CORRECT ANSWER IS B.

Statement (1): insufficient. The fact that EF bisects BC simply means that the distance from point C to the point where EF meets BC is 2. From this, we know that the overlapping region has at least one side of length 2, but we can determine neither the lengths of the other sides nor the angles of intersection from the given information. We thus cannot find the area, and statement (1) is insufficient.

Statement (2): sufficient. If CE = CF = , then we know that C is the center of EFGH. This is because side EF of triangle ECF is of length 4, and each leg is of length . Since two sides of triangle ECF have a length of and one side of this triangle has a length of 4, the ratio of the lengths of the side of triangle ECF is 1 : 1 : , which is the leg length to leg length to hypotenuse length ratio of an isosceles right triangle. Thus, triangle ECF is an isosceles right triangle. Knowing that C is the center of EFGH does not allow us to determine the angle of rotation between the two squares, but this does not matter. No matter what the rotation, the overlapping region will always be one-quarter of the size of one of the larger squares. Think of it this way. If the overlapping region is in the shape of a square, then the area will be one-quarter of the larger square, or 4. Even if we rotated the figures such that E and F lay on DC and BC respectively, such that the overlapping region was triangle ECF, the overlapping area would still be 4:

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Any rotation in between would take a triangular chunk out of the overlapping region on one side, but add an identical triangular chunk on the other side. Thus, the area of the overlapping region will always be 4, and statement (2) is sufficient. Choice (B) is therefore correct.