AMC 8 L1: Calculation Tricks

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? (2018 AMC 8 Problem, Question #5)

  • A.

    -1010

  • B.

    -1009

  • C.

    1008

  • D.

    1009

  • E.

    1010

Answer:E

Solution 1: (1+3+5+\cdots +2017+2019)-(2+4+6+\cdots +2018)

=1010\times1010-(2+2018)\times1009\div 2=1010

Solution 2: 1+(3-2)+(5-4)+\cdots +(2019-2018)=1+1+1+\cdots +1=1010

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