In the diagram above, the fourteen rectangular tiles are all : GMAT Data Sufficiency (DS)
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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 [#permalink]

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10 Mar 2013, 14:55
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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

Last edited by Bunuel on 04 Feb 2014, 02:22, edited 1 time in total.
Edited the question.
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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]

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11 Mar 2013, 01:32
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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

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

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

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28 Mar 2013, 13:47
BUMP! Any quicker ways to solve this?
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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]

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02 May 2013, 00:14
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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.

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

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03 Oct 2014, 06:30
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(1) SUFFICIENT: Let the length (longer dimension) of each rectangular tile be called L, and the width (shorter dimension) of each tile W. Then each horizontal side of square ABCD has total length 2W + 3L, and each vertical side has total length 4L.

Because ABCD is a square, these total lengths must be equal: 2W + 3L = 4L, which reduces to L = 2W. Therefore, each side of square ABCD is equal to 4L = 8W, and the total area of square ABCD is (8W)(8W) = 64W2.

The total area of the tiles is 14(L × W) = 14(2W × W) = 28W2. The desired fraction is thus (28W2)/(64W2) = 28/64. There is no need to reduce this fraction; the statement is sufficient.

(2) SUFFICIENT: Let the length (longer dimension) of each rectangular tile be called L, and the width (shorter dimension) of each tile W. Then each horizontal side of square ABCD has total length 3L, and each vertical side has total length 4L – 2W.

Because EFGH is a square, these total lengths must be equal: 3L = 4L – 2W, which reduces to L = 2W. Therefore, each side of square ABCD is equal to 3L = 6W.

In turn, ABCD must also be a square, since each of its sides is 2W longer than the corresponding side of EFGH (i.e., longer by W on each side). Therefore, each side of ABCD is equal to 6W + 2W = 8W, and the total area of square ABCD is (8W)(8W) = 64W2.

The total area of the tiles is 14(L × W) = 14(2W × W) = 28W2. The desired fraction is thus (28W2)/(64W2) = 28/64. There is no need to reduce this fraction; the statement is sufficient.

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

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08 Oct 2014, 01:43
Hey Bunuel,
thanks..
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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]

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22 Oct 2015, 11:59
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26 Oct 2016, 12:38
Just did a mock and doing a review, noticed something really weird. Can anyone help me understand? I thought this was a freebie from one or two wrong questions before but its 700-800 level, even their explanation doesnt make sense.

***if you cant see the image, it's a square(abcd) in a square(efgh). has a 14 tile border that is positioned lengthwise along the inside of the big square. 3 tiles plus 2 ends on one side (as Length) and 4 tiles on the other (Width).

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.

-----

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

*right* EACH statement ALONE is sufficient.

*ME* Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: In the diagram above, the fourteen rectangular tiles are all [#permalink]

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26 Oct 2016, 19:47
mpejic wrote:
Just did a mock and doing a review, noticed something really weird. Can anyone help me understand? I thought this was a freebie from one or two wrong questions before but its 700-800 level, even their explanation doesnt make sense.

***if you cant see the image, it's a square(abcd) in a square(efgh). has a 14 tile border that is positioned lengthwise along the inside of the big square. 3 tiles plus 2 ends on one side (as Length) and 4 tiles on the other (Width).

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.

-----

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

*right* EACH statement ALONE is sufficient.

*ME* Statements (1) and (2) TOGETHER are NOT sufficient.

Merging topics. Please refer to the discussion above.

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Re: In the diagram above, the fourteen rectangular tiles are all   [#permalink] 26 Oct 2016, 19:47
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