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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