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A square wooden plaque has a square brass inlay in the

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Joined: 23 Dec 2013
Posts: 235

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Location: United States (CA)
GMAT 1: 760 Q49 V44
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Re: A square wooden plaque has a square brass inlay in the [#permalink]

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New post 25 May 2017, 13:06
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?

I. 1
II. 3
III. 4

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II , and III

Problem Solving
Question: 175
Category: Geometry Area
Page: 85
Difficulty: 600


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L = length of wooden plaque
X - length of brass inlay

We are told that x^2/(L^2-x^2) = 25/39

39x^2 = 25L^2 - 25x^2
64x^2 = 25L^2
8x = 5L
x/L = 5/8

Now we know that the width of the frame is (L - x)/2

8x/5 = L

(8x/5 - x)/2 = (16x - 5x)/10*2

11x/20

or

x = 5L/8
(L - 5/8L)/2

= 3L / 16

Any values for x or L are possible because neither needs to be an integer.

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Re: A square wooden plaque has a square brass inlay in the [#permalink]

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New post 11 Jun 2017, 11:19
If the ratio of areas is given then the areas can be anything,
If the areas can be anything​ then the sides can be anything,
If the sides can be anything then the width can be anything.
Answer: E

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Re: A square wooden plaque has a square brass inlay in the [#permalink]

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New post 12 Sep 2017, 11:06
Bunuel wrote:
mymbadreamz wrote:
Why is it not y-x? Why do we calculate (y-x)/2?


Consider the diagram below:
Attachment:
Wooden strip.png
As you can see the width of the wooden strip (the width of grey strip) is \(\frac{y-x}{2}\).


I still don't understand the fact that why do width of wooden strip is Y-X/2 but not Y-X.
Please do elaborate little more.

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Re: A square wooden plaque has a square brass inlay in the [#permalink]

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New post 12 Sep 2017, 11:09
rkantsah wrote:
Bunuel wrote:
mymbadreamz wrote:
Why is it not y-x? Why do we calculate (y-x)/2?


Consider the diagram below:
Attachment:
Wooden strip.png
As you can see the width of the wooden strip (the width of grey strip) is \(\frac{y-x}{2}\).


I still don't understand the fact that why do width of wooden strip is Y-X/2 but not Y-X.
Please do elaborate little more.

Posted from my mobile device


Please go through the whole thread: https://gmatclub.com/forum/a-square-woo ... l#p1068331

Hope it helps.
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Re: A square wooden plaque has a square brass inlay in the [#permalink]

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New post 15 Sep 2017, 12:19
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Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?

I. 1
II. 3
III. 4

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II , and III


Let's say we want to create a plaque with a square brass inlay in the center, and we want the brass to wood ratio to be 25:39

Let's begin a square wooden board with ANY dimensions.
Image


Now place a square brass inlay in the middle of the wooden board, and keep adjusting the size of the brass inlay until we have a brass to wood ratio that is 25:39
Image

At this point, if we shrink or expand the plaque . . .
Image
. . . the brass to wood ratio will remain at 25:39

So, as you can see, this plaque can be ANY size, which means the width of the wooden strip can have ANY measurement.

Answer:
[Reveal] Spoiler:
E


Cheers,
Brent
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Re: A square wooden plaque has a square brass inlay in the   [#permalink] 15 Sep 2017, 12:19

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