If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?I

题目

If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.

II. x is a nonzero integer.

III. x is a multiple of 5.

选项

I only

III only

I and II only

I and III only

I, II, and III

解析

首先注意，题目问的是“下列哪项**一定**正确”，而非“**可能**正确”。同时要注意：5个连续偶数的平均数等于其中位数，也就是中间项。所以，I一定正确：集合里的元素都是偶数（{偶, 偶, 偶, 偶, 偶}）。接下来： II. \(x\)是一个非零整数。不一定正确，比如集合{−4, −2, 0, 2, 4}； III. \(x\)是5的倍数。不一定正确，比如集合{0, 2, 4, 6, 8}。答案：A

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