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.
For real numbers a, b, and c, is ab=bc+3?
   (1) ab=3b
   (2) b+3=c
选项
答案C
解析 To answer this question, the statements have to prove either that the equation above is true or that it cannot be true. (1) alone is insufficient; it allows the equation to be restated as 3b=bc+3, which could be true or not true depending on the values of b and c. (2) alone is insufficient; it allows the equation to be restated as ab=b2+3b+3, which could be true or not true depending on the values of a and b. If the two are combined, the equation can be restated as 3b=b2+3b+3, which can be restated as b2+3=0. Since b is a real number, b2 has to be either a positive number or 0, in which case b2+3=0 cannot be true. Therefore, the equation must be false.
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