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An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the

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An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the

by Gmat_mission » Thu Aug 27, 2020 8:11 am

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An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 200 sculptures are not on display, how many pieces of art does the gallery have?

A. 360
B. 450
C. 540
D. 640
E. 720

Answer: B

Source: Veritas Prep
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Re: An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the

by dg1900 » Thu Aug 27, 2020 9:36 am
Read the question carefully once again before getting to the solution.

The only number we have is number of sculptures not on display that is 200.
We will use this piece of info to get to the number of pieces of art the gallery has.
Let N be the number of pieces of art the gallery has.

Firstly,
If 1/3 of the pieces are on display this shows us 2/3 of pieces of art are not on display.
Secondly,
If 1/3 of pieces not on display are painting we know that out of the pieces not on display 2/3 are sculptures.

Using the 2 points above we can conclude,
N*(2/3)*(2/3) = Number of sculptures not on display = 200
Solving this alebra for the value of N we get:
N=(200*3*3)/(2*2) = 450
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