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# OG M # 175 A square countertop has a square tile inlay in

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Manager
Joined: 31 Jul 2006
Posts: 220
OG M # 175 A square countertop has a square tile inlay in [#permalink]

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10 Oct 2008, 21:32
OG M # 175
A square countertop has a square tile inlay in the center, leaving an untiled strip
of uniform width around the tile. If the ratio fo the tiled are to the untiled area is
25 to 39, which of the ff could be the width, in inches, of the strip?
I. 1
II. 3
III. 4

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VP
Joined: 30 Jun 2008
Posts: 1007
Re: OG M # 175 [#permalink]

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10 Oct 2008, 21:53
A square countertop has a square tile inlay in the cente, leaving an untiled stripof 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?
a) 1.5
b) 3
c) 4.5

A) a only
B) b only
C) a and b only
D) a and c only
E) a, b and c

I believe this is the full question.

Now say X is the length of one of the sides of the Square counter-top. And there is another small square tile in between the larger square. The smaller square leaves equal width on all four sides.

Now given that the ratio of Tiled portion to Untiled portion is 25/39
So tiled portion is a multiple of 25 and untiled portion is a multiple of 39.
We can rewrite the ratio as 25y/39y where y is the common multiple of 25 and 39.
y can be any positive integer.

the area of the tile will be = 25y and area of untiled portion = 39y
Now the area of the counter-top = X² = Area of tile + Area of untiled portion = 25y + 39y = 64y

when y=1, X²=64 and X=8 and Area of tiled portion = 25, length of side of tile = 5

width of untiled portion = (8-5)/2 =1.5

When y=2, width = 3
When y=3, width = 4.5

So answer is E. All three are possible widths of the untiled portion.

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: OG M # 175   [#permalink] 10 Oct 2008, 21:53
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# OG M # 175 A square countertop has a square tile inlay in

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