Question

如图所示，一个 $4 \times 4$ 的日历日期方块。先将第二行数字的顺序反过来。然后将第四行数字的顺序反过来。最后，把两条对角线上的数字分别相加。两个对角线和的正差是多少？

A $4 \times 4$ block of calendar dates is shown. The order of the numbers in the second row is to be reversed. Then the order of the numbers in the fourth row is to be reversed. Finally, the numbers on each diagonal are to be added. What will be the positive difference between the two diagonal sums?

$2$

$4$

$6$

$8$

$10$

答案：B

知识点：等差数列找规律

难度评级：1020

解答：

将第二行和第四行反向后，数组的各行是 $1\,2\,3\,4$ 、 $11\,10\,9\,8$ 、 $15\,16\,17\,18$ 和 $25\,24\,23\,22$ 。

主对角线和为 $1 + 10 + 17 + 22 = 50$ ，另一条对角线和为 $4 + 9 + 16 + 25 = 54$ 。

正差为 $54 - 50 = 4$ 。

因此，正确答案是 B。

Reversing the second and fourth rows gives the array with rows $1\,2\,3\,4,$ $11\,10\,9\,8,$ $15\,16\,17\,18,$ and $25\,24\,23\,22.$

The main diagonal sums to $1 + 10 + 17 + 22 = 50,$ and the other diagonal sums to $4 + 9 + 16 + 25 = 54.$

The positive difference is $54 - 50 = 4.$

Thus, the correct answer is B.

2008 AMC 12B 第 2 题

答案：B

难度评级：1020

解答：

其他年份的第 2 题