Question

下列表达式的值是多少？

$\begin{gathered} \small (1901 + 1902 + 1903 + \cdots + 1993) \\ \small {}- (101 + 102 + 103 + \cdots + 193) \end{gathered}$

What is the value of the following expression?

$\begin{gathered} \small (1901 + 1902 + 1903 + \cdots + 1993) \\ \small {}- (101 + 102 + 103 + \cdots + 193) \end{gathered}$

$167{,}400$

$172{,}050$

$181{,}071$

$199{,}300$

$362{,}142$

把上面和下面的对应项配对： $1901 - 101$ 、 $1902 - 102$ 、 $\ldots$

Pair each term with the one below it: $1901 - 101,$ $1902 - 102,$ $\ldots$

每一对的差都是 $1800$ ，共有 $93$ 对

Each of the $93$ pairs has difference $1800$

第一个和中的每个数都比第二个和中对应的数大 $1800$ ，并且共有 $93$ 对。

所以差为 $93 \times 1800 = 167{,}400$ 。

所以正确答案是 A。

Each number in the first sum is exactly $1800$ more than the matching number in the second sum, and there are $93$ such pairs.

So the difference is $93 \times 1800 = 167{,}400.$

Thus, the correct answer is A .