Problem Solving

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.