Question

What is the value of the following expression?

$\begin{aligned} &1990 - 1980 + 1970 - 1960 \\ &\quad {}+ \cdots - 20 + 10 \end{aligned}$

$-990$

$-10$

$990$

$1000$

$1990$

Answer: D

Concepts:pairing and grouping

Difficulty rating: 1060

Solution:

Group the terms as $(1990 - 1980)$ $+ (1970 - 1960)$ $+ \cdots$ $+ (30 - 20)$ $+ 10.$ Each parenthesized pair equals $10$ .

The first elements $1990, 1970, \ldots, 30$ number $99$ , so there are $99$ pairs, giving $990$ , plus the leftover $+10$ at the end for a total of $1000$ .

Thus, the correct answer is D .

1990 AMC 8 Problem 16

Answer: D

Solution:

Problem 16 in Other Years