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

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Bunuel
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The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   10 Jun 2019, 01:49
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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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D
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   10 Jun 2019, 01:59
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Bunuel wrote:
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


Let the shelves on 1st floor = 30
--> Shelves on 2nd floor = 2/3*30 = 20

Let the number of books per shelf on 1st floor = 6
--> The number of books per shelf on 2nd floor = 5/6*6 = 5

Total books on 1st floor = 30*6 = 180
Total books on 2nd floor = 20*5 = 100

Fraction of library's books on 1st floor = 180/280 = 9/14

IMO Option D.

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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   10 Jun 2019, 01:59
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Let the books on first floor be x then books on second floor is x*2/3*5/6= 10/18x.

Total books = x+10x/18 = 14x/9
Fraction of books on the first floor =x/14x/9 = 9/14. IMO option D

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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   17 Jun 2020, 08:16
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1st floor : 2nd floor : Total
=3*6 : 2*5 : (3*6)+(2*5)
=18 : 10 : 28

18/28 = 9/14

Ans: Option D
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   11 Mar 2022, 07:04
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Bunuel wrote:
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


Let's choose values that satisfy the given information...

The library has 2/3 as many shelves on its 2nd floor as it does on its 1st.
So, let's say there are 3 shelves on the 1st floor, which means there are 2 shelves on the 2nd floor

The second floor has 5/6 as many books per shelf as the first floor
So, let's say there are 6 books per shelf on the first floor, which means there are 5 books per shelf on the second floor.

The total number of books on the first floor = (3)(6) = 18 books
The total number of books on the second floor = (2)(5) = 10 books
The TOTAL number of books in the library = 18 + 10 = 28

What fraction of the library's books are on the first floor?
Of the library's 28 books, 18 are on the first floor.
Answer: 18/28 = 9/14

Answer: D
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   10 Jun 2019, 11:32
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Bunuel wrote:
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


word based question
let shelfs on 1st floor = 12
2nd floor shels; 8
books on 1st floor = 6
2nd floor books= 5
so total books 1st floor= 12*6 ; 72 and 2nd floor books ; 8*5 ; 40
total books ; 112
ratio of 1st floor books ; 72/112; 9/14
IMO D
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The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   13 Jun 2019, 00:48
It looks eGMAT question. I solved same question in the eGMAT. Please change source to eGMAT. It may be useful, if some one looking for only eGMAT questions in the gmatclub
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   20 Jun 2020, 15:32
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Bunuel wrote:
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


Solution:

We can let the second floor of the library have 2 shelves, and each of its shelves has 5 books. Thus the first floor has 3 shelves, and each of the shelves has 6 books. So, there are 2 x 5 = 10 books on the second floor and 3 x 6 = 18 books on the first floor. Therefore, 18/(10 + 18) = 18/28 = 9/14 of the library's books are on the first floor.

Answer: D
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink] New post   11 Mar 2023, 22:09
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on [#permalink]
11 Mar 2023, 22:09
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