(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.
The correct answer is D.
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