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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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George has a total of B books in his library

Post Thu Jul 27, 2017 12:11 pm
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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Top Reply
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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