At Joels bookstore, the current inventory is 40% historical fiction.

Question

At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 50% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?

A. 4/25
B. 8/23
C. 2/5
D. 8/15
E. 2/3

Source: Veritas Prep.

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Dereno · Answer

Let the total number of books be 100.

Of this 40%(100) = 40 are Historical Fiction (HF)

Rest are Non Historical Fiction (NHF) = 100 - 40 = 60 books.

Of the HF = 40%(40) = New Release . Hence , NR_HF = 16. Not NR_HF = 24.

Of the Non HF = 60, 50% are New Release (NR) = Non_HF_NR = 30, the rest amongst these = 60-30 = 30 denotes the Non_HF_Not NR = 30.

Total new releases = 16+ 30 = 46

Fraction of New releases which are HF = 16/46 =  8/23

Option B

findingmyself · Answer

When such question arises, first step is to give a value to total number of books, let's call it X 
 Now as per question, History =0.4X, Thus others will be=0.6X (0.6X+0.4X=X)

Now we are told that of History F books (0.4X), 40% are new releases, which is 0.4*0.4X= 0.16X 
 Also we are told 0.5% of other books are new releases, which is 0.5*0.6X=0.30X 
 Total new releases=0.46X 
 History new releases is 0.16X 
 Fraction of all new releases to the historical fiction new releases= (History new release)/(Total new release)= \frac{0.16X}{0.46X} = \frac{8}{23}

Souradeep17 · Answer

Let total books be 100.
Historical fiction then is 40
New released historical fiction is 40% of 40 =16

50% of other half (new realeses)= 60/2=30

Total new release=30+16=46
Historical new release=16

Fraction 16/46=8/23 (option B)

GraemeGmatPanda · Answer

We define our variables to represent the total number of books, the number of historical fiction books, the historical fiction new releases, and the new releases among the other books.
 B = 	ext{total books} 
 H = 	ext{historical fiction books} 
 N_H = 	ext{historical fiction new releases} 
 N_O = 	ext{new releases among other books}

We translate the provided information into:
 \frac{40}{100} 	imes B = H

\frac{40}{100} 	imes H = N_H

\frac{50}{100} 	imes (B - H) = N_O

We express the total number of new releases as the sum of the two categories.
 N_{	ext{total}} = N_H + N_O

The desired fraction is the ratio of historical fiction new releases to the total new releases.
 \frac{N_H}{N_{	ext{total}}}

We substitute and simplify step by step to find the fraction.
 \frac{N_H}{N_{	ext{total}}} = \frac{\frac{40}{100}H}{\frac{40}{100}H + \frac{50}{100}(B - H)}

= \frac{\frac{40}{100}	imes \frac{40}{100}B}{\frac{40}{100}	imes \frac{40}{100}B + \frac{50}{100}	imes (1 - \frac{40}{100})B}

= \frac{0.16B}{0.16B + 0.30B}

= \frac{0.16}{0.46}

= \frac{\frac{16}{100}}{\frac{46}{100}}

= \frac{16}{46}

= \frac{8}{23}

Answer 8/23

Hope this helps! 
ʕ•ᴥ•ʔ

atilasol · Answer

Let's assume that the total number of books is 100 (see the attachment):

Number of new released HF books / Total number of new releases = 16/46 = 8/23

At Joels bookstore, the current inventory is 40% historical fiction.

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At Joels bookstore, the current inventory is 40% historical fiction.

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