Width of the strip

[minar]

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

[Rahul@gurome]

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).

[minar]

very convincing explanation.
Many thanks!

[GMATGuruNY]

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.

[pesfunk]

Perfect....awesome answer....was so simple.

@Rahul - No offence but one more example of explanation where you dont need a FORMULA..just common sense

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.