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A square countertop has a square tile inlay in the center,

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A square countertop has a square tile inlay in the center, [#permalink]  04 Jan 2004, 16:51
A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ration of the tiled area to the untiled area is 25 to 39, which of the following could be the width of the strip?

I) 1 1/2
II) 3
III) 4 1/2
Director
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all of these could be the width.. weird haan..!

I am getting, width = 3/10 * X
X, is the length of square tile..
or, X = 10/3 * width

width: 3/2 or 3 or 9/2

something 's wrong..
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Let X = the side of the tiled area
Let X+2Y = the side of the countertop

We know that X^2 / [ ( X + 2Y )^2 - X^2 ] = 25 / 39
Thus, the nominator X^2 = 25 and X = 5

The denominator [ ( X + 2Y )^2 - X^2 ] = 39
X^2 + 4XY + 4Y^2 - X^2 = 39
4XY + 4Y^2 = 39
But we know that X = 5
The equation simplifies to : 4Y^2 + 20Y = 39
Plugging in 1 1/2, 3, 4 1/2, we find that only 1 1/2 satifies the equation
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Paul

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Hey, rc197906, if you're going to post these questions, at least note that more than one answer could be correct, lest you confuse dj-- who must not remember this question from the OG-- by making him think that only one answer is correct.
Director
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answer is all of the above:

think of it this way (sorry for the crude diagram - art was never my calling).

1.5 as a possible width

assume side of the square is 8 thus you have the total area of the countertop = 64

Therefore, if 1.5 is the width of the side of the tiled countertop then the side of the inlay is 5. the area of the inlay is 5x5=25. and the area of the sides are 8x8=64 minus the inlay = 39. thus we have the ratio 25/39

The other two choices are multiples of 1.5 so they will work too.

Hope this helps.
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GMAT Club Legend
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Right, I see my mistake. So any could be the answer How could I assume that X = 5?!
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Best Regards,

Paul

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stoolfi wrote:
Hey, rc197906, if you're going to post these questions, at least note that more than one answer could be correct, lest you confuse dj-- who must not remember this question from the OG-- by making him think that only one answer is correct.

oohhh, yeh. each answer satisfied the solution and that made me look upside down..

gotcha..thanks!!
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Titleist wrote:
answer is all of the above:

think of it this way (sorry for the crude diagram - art was never my calling).

1.5 as a possible width

assume side of the square is 8 thus you have the total area of the countertop = 64

Therefore, if 1.5 is the width of the side of the tiled countertop then the side of the inlay is 5. the area of the inlay is 5x5=25. and the area of the sides are 8x8=64 minus the inlay = 39. thus we have the ratio 25/39

The other two choices are multiples of 1.5 so they will work too.

Hope this helps.

eeeeeeehhhhhhh hooooooooo..!!
TITLEIST came for my rescue
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dj wrote:
all of these could be the width.. weird haan..!

I am getting, width = 3/10 * X
X, is the length of square tile..
or, X = 10/3 * width

width: 3/2 or 3 or 9/2

something 's wrong..

I'll give it to you - you had the answer right from the get-go!

You like my new dog?
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Director
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Is that a Corgi or a Finnish Spitz?
Director
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stoolfi wrote:
Is that a Corgi or a Finnish Spitz?

Shiba Inu - just ordered a puppy from a breeder. I'm thinking of a name - any suggestions?
Director
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Titleist wrote:
I'll give it you - you had the answer right from the get-go!

You like my new dog?

oohhh yeh. I am jealous.. he doesn't need to solve creepy DS problems
Director
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The life of a dog is good. Eat, sleep, and cuddle with beautiful women who think you're cute and cuddly. Why we were born human (especially as aspiring MBA students) beats me.
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Last edited by Titleist on 04 Jan 2004, 19:56, edited 1 time in total.
Director
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now, I am going to have my genes transmuted.
Director
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Hey, Titleist-- do you call the pretty woman your girlfriend, or does she just like your dog?
Director
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stoolfi wrote:
Hey, Titleist-- do you call the pretty woman your girlfriend, or does she just like your dog?

She's not my girlfriend. My girlfriend is not as pretty - It's a good thing I'm some anonymous bloke.
Director
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You interested stoolfi? I can possibly get you her number.
Director
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Titleist wrote:
You interested stoolfi? I can possibly get you her number.

aaahh haaa..! got you, titleist.
Secret Agent - http://www.americansingles.com
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Titleist wrote:
dj wrote:
Titleist wrote:
You interested stoolfi? I can possibly get you her number.

aaahh haaa..! got you, titleist.
Secret Agent - http://www.americansingles.com

Huh???!!!

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Titleist--
I've got my own girl, and she's the greatest.

Since you said that the girl in the photo is prettier than your girl, though, I'd watch my back if I were you. Or at least clean my cache!

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