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Width of the strip

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Width of the strip

by minar » Wed Oct 27, 2010 10:39 pm
Couldn't be able to solve it. Please help.

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A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform 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

A) I only
B) II only
C) I and II only
D) I and III only
E) I, II, III only

OA: E
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by Rahul@gurome » Wed Oct 27, 2010 11:10 pm
Solution:
Let the length of the square tile inlay in the centre be x.
Let the width of the strip be d.
So area of tiled region is x^2.
So area of untiled region is (x+d)^2 - x^2.
So x^2 : (x+d)^2 - x^2 = 25:39.
So x^2 : (x+d)^2 = 25 : 25+39 = 25 : 64.
Or x: (x+d) = sqrt(25) : sqrt(64) = 5:8.
Or 8x = 5x+5d.
So 3x = 5d.
Or d = 3x/5.
Since x can take any positive real value, even d can take any positive real value.
Hence I, II and III can be the value of d.

The correct answer is E).
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by minar » Wed Oct 27, 2010 11:20 pm
very convincing explanation.
Many thanks!
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by GMATGuruNY » Thu Oct 28, 2010 7:15 am
minar wrote:Couldn't be able to solve it. Please help.

_______________________________

A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform 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

A) I only
B) II only
C) I and II only
D) I and III only
E) I, II, III only

OA: E
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.
Last edited by GMATGuruNY on Fri Sep 02, 2011 4:47 pm, edited 1 time in total.
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by pesfunk » Fri Oct 29, 2010 6:35 pm
Perfect....awesome answer....was so simple.

@Rahul - No offence but one more example of explanation where you dont need a FORMULA..just common sense :)
GMATGuruNY wrote:
minar wrote:Couldn't be able to solve it. Please help.

_______________________________

A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform 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

A) I only
B) II only
C) I and II only
D) I and III only
E) I, II, III only

OA: E
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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