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by sl750 » Tue Aug 16, 2011 3:37 am
In a certain art museum, 15 percent of the collection consists of oil paintings from the Impressionist period. If 40 percent of the oil paintings in the museum's collection are not from the Impressionist period, what percent of the museum's collection consists of oil paintings?

A 80%
B 65%
C 33.5 %
D 25%
E 20%

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I was unable to solve this problem, because I approached it with a different understanding. I thought, my goal is to find the percent of oil paintings (Impressionist and Non impressionist) out of the total number of paintings. But the explanation says, if 40%of the paintings are from the Non impressionist period, then 60% of the paintings are from the Impressionist period. I did not follow this line of reasoning. I mean why are we assuming that there are only two types of oil paintings?

Any help is appreciated. Thanks
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by GMATGuruNY » Tue Aug 16, 2011 4:55 am
if 40%of the paintings are from the Non impressionist period, then 60% of the paintings are from the Impressionist period. I did not follow this line of reasoning. I mean why are we assuming that there are only two types of oil paintings?
A marble is either green or not green.
A sweater is either wool or not wool.
A painting is either Impressionist or not Impressionist.

This is the reasoning being used.
"Not Impressionist" includes EVERY kind of painting that is NOT Impressionist.
sl750 wrote:In a certain art museum, 15 percent of the collection consists of oil paintings from the Impressionist period. If 40 percent of the oil paintings in the museum's collection are not from the Impressionist period, what percent of the museum's collection consists of oil paintings?

A 80%
B 65%
C 33.5 %
D 25%
E 20%
We can plug in the answers, which represent what percent of the collection consists of oil paintings.

Let total paintings = 100.

Answer choice C (33.5%) seems unlikely. The correct answer is probably an integer value.

Answer choice D: 25 oil paintings.
Since 40% of the oil paintings are not Impressionist, Oil but Not Impressionist = .4*25 = 10.
Thus, Oil and Impressionist = 25-10 = 15.
(Oil and Impressionist)/Total = 15/100 = 15%.
Success!

The correct answer is D.
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by HarryPotter » Tue Aug 16, 2011 5:41 am
Non impressionist : NI
impressionist : I

Let us say, there are 10 paintings from 'I' period and 10 from 'NI' period.
Total paintings in the museum = 20

'15 percent of the collection consists of oil paintings from the Impressionist period'
Therefore, Oil painting from I period = 15% of 20 = 3 ...(i)

' 40 percent of the oil paintings in the museum's collection are not from the Impressionist period'
Let total number of oil paintings be 'x', then oil paintings that belong to NI period = .4x ...(ii)

From (i) and (ii)

Total number of oil paintings from I and NI period: x = 3 + .4x
Therefore x = 5

% of oil paintings in the museum = [spoiler]x/20 = 5/20 = 1/4 [/spoiler]
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by imhimanshu » Tue Aug 16, 2011 8:38 pm
Hi, Can this be solved using double matrix. If yes, can someone give a try on this.
Thanks
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