2013 AMC 8 Problems/Problem 3: Difference between revisions
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==Problem== | ==Problem== | ||
What is the value of <math>4 \cdot (-1+2-3+4-5+6-7+\cdots+1000)</math>? | What is the value of <math>4 \cdot (-1+2-3+4-5+6-7+\cdots+1000)</math>? | ||
<math>\textbf{(A)}\ -10 \qquad \textbf{(B)}\ 0 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 500 \qquad \textbf{(E)}\ 2000</math> | <math>\textbf{(A)}\ -10 \qquad \textbf{(B)}\ 0 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 500 \qquad \textbf{(E)}\ 2000</math> | ||
Revision as of 09:15, 2 September 2016
Problem
What is the value of 
?
Solution
Notice that we can pair up every two numbers to make a sum of 1:
Therefore, the answer is 
.
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
