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An art gallery has only paintings and sculptures. Currently, 1/3

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An art gallery has only paintings and sculptures. Currently, 1/3 [#permalink]

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New post 20 Sep 2014, 23:43
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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
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Re: An art gallery has only paintings and sculptures. Currently, 1/3 [#permalink]

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New post 21 Sep 2014, 01:12
gmatquant25 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


Too many words and redundant info there.

(i) 1/3 of the pieces of art are displayed, hence 2/3 of the pieces of art are NOT displayed.

(ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.

(iii) 1/3 of the pieces NOT on display are paintings, hence 2/3 of the pieces NOT on display are sculptures.

200 sculptures are not on display, so according to (iii) 2/3*{not on display} = 200 --> {not on display} = 300.

According to (i) 2/3*{total} = 300 --> {total} = 450.

Answer: B.
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Re: An art gallery has only paintings and sculptures. Currently, 1/3 [#permalink]

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New post 22 Sep 2014, 01:51
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Solved using matrix method:

Attachment:
scul.png
scul.png [ 5.14 KiB | Viewed 4323 times ]


1. Let total art = x

2. \(\frac{1}{3}\) are on display = \(\frac{x}{3}\)

3. So total not on display\(= x - \frac{x}{3} = \frac{2x}{3}\)

4. 1/3 NOT on display are paintings \(= \frac{2x}{3} * \frac{1}{3} = \frac{2x}{9}\)

5. Sculptures NOT on display = 200

Setting up the equation:

\(\frac{2x}{9} + 200 = \frac{2x}{3}\)

x = 450

Answer = B
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Re: An art gallery has only paintings and sculptures. Currently, 1/3 [#permalink]

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New post 15 Feb 2016, 07:43
used the table thing and it took me exactly 4.11 in the CAT and my eyes went clocky and dizzy towards the solution that i had to close my eyes and breathe before getting comfortable enough to do the next question. i guess @bunuel's equation method needs a good learning.
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Re: An art gallery has only paintings and sculptures. Currently, 1/3 [#permalink]

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New post 03 Oct 2016, 00:16
Guys,
The info "1/6 of the pieces on display are sculptures" is useless, right?
I have answer without using it. Is it added to the question for distract?
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Re: An art gallery has only paintings and sculptures. Currently, 1/3 [#permalink]

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New post 03 Oct 2016, 05:53
ThangLe wrote:
Guys,
The info "1/6 of the pieces on display are sculptures" is useless, right?
I have answer without using it. Is it added to the question for distract?


Correct, even if that information is not given, we can calculate the answer. Hence, Its just to distract test takers.
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Re: An art gallery has only paintings and sculptures. Currently, 1/3 [#permalink]

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New post 05 Mar 2018, 12:55
Hi All,

This question can be solved either algebraically or by TESTing 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:

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Re: An art gallery has only paintings and sculptures. Currently, 1/3   [#permalink] 05 Mar 2018, 12:55
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