Question

Yunji 把 $1$ 到 $9$ 的所有整数相加时，错误地漏掉了一个数。她得到的错误和恰好是一个平方数。Yunji 漏掉了哪个数？

When Yunji added all the integers from $1$ to $9,$ she mistakenly left out a number. Her incorrect sum turned out to be a square number. Which number did Yunji leave out?

$5$

$6$

$7$

$8$

$9$

答案：E

知识点：三角形数完全平方数

难度评级：770

视频讲解：

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文字解答：

要求 Yunji 漏掉的数，先求从 $1$ 到 $9$ 的总和，再看它与最近的较小平方数之差。整数从 $1$ 到 $9$ 的和为小于 $45$ 的最大平方数是 $36$ ，所以漏掉的是 $45 - 36 = 9$ 。 $1 + \ldots + 9 = \dfrac{9(9+1)}{2} = 45$

所以正确答案是 E。

To find the number that Yunji left out, we need to find the sum of the integers from $1$ to $9$ and find its difference with the largest perfect square below the sum. We can calculate the sum of the integers from $1$ to $9$ as follows: $1 + \ldots + 9 = \dfrac{9(9+1)}{2} = 45$ The largest perfect square less than $45$ would be $36$ and $45 - 36 = 9$ .

Thus, E is the correct answer.

2024 AMC 8 第 4 题

答案：E

难度评级：770

视频讲解：

文字解答：

其他年份的第 4 题