Bunuel wrote:

A certain collector sold \(\frac{5}{8}\) of her paintings, including \(\frac{2}{3}\) of her impressionist paintings. If \(\frac{3}{5}\) of her paintings were impressionist, what fraction of the paintings that were NOT SOLD were impressionist?

A. \(\frac{1}{4}\)

B. \(\frac{3}{8}\)

C. \(\frac{2}{5}\)

D. \(\frac{8}{15}\)

E. \(\frac{5}{8}\)

s

Every painting is EITHER sold OR not sold.

Every painting is EITHER impressionist OR not impressionist.

For an either/or problem, use a DOUBLE-MATRIX to organize the data.

Let S = sold, NS = not sold, I = impressionist and NI = not impressionist.

Let the total number of paintings = the LCM of the 3 denominators in the prompt = 8*3*5 = 120.

The following matrix is yielded:

A certain collector sold \(\frac{5}{8}\) of her paintings.

Since total sold = \(\frac{5}{8} * 120 = 75\), the following matrix is yielded:

\(\frac{3}{5}\) of her paintings were impressionist.

Since total impressionist = \(\frac{3}{5} * 120 = 72\), the following matrix is yielded:

A certain collector sold...\(\frac{2}{3}\) of her impressionist paintings.Since \(\frac{2}{3}\) of the 72 impressionist paintings = \(\frac{2}{3} * 72 = 48\), the following matrix is yielded:

What fraction of the paintings that were NOT SOLD were impressionist?In the resulting matrix:

\(\frac{(impressionist-not-sold)}{(total-not-sold)} = \frac{24}{45} = \frac{8}{15}\).

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