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# A square wooden plaque has a square brass inlay in the

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Manager
Joined: 23 Dec 2013
Posts: 235
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
Re: A square wooden plaque has a square brass inlay in the [#permalink]

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25 May 2017, 12:06
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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Joined: 20 May 2017
Posts: 2
Re: A square wooden plaque has a square brass inlay in the [#permalink]

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11 Jun 2017, 10:19
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.

Posted from my mobile device

Posted from my mobile device
Intern
Joined: 24 Aug 2017
Posts: 3
Re: A square wooden plaque has a square brass inlay in the [#permalink]

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12 Sep 2017, 10:06
Bunuel 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.

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 43898
Re: A square wooden plaque has a square brass inlay in the [#permalink]

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12 Sep 2017, 10:09
rkantsah wrote:
Bunuel 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.

Posted from my mobile device

Hope it helps.
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Posts: 2069
Re: A square wooden plaque has a square brass inlay in the [#permalink]

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15 Sep 2017, 11:19
Expert's post
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.

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

At this point, if we shrink or expand the plaque . . .

. . . 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.

[Reveal] Spoiler:
E

Cheers,
Brent
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Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39
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A square wooden plaque has a square brass inlay in the [#permalink]

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27 Dec 2017, 20:51
Bunuel wrote:
hrish88 wrote:
so doest it mean any width <= 39/4 is possible.

this is the 2nd last problem in OG.so i thought it would be difficult.

No I mean ANY width is possible.

Let the the side of small square be $$x$$ and the big square $$y$$.

Given: $$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$ --> $$\frac{x^2}{y^2}=\frac{25}{64}$$ --> $$\frac{x}{y}=\frac{5}{8}$$.

We are asked which value of $$\frac{y-x}{2}$$ is possible. $$\frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y=?$$.

Well, expression $$\frac{3}{16}y$$ can take ANY value depending on $$y$$: 1, 3, 4, 444, 67556, 0,9, ... ANY. Basically we are given the ratios of the sides (5/8), half of their difference can be any value we choose, there won't be any "impossible" values at all.

Hope it's clear.

I have difficulties this this part $$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$ --> $$\frac{x^2}{y^2}=\frac{25}{64}$$

How do you get it?
Math Expert
Joined: 02 Sep 2009
Posts: 43898
Re: A square wooden plaque has a square brass inlay in the [#permalink]

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27 Dec 2017, 21:06
1
KUDOS
Expert's post
Erjan_S wrote:
Bunuel wrote:
hrish88 wrote:
so doest it mean any width <= 39/4 is possible.

this is the 2nd last problem in OG.so i thought it would be difficult.

No I mean ANY width is possible.

Let the the side of small square be $$x$$ and the big square $$y$$.

Given: $$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$ --> $$\frac{x^2}{y^2}=\frac{25}{64}$$ --> $$\frac{x}{y}=\frac{5}{8}$$.

We are asked which value of $$\frac{y-x}{2}$$ is possible. $$\frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y=?$$.

Well, expression $$\frac{3}{16}y$$ can take ANY value depending on $$y$$: 1, 3, 4, 444, 67556, 0,9, ... ANY. Basically we are given the ratios of the sides (5/8), half of their difference can be any value we choose, there won't be any "impossible" values at all.

Hope it's clear.

I have difficulties this this part $$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$ --> $$\frac{x^2}{y^2}=\frac{25}{64}$$

How do you get it?

$$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$;

Cross multiply: $$39x^2=25y^2-25x^2$$;

Re-arrange: $$64x^2=25y^2$$;

$$\frac{x^2}{y^2}=\frac{25}{64}$$.

Hope it's clear.
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Re: A square wooden plaque has a square brass inlay in the   [#permalink] 27 Dec 2017, 21:06

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