Problem Solving

Hi All,

We're told that of the paintings that a certain artist created last year, the number of paintings that were UNFRAMED was 5 times the number of paintings that were FRAMED and 48 percent of the UNFRAMED paintings and 30 percent of the FRAMED paintings were SOLD. We're asked for the percent of the paintings that the artist created last year were SOLD. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF....
# of unframed paintings = 100
# of framed paintings = 100/5 = 20
Total number of paintings = 100 + 20 = 120

# of SOLD unframed paintings = (.48)(100) = 48
# of SOLD framed paintings = (.3)(20) = 6
Total number of SOLD paintings = 48 + 6 = 54

Percent of paintings sold = 54/120 = 9/20 = 45%

Final Answer: E

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BTGmoderatorDC wrote:Of the paintings that a certain artist created last year, the number of paintings that were unframed was 5 times the number of paintings that were framed. If 48 percent of the unframed paintings and 30 percent of the framed paintings were sold, what percent of the paintings that the artist created last year were sold?

A. 33%
B. 36%
C. 39%
D. 42%
E. 45%

OA E

Source: GMAT Prep

We can let f = the number of framed paintings and u = unframed; thus, the total number of paintings is (u + f), and:

u = 5f

and

0.48u + 0.3f = sold

So we have:

sold/total = (0.48u + 0.3f)/(u + f)

Substituting u = 5f, we have:

(0.48 x 5f + 0.3f)/(5f + f)

(2.4f + 0.3f)/6f

2.7f/6f = 27/60 = 9/20 = 45/100 = 45%.

Alternate solution:

We can let the number of framed paintings = 20 and thus the number of unframed paintings = 100. Furthermore, 0.48 x 100 = 48 unframed paintings and 0.3 x 20 = 6 framed paintings were sold. Therefore, the percentage of the paintings that the artist created last year that were sold is:

(48 + 6)/(100 + 20)

54/120 = 9/20 = 45/100 = 45%

Answer: E