2. 外语
  3. For each positive integer k，let ak=. Is the product a1a2. . . an an integer? (1) n+1 is a multiple of 3． (2) n is a multiple o

For each positive integer k，let ak=. Is the product a1a2. . . an an integer? (1) n+1 is a multiple of 3． (2) n is a multiple o

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问题 For each positive integer k，let ak=. Is the product a1a2. . . an an integer?
(1) n+1 is a multiple of 3．
(2) n is a multiple of 2．
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) TOGEHER are NOT sufficient．
答案B
解析 Since , it follows that the product can be written as
. Therefore, the product a1a2 ... an is an integer if and only if is an integer, or if and only if n is an even integer.
(1)     If n = 2, then n + 1 = 3 is a multiple of 3 and the product is , which is an integer. However, if n = 5, then n + 1 = 6 is a multiple of 3 and the product, is , which is not an integer,                     
NOT sufficient.
(2)     If n is a multiple of 2, then by the remarks above it follows that the product is an integer; SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
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