2. 外语
  3. The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are

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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.
In triangle ABC above, if ∠BAD and ∠ADB have measures of 2n, and if ∠ACB has a measure of n, what is the length of side AB? (Figure not necessarily drawn to scale.)
   (1) n=25°
   (2) CD=4
选项
答案B
解析 alone is insufficient because it offers no information about any lengths in the triangle. (2) alone is sufficient; the crucial principle to remember here is that an exterior angle of a triangle--such as ∠ADB--is equal to the sum of the remote interior angles of the triangle, in this case triangle BDC. Thus, n+ ∠CBD=2n, or ∠CBD=n. Since sides of a triangle opposite angles of identical degree are of identical length, BD is the same length as CD, or 4. By this same principle, BD and AB are of identical lengths, so AB is also 4.
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