2. 外语
  3. Each entry in the multiplication table above is an integer that is either positive, negative, or zero. What is the value of a ?

Each entry in the multiplication table above is an integer that is either positive, negative, or zero. What is the value of a ?

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问题
Each entry in the multiplication table above is an integer that is either positive, negative, or zero. What is the value of a ?
(1) h≠0
(2) c = f
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C
解析 (1)     If a, b, c equal 1,2,3 in this order, then each entry will be an integer, h ≠ 0, and a=1. However, if a, b, c equal 2,3,4 in this order, then each entry will be an integer, h ≠ 0, and a = 2. Hence, the value of a cannot be determined; NOT sufficient.
(2)     The assumption c =f is equivalent to ac = c, or (a -1)c = 0. Hence, c =f is equivalent to a = 1 or c = 0. If a, b, c equal 1,2,3 in this order, then each entry will be an integer, c =f, and a=1. However, if a, b, c equal -2, -1,0 in this order, then each entry will be an integer, c =f, and a = -2. Hence, the value of a cannot be determined; NOT sufficient.
Given (1) and (2), then from (1) we have bc = h≠0, and hence b ≠ 0 and c ≠ 0. From (2) we have a = 1 or c = 0, but since c ≠ 0, it follows that a = 1. Hence, the value of a can be determined.
The correct answer is C;
both statements together are sufficient.
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