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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 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

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.

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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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.

Attachments

square in square.gif [ 1.29 KiB | Viewed 555 times ]

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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