Question

从 $-10$ 到 $14$ （含端点）的 $25$ 个整数可以排列成一个 $5$ 乘 $5$ 的方阵，使得每一行的和、每一列的和以及两条主对角线上的数之和都相同。这个共同的和是多少？

The $25$ integers from $-10$ to $14,$ inclusive, can be arranged to form a $5$ -by- $5$ square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum?

$2$

$5$

$10$

$25$

$50$

答案：C

知识点：幻方等差数列

难度评级：1130

解答：

这 $25$ 个整数的和为 $\dfrac{(-10 + 14) \cdot 25}{2} = 50$ 。

五行的和都相同，并且合起来就是总和，所以每行的和为 $50 \div 5 = 10$ 。

因此，正确答案是 C。

The sum of the $25$ integers is $\dfrac{(-10 + 14) \cdot 25}{2} = 50.$

The five rows each have the same sum and together account for the total, so each row sums to $50 \div 5 = 10.$

Thus, C is the correct answer.

2020 AMC 12A 第 5 题

答案：C

难度评级：1130

解答：

其他年份的第 5 题