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An art gallery has only paintings and sculptures. Currently,

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An art gallery has only paintings and sculptures. Currently,

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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

OA B

Source: Veritas Prep

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If 1/3 of the non-displayed things are paintings, 2/3 of them are sculptures. So if 200 are sculptures, we have 300 non-displayed things in total. Since 1/3 of things are on display, the ratio of displayed to not is 1 to 2, so we have 150 things on display, and 150+300 = 450 things in total.

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BTGmoderatorDC wrote:
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

OA B

Source: Veritas Prep
We see that 2/3 of the art pieces are not on display. So 1/3 x 2/3 = 2/9 of the art pieces are paintings not on display, and 2/3 x 2/3 = 4/9 of the art pieces are sculptures not on display. Since there are 200 sculptures not on display, and if we let x = total number of art pieces, we have:

(4/9)x = 200

x = 200 * (9/4) = 50 * 9 = 450

Answer: B

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Quote:
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?

360

450

540

640

720

OAB
This is an EITHER/OR group problem.
Every piece of art is EITHER a painting OR a sculpture.
Every piece of art is EITHER displayed OR not displayed.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.

Let P = paintings, S = sculptures, D = displayed, ND = not displayed.
Let the total number of pieces of art = 18x.
Here's the grid:

In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column.

Currently, 1/3 of the pieces of art are displayed.
The following grid is yielded:


1/6 of the pieces on display are sculptures.
The following grid is yielded:


1/3 of the pieces not on display are paintings.
The following grid is yielded:


200 sculptures are not on display.
According to the completed grid, sculptures not displayed = 8x.
Thus:
8x = 200
x = 25.

How many pieces of art does the gallery have?
Total number of pieces of art = 18x = 18*25 = 450.

The correct answer is B.

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