题目信息
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 
is midway between consecutive integers?
is midway between consecutive integers?
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
参考答案及共享解析
共享解析来源为网络权威资源、GMAT高分考生等； 如有疑问，欢迎在评论区提问与讨论
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已选答案：
正确答案：
D:All even prime numbers
Arithmetic Properties of integers
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
= 1 is not midway between consecutive integers.
Does k = 2 satisfy the condition? YES. For each positive odd integer n, the value of
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
is not midway between consecutive integers.
It is easy to see that no other positive integer satisfies the condition, by considering the value of
when n = 1. Therefore, 2 is the only positive integer value of k that satisfies the condition.
The correct answer is D.
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
= 1 is not midway between consecutive integers.Does k = 2 satisfy the condition? YES. For each positive odd integer n, the value of
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
is not midway between consecutive integers.It is easy to see that no other positive integer satisfies the condition, by considering the value of
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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