2. 外语
  3. If n is an integer, is n/15 an integer? (1) 3n/15 is an integer. (2) 8n/15 is an integer.

If n is an integer, is n/15 an integer? (1) 3n/15 is an integer. (2) 8n/15 is an integer.

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问题 If n is an integer, is n/15 an integer?
(1) 3n/15 is an integer.
(2) 8n/15 is an integer.
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B
解析 (1)    We are given that 3n/15 = n/5 is an integer.
If n = 15, then n/5 is an integer and n/15 is an integer. However, if n = 5, then n/5 is an integer and n/15 is not an integer; NOT sufficient.
(2)     We are given that 8n/15 = k, where k is an integer. Since 8n = 15k, it follows that both 3 and 5 are factors of 8n. Therefore, the prime factorization of 8n = 23 × n includes at least one factor of 3 and at least one factor of 5, and it is clear that each of these factors must be among the prime factors of n. Thus, both 3 and 5 are factors of n, and hence n is divisible by 15.
Alternatively, since 15 divides Sn, and 8 and 15 are relatively prime, then it follows that 15 divides n; SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
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