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Geometry Problem from Quant Review

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by MoniqueK » Wed Nov 19, 2008 12:51 pm
Does anyone have a better explanation for the following question (#175 - PS from Quant. REview Book)?

A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches of the strip?

I. 1
II. 3
III. 4

Thank you!
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by aditi_bc » Wed Nov 19, 2008 8:25 pm
Let B be the length/side of the sqaure countertop.
Let A be the length/side of the square inlay
Thus width of the strip will be W=B-A and area of the strip will be B^2-A^2

Now from the information, area of inlay:area of strip=25:39
Thus A^2/B^2-A^2=25/39 , SOLVING 64A^2=25B^2 => A/B=5/8

SO B-A=8-5=3

Ans 3
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by Mozartain » Fri Nov 21, 2008 6:09 am
Hi Aditi,

what am i missing here? Isn't W = (B-A)/2, because the strip is on both sides of the inner square?
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by mals24 » Fri Nov 21, 2008 6:36 am
Area of the square tile = a^2 = 25
a = 5

Area of the outer square, A^2 = 25+39 = 64
A = 8

Ratio of a^2 : (A^2-a^2) = 25:39

When a = 5
A = 8
Width = (8-5)/2 = 1.5

a = 10
A = 16
Width = 6/2 = 3

When a = 15
A = 24
Width = 9/2 = 4.5

Hence the answer is II) 3.
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by 4meonly » Sun Nov 23, 2008 12:08 pm
I think all of the answers can be the width.

I'll mark the answer where are all of this.
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