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by tonebeeze » Mon Jan 17, 2011 11:01 am
A square wooden plaque has a 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
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by maihuna » Mon Jan 17, 2011 11:58 am
OA E:

Try to solve the eqns in terms of Length and breadth, you get final eqn in terms of each other meaning any value will suffice. I am not sure how to embed image let me try.
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by anshumishra » Mon Jan 17, 2011 12:15 pm
Will keep it short as I am on mobile.
a^2/[(a+d)^2 - a^2] = 25/39
=> [a/(a+d)]^2 = 25/(25+39) = (5/8)^2
=> 8a = 5a + 5 d
=> d = 3a/5
width of one side = d/2 = 3a/10.
so, d can have any value depending on the value of a.
So, answer E.


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by GMATGuruNY » Mon Jan 17, 2011 4:02 pm
tonebeeze wrote:A square wooden plaque has a 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
There is no math to be done here; just use common sense. Why couldn't the width of the strip be any value? We could choose a width for the strip, then shrink or expand the inlay until the ratio of inlay area:strip area = 25:39.

The correct answer is E.
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by anshumishra » Mon Jan 17, 2011 6:03 pm
GMATGuruNY wrote:
tonebeeze wrote:A square wooden plaque has a 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
There is no math to be done here; just use common sense. Why couldn't the width of the strip be any value? We could choose a width for the strip, then shrink or expand the inlay until the ratio of inlay area:strip area = 25:39.

The correct answer is E.
Perfect ! Makes sense !
Thanks
Anshu

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by tonebeeze » Tue Jan 18, 2011 9:25 am
GMATGuruNY wrote:
tonebeeze wrote:A square wooden plaque has a 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
There is no math to be done here; just use common sense. Why couldn't the width of the strip be any value? We could choose a width for the strip, then shrink or expand the inlay until the ratio of inlay area:strip area = 25:39.

The correct answer is E.
Exactly! I got the answer correct intuitively, however the answer in the book made me feel as if I did not understand the underlying logic. Thanks.
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