2013 AMC 8 Problems/Problem 3

Revision as of 19:41, 12 March 2021 by Notmyopic667 (talk | contribs) (Solution)

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 500. Now we just multiply that by 4 to get 2000. So the answer is E.

See Also

2013 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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