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  3. The following data sufficiency problems consist of a question and two stateme

The following data sufficiency problems consist of a question and two stateme

游客2025-02-27  27
问题    The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether
   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. [br] A rectangle is equal in area to a square with sides of length 12. Is the diagonal of the rectangle greater in length than 20?
   (1) The rectangle has a length of 16.
   (2) The rectangle has a width of 9.
选项
答案 D
解析 Both (1) and (2) independently allow you to infer both the length and the width of the rectangle, because ff the rectangle is equal in area to a square with sides of length 12, then its area=12×12=144, and so the width is 144/16=9 and the length is 144/9=16. By the Pythagorean theorem, we can determine that the diagonal is equal to the square root of 92+162=337. You do not have to determine the actual square root of 337 to determine that it is less than 20, because 20×20=400.
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