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Of the paintings that a certain artist created last year, the number..

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Of the paintings that a certain artist created last year, the number..  [#permalink]

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New post 30 Nov 2018, 16:29
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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%
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Re: Of the paintings that a certain artist created last year, the number..  [#permalink]

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New post 30 Nov 2018, 19:56
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dcummins 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%



You can do it in many ways..
Weighted average method
A very good and quick method if you can get hang of it..
So two percentages 48 and 30 and we are looking for final average percentage..
The ratio of U to F is 5:1 and % are 48 : 30..
As per the method.. average = 48-( \(\frac{48-30}{5+1}\)-1) = 48-3=45

You can also make equations and do it..
Let the number of framed be 100, so unframed = 500...
48% of 500 = 500*48/100=240
30% of 100 = 30
So total sold is 240+30=270..
% sold = \(\frac{270}{600}\)*100=270/6=45

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Of the paintings that a certain artist created last year, the number..  [#permalink]

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New post 30 Nov 2018, 20:41
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dcummins 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%


Let Unframed = UF, Framed = F.
So, UF = 5 * F (as given in question)

so let F = 20, hence UF = 100 (for simplicity and faster calculation)

therefore 48% of UF = 48
30% of F = 6

so total painting sold = 48 + 6 = 54
total paintings made = 100 + 20 = 120

required percentage = painting sold/painting made
=> (54/120)*100
=> (9/20)*100
=> 45% (Answer = E)
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Re: Of the paintings that a certain artist created last year, the number..  [#permalink]

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New post 01 Dec 2018, 01:50
dcummins 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%



let framed paintings be y and un framed be x
x=5y

let y be 20 so x 100 and total 120
48% of 100 and 30% of 20 ; 48+6 = 54 paintings were sold

54/120 *100= option E 45 %
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Of the paintings that a certain artist created last year, the number..  [#permalink]

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New post 01 Dec 2018, 03:55
dcummins 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%



unframed 100
framed 20

\(\frac{(48+6)}{120} *100% = 45%\)
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Re: Of the paintings that a certain artist created last year, the number..  [#permalink]

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New post 01 Dec 2018, 04:16
dcummins 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%



unframed paintings are 5x/6 and framed = x/6, where x are total. sold are (5x*(0.48))/6 + x*(0.30)/6 = 0.45x = 45%
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Re: Of the paintings that a certain artist created last year, the number..  [#permalink]

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New post 29 Dec 2018, 12:51
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%

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Re: Of the paintings that a certain artist created last year, the number..   [#permalink] 29 Dec 2018, 12:51
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