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George has a total of B books in his library

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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George has a total of B books in his library

Post Thu Jul 27, 2017 12:11 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

    (1) 40 of the B books are fiction and the rest are nonfiction
    (2) 60 of the B books are hardcovers and the rest are paperbacks

    Official Guide question
    Answer: E

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    Post Thu Jul 27, 2017 11:02 pm
    jjjinapinch wrote:
    George has a total of B books in his library, 25 of which are hardcover fiction books. What is the value of B?

    (1) 40 of the B books are fiction and the rest are nonfiction
    (2) 60 of the B books are hardcovers and the rest are paperbacks

    Official Guide question
    Answer: E
    We have the total number of books = B;

    Say,
    Number of Hardcover books = H;
    Number of Hardcover Fiction books = HF;
    Number of Hardcover Non-fiction books = HNF;

    Number of Paperback books = P;
    Number of Paperback Fiction books = PF;
    Number of Paperback Non-fiction books = PNF

    Thus,
    B = H + P ---(1)

    B = [HF + HNF] + [PF + PNF] ---(2)

    B = [25 + HNF] + [PF + PNF] ---(2)

    We have to get the value of B.

    Statement 1: 40 of the B books are fiction and the rest are nonfiction.

    => HF + PF = 40 and HNF + PNF = B - 40
    => PF = 40 - 25 = 15

    From eqn (2), we have

    B = [25 + HNF] + [15 + PNF] ---(2)
    B = 40 + HNF + PNF
    B = 40 + B - 40
    B = B. Can't get B. Insufficient.

    Statement 2: 60 of the B books are hardcovers and the rest are paperbacks.

    => H = 60 => H = HF + HNF => 60 = 25 + HNF => HNF = 35

    From eqn (1), we have

    B = H + P ---(1)

    B = 40 + P. We do not know the value of P. Insufficient.

    Statement 1 and 2:

    Even after combining both the statement, we cannot get the value of PNF, thus the value of B. Insufficient.

    The correct answer: E

    Hope this helps!

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