So as you can see from the table I've attached, total number of books on each floor = Number of shelves*Number of books per shelf.

So you get:

Floor 1: $$xn$$
Floor 2: $$\frac{2}{3}x*\frac{5}{6}n = \frac{5}{9}xn$$

So total number of books = $$xn+\frac{5}{9}xn$$ = $$\frac{14}{9}xn$$

So the fraction of number of books on Floor 1: $$\frac{xn}{\frac{14}{9}xn}=\frac{9}{14}$$

Hope this helps.
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Joined: 09 Sep 2013
Posts: 8105
Re: The public library has exactly 2 floors. It has 2/3 as many shelves on  [#permalink]

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27 Mar 2017, 16:36
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on &nbs [#permalink] 27 Mar 2017, 16:36
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