2013 AMC 8 Problems/Problem 3

Problem

What is the value of $4 \cdot (-1+2-3+4-5+6-7+\cdots+1000)$ ?

$\textbf{(A)}\ -10 \qquad \textbf{(B)}\ 0 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 500 \qquad \textbf{(E)}\ 2000$

Solution

.
 We see that if we group two numbers at a time, we see that it would make 1 on each. There are 500 pairs so the answer inside the parentheses is 1 times 500 equals to 500. Now we just multiply that by 4 to get 2000.

2013 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AJHSME/AMC 8 Problems and Solutions

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2013 AMC 8 Problems/Problem 3

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