2018 AMC 8 Problems/Problem 5

Problem 5

What is the value of $1+3+5+\cdots+2017+2019-2-4-6-\cdots-2016-2018$ ?

$\textbf{(A) }-1010\qquad\textbf{(B) }-1009\qquad\textbf{(C) }1008\qquad\textbf{(D) }1009\qquad \textbf{(E) }1010$

Solution 1

Rearranging the terms, we get $(1-2)+(3-4)+(5-6)+...(2017-2018)+2019$ , and our answer is $-1009+2019=\boxed{1010}, \textbf{(E)}$

Solution 2

We can see that the last numbers of each of the sets (even numbers and odd numbers) have a difference of one. So do the second last ones, and so on. Now, all we need to find is the number of intigers in any of the sets (I chose even) to get $\boxed{\textbf{(E) }1010}$ ~avamarora

2018 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AJHSME/AMC 8 Problems and Solutions

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2018 AMC 8 Problems/Problem 5

Contents

Problem 5

Solution 1

Solution 2

See Also