2. 外语
  3. Which of the following describes the set of all possible values of the positive integer k such that，for each positive odd intege

Which of the following describes the set of all possible values of the positive integer k such that，for each positive odd intege

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问题 Which of the following describes the set of all possible values of the positive integer k such that，for each positive odd integer n，the value of n/k is midway between consecutive integers?
选项 A、All positive integers greater than 2
B、All prime numbers
C、All positive even integers
D、All even prime numbers
E、All positive even multiples of 5
答案D
解析 The logical complexities involved in this question are lessened by testing individual values of k.
Does k = 1 satisfy the condition? NO. If n = 1, then n/k = 1/1 = 1 is not midway between consecutive integers.
Does k = 2 satisfy the condition? YES. For each positive odd integer n, the value of n/k = n/2 is an
odd integer divided by 2, and hence is midway between consecutive integers.
Does k = 3 satisfy the condition? NO. If n = 1, then n/k = 1/3 is not midway between consecutive integers.
It is easy to see that no other positive integer satisfies the condition, by considering the value of n/k when n = 1. Therefore, 2 is the only positive integer value of k that satisfies the condition.
The correct answer is D.
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