2. 职称英语
  3. Which of the following describes the set of all possible values of the positive

Which of the following describes the set of all possible values of the positive

游客2024-01-13  50
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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