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  3. The top surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimensio

The top surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimensio

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问题 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?
(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.
选项 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.
答案D
解析 Letting S be the side length of the square tabletop, the surface area before the change was S2, and the area after the change is (S - 1)(S + 2). Determine S2.
(1)     It is given that (S - 1)(5 + 2) = 70. Solving this equation gives S = -9 and 5=8. Discarding S = -9, it follows that 5=8 and the surface area before the changes was 64 square inches; SUFFICIENT.
(2)     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 5=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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