The value of $490-491+492-493+494-495+\ldots-509+510$ is
(A) 500
(B) -10
(C) -11
(D) 499
(E) 510
The value of $490-491+492-493+494-495+\ldots-509+510$ is
(A) 500
(B) -10
(C) -11
(D) 499
(E) 510

## Solution

The value of $490-491+492-493+494-495+\ldots-509+510$ is

$$
\begin{aligned}
(490-491)+(492-493)+(494-495)+\ldots+(508-509)+510 & =\underbrace{(-1)+(-1)+(-1)+\ldots+(-1)}_{10 \text { pairs, each add to }-1}+510 \\
& =-10+510 \\
& =500
\end{aligned}
$$