Hi gmat_guy666,

This question can be solved either algebraically or by TESTing THE ANSWERS. Here's how you can use TEST THE ANSWERS;

We're asked for the TOTAL PIECES OF ART the gallery has....we know that there are only 2 types: paintings and sculptures....

First, we're told that 1/3 of the pieces are on display, so the total MUST be a multiple of 3. Let's TEST Answer B first (Answer D is NOT a multiple of 3, so it CANNOT be the answer).

If....
Total pieces of art = 450
Pieces on Display = (1/3)(450) = 150

1/6 of the pieces on display are sculptures
Pieces on Display = 150
Sculptures on Display = (1/6)(150) = 25
Paintings on Display = 125

Pieces NOT on Display = 300
Paintings = (1/3)(300) = 100
Sculptures = 200 --> This matches the last piece of information PERFECTLY.

Thus, the total number of pieces MUST be 450.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

I'd like to point out that Mitch's "group grid" (aka Double Matrix Method) can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of art pieces, and the two characteristics are:
- painting or sculpture
- on display or not on display

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3