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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