题目信息
The top surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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正确答案：
D:EACH statement ALONE is sufficient.
Geometry Quadrilaterals; First- and second-degree equations
Letting S be the side length of the square tabletop, the surface area before the change was S 2, and the area after the change is (S − 1)(S + 2). Determine S 2.
It is given that (S − 1)(S + 2) = 70. Solving this equation gives S = −9 and S = 8. Discarding S = −9, it follows that S = 8 and the surface area before the changes was 64 square inches; SUFFICIENT. Since only one dimension was increased and that increase was 2 inches, it follows from (2) that S + 2 = 1.25S. Solving this equation gives S = 8. Therefore, the surface area before the changes was 64 square inches; SUFFICIENT.
The correct answer is D;each statement alone is sufficient.
Letting S be the side length of the square tabletop, the surface area before the change was S 2, and the area after the change is (S − 1)(S + 2). Determine S 2.
It is given that (S − 1)(S + 2) = 70. Solving this equation gives S = −9 and S = 8. Discarding S = −9, it follows that S = 8 and the surface area before the changes was 64 square inches; SUFFICIENT. Since only one dimension was increased and that increase was 2 inches, it follows from (2) that S + 2 = 1.25S. Solving this equation gives S = 8. Therefore, the surface area before the changes was 64 square inches; SUFFICIENT.
The correct answer is D;each statement alone is sufficient.
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