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# A certain collector sold 5/8 of her paintings, including 2/3 of her

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Math Expert
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A certain collector sold 5/8 of her paintings, including 2/3 of her  [#permalink]

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18 Jun 2018, 21:42
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55% (hard)

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67% (02:46) correct 33% (02:57) wrong based on 94 sessions

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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. $$\frac{5}{8}$$

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Re: A certain collector sold 5/8 of her paintings, including 2/3 of her  [#permalink]

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18 Jun 2018, 21:55
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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. $$\frac{5}{8}$$

Let's assume that the collector has 80 paintings.

We are told that $$\frac{5}{8}$$ of the paintings ($$\frac{5}{8}*80 = 50$$ paintings) are sold.

$$\frac{3}{5}$$ of her paintings were impressionist -> $$\frac{3}{5}*80 = 48$$ paintings were impressionist.

Of the impressionist paintings, $$\frac{2}{3}*48 = 32$$ paintings are sold.

Therefore, the fraction of impressionist paintings that were not sold is $$\frac{48-32}{80-50} = \frac{16}{30} = \frac{8}{15}$$(Option D)
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Re: A certain collector sold 5/8 of her paintings, including 2/3 of her  [#permalink]

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19 Jun 2018, 05:17
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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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Re: A certain collector sold 5/8 of her paintings, including 2/3 of her  [#permalink]

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18 Jun 2018, 22:16

Solution

Given:
• A collector sold $$\frac{5}{8}$$ of her paintings, which include $$\frac{2}{3}$$ of her impressionist paintings
• $$\frac{3}{5}$$ of her paintings were impressionist

To find:
• The fraction of the paintings that were not sold were impressionist

Approach and Working:
As we have 3 fractional terms to deal with, we can assume the total number of paintings to be the LCM (8, 3, 5) = 120 [LCM of the denominators of the fractions]
• Total impressionist paintings = $$120 * \frac{3}{5} = 72$$
• Number of paintings sold = $$120 * \frac{5}{8} = 75$$
o Hence, number of paintings not sold = $$120 – 75 = 45$$

• Number of impressionist paintings sold = $$72 * \frac{2}{3} = 48$$
o Hence, number of impressionist paintings not sold = $$72 – 48 = 24$$

• Therefore, the fraction of paintings that were not sold were impressionist = $$\frac{24}{45} = \frac{8}{15}$$

Hence, the correct answer is option D.

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Re: A certain collector sold 5/8 of her paintings, including 2/3 of her  [#permalink]

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19 Jun 2018, 04:12
I picked number to start with. to selected easy number, i multiplied denominators of all fractions, 8*3*5=120, so total nu of painings assumed is 120. She sold a total of 75 painings, while she owned a total of 72 impressionist paintings, out of which she sold 2/3 or 48. So she has the remaining of 24 impress. painings, while total nu is 120-75, 45. so it is 24/45
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Re: A certain collector sold 5/8 of her paintings, including 2/3 of her  [#permalink]

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26 Mar 2019, 13:53
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. $$\frac{5}{8}$$

HELLO!
LCM (8, 3, 5) = 120
Sold=120*5/8=75
Impression=120*3/5=72
Imp sold=72*2/3=48
Imp unsold =72-48=24
Unsold=120-75=45
Fr=24/45=8/15
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Re: A certain collector sold 5/8 of her paintings, including 2/3 of her   [#permalink] 26 Mar 2019, 13:53
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