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 the figure above, with B a point on the line AC, what is the measure of ∠XBZ? (Figure not necessarily drawn to scale.)
   (1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC.
   (2) ∠ABX=∠XBY=∠YBZ=∠ZBC
选项
答案D
解析 alone is sufficient, because if ∠ABY is a right angle, then ∠TBC must also be a right angle, and since both right angles are bisected, ∠XBY and ∠YBZ must both be equal to 45°, and therefore ∠XBZ=90°. (2) alone is sufficient, because if all four of those angles are equal, and there can be only 180° on one side of a line, then each angle must equal 45°, and therefore ∠XBZ=90°.
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