In the diagram above, the fourteen rectangular tiles are all

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In the diagram above, the fourteen rectangular tiles are all [#permalink]

10 Mar 2013, 15:55

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In the diagram above, the fourteen rectangular tiles are all identical. What percent of the area of rectangle ABCD is covered by the tiles?

(1) ABCD is a square.

(2) EFGH is a square.

[Reveal] Spoiler: OA

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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]

11 Mar 2013, 02:32

nave81 wrote:

In the diagram above, the fourteen rectangular tiles are all identical. What percent of the area of rectangle ABCD is covered by the tiles?

(1) ABCD is a square.

(2) EFGH is a square.

Figure attached
Suppose the dimention of the tiles are l*b

STAT1
Let side of Square ABCD = a
then if you consider side AB then
AB = a = 3l + 2b

if you consider side AD then
AD = a = 4l

so, 4l = 3l + 2b
or, l =2b

Also, we know that a = 4l
so, l = a/4
b = l/2 = a/8
So, we can find the area of the tile in terms of "a"
Area of all the tiles = (constant)* a^2
So, we can find the percentage of area occupied by tile = ((constant)* a^2 / a^2 ) * 100
So, SUFFICIENT

STAT2
Let side of EFGH = c
then if you consider EF then
EF = c = 3l

if you consider EH then
EH = c = 2l + l-b + l-b = 4l-2b

=> 3l = 4l-2b
l = 2b

And we have c = 3l
=> l = c/3
b = l/2 = c/6

AB = 4l = 4c/3

So, we can find area of ABCD in terms of C And we can find area of the tiles in terms of c
So, we can find the percentage of area occupied by tiles
So, SUFFICIENT

Hence answer will be D

Hope it helps!

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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]

28 Mar 2013, 14:47

BUMP! Any quicker ways to solve this?
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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]

02 May 2013, 01:14

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manimgoindowndown wrote:

BUMP! Any quicker ways to solve this?

Statement 1 :
AB = BC as the figure is square
Hence 3l+2b = 4l ==> l=2b and 4l = S (S = side of the square)

% = (14*l*b) *100/S^2 ==> as you know all the relationships, you can make this one variable equation and get the answer.

Statement 2 :
EF = FG as the figure is square
Hence 3l = 2l + 2b ==> l=2b and 4l = S (S = side of the square)

% = (14*l*b) *100/S^2 ==> as you know all the relationships, you can make this one variable equation and get the answer.

Answer hence is D
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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink] 02 May 2013, 01:14

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In the diagram above, the fourteen rectangular tiles are all

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In the diagram above, the fourteen rectangular tiles are all

In the diagram above, the fourteen rectangular tiles are all

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