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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] New post 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
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 [#permalink] New post 04 Jan 2004, 17:09
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.. :shock:
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 [#permalink] New post 04 Jan 2004, 17:42
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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 [#permalink] New post 04 Jan 2004, 17:51
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.
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 [#permalink] New post 04 Jan 2004, 18:28
answer is all of the above:

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

Start with 1.5

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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 [#permalink] New post 04 Jan 2004, 18:55
Right, I see my mistake. So any could be the answer :oops: How could I assume that X = 5?!
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 [#permalink] New post 04 Jan 2004, 19:08
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.. :wink:

gotcha..thanks!!
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 [#permalink] New post 04 Jan 2004, 19:10
Titleist wrote:
answer is all of the above:

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

Start with 1.5

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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 [#permalink] New post 04 Jan 2004, 19:28
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.. :shock:



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

You like my new dog?
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 [#permalink] New post 04 Jan 2004, 19:33
Is that a Corgi or a Finnish Spitz?
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 [#permalink] New post 04 Jan 2004, 19:35
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?
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 [#permalink] New post 04 Jan 2004, 19:36
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 :wink:
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 [#permalink] New post 04 Jan 2004, 19:42
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.
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 [#permalink] New post 04 Jan 2004, 19:47
your dog has a fortune..!

now, I am going to have my genes transmuted. :wink: :twisted: :wink:
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 [#permalink] New post 04 Jan 2004, 21:07
Hey, Titleist-- do you call the pretty woman your girlfriend, or does she just like your dog?
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 [#permalink] New post 04 Jan 2004, 21:09
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.
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 [#permalink] New post 04 Jan 2004, 21:11
You interested stoolfi? I can possibly get you her number. :P
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 [#permalink] New post 04 Jan 2004, 21:14
Titleist wrote:
You interested stoolfi? I can possibly get you her number. :P


aaahh haaa..! got you, titleist.
Secret Agent - http://www.americansingles.com :wink:
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 [#permalink] New post 04 Jan 2004, 21:32
Titleist wrote:
dj wrote:
Titleist wrote:
You interested stoolfi? I can possibly get you her number. :P


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


Huh???!!!


:P
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 [#permalink] New post 04 Jan 2004, 21:43
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!
  [#permalink] 04 Jan 2004, 21:43
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