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Jack has a total of b hardback and paperback books in his library. If

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Jack has a total of b hardback and paperback books in his library. If [#permalink]

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New post 05 Feb 2017, 23:39
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  25% (medium)

Question Stats:

85% (01:20) correct 15% (07:58) wrong based on 48 sessions

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Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?

(A) (1/9)b
(B) (3/20)b
(C) (3/16)b
(D) (1/3)b
(E) (9/16)b
[Reveal] Spoiler: OA

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Re: Jack has a total of b hardback and paperback books in his library. If [#permalink]

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New post 06 Feb 2017, 23:35
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Suppose the number of paperback books = p;
So, the number of hardback books = p/3;

total books = b = p + p/3 = 4p/3
=> p = 3b/4

Now, biographies books = (3b/4)*3/4 = 9b/16. Ans E.
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Re: Jack has a total of b hardback and paperback books in his library. If [#permalink]

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New post 08 Feb 2017, 18:53
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SajjadAhmad wrote:
Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?

(A) (1/9)b
(B) (3/20)b
(C) (3/16)b
(D) (1/3)b
(E) (9/16)b


We are given that Jack as a total of b hardback and paperback books in his library. We can let h = the number of hardback books and p = the number of paperback books, and thus h + p = b.

We know that the number of hardback books is 1/3 the number of paperback books, and thus:

h = (1/3)p

We can now substitute (1/3)p for h in the equation h + p = b:

(1/3)p + p = b

Multiplying the entire equation by 3, we have:

p + 3p = 3b

4p = 3b

p = 3b/4

Finally, we are given that 3/4 of the paperback books are biographies. Since p = 3b/4, we have:

(3/4)(3b/4) = biographies

9b/16 = biographies

Answer: E
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Re: Jack has a total of b hardback and paperback books in his library. If   [#permalink] 08 Feb 2017, 18:53
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