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A library branch originally contained 18360 volumes, 30% of

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A library branch originally contained 18360 volumes, 30% of

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A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/3 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?

A. \(2.5\%\)
B. \(17.67\%\)
C. \(28.3\%\)
D. \(45.2\%\)
E. \(73.6\%\)

OA C

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A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/3 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?

A. \(2.5\%\)
B. \(17.67\%\)
C. \(28.3\%\)
D. \(45.2\%\)
E. \(73.6\%\)
Since the answer choices are PERCENTS, the total number of books can be ANY POSITIVE VALUE.
30% = 3/10, implying a denominator of 10.
Let the total number of books = the product of the three denominators 10, 3 and 3 = 10*3*3 = 90.

Since 30% of the books are fiction, the number of fiction books = 30% of 90 = 27.

Since 1/3 of all the 90 books are transferred, the number of transferred books= (1/3)(90) = 30, implying that the number of remaining books = 90-30 = 60.

Since 1/3 of the 30 transferred books are fiction, the number of transferred fiction books = (1/3)(30) = 10, implying that the number of remaining fiction books = 27-10 = 17.

What percent of the remaining collection was fiction novels?
(remaining fiction books)/(total remaining books) * 100 = 17/60 * 100 ≈ 28.3.

The correct answer is C.

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