2018 AMC 8

Complete problem set with solutions and individual problem pages

Problem 5 Easy

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

  • A.

    -1010

  • B.

    -1009

  • C.

    1008

  • D.

    1009

  • E.

    1010

Answer:E

Solution 1

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

 

Solution 2

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