AMC 8 Daily Practice - Calculation Tricks by Grouping

Complete problem set with solutions and individual problem pages

Problem 2 Easy

What is the value of 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 + \dots + 99 - 100?

  • A.

    5050

  • B.

    -51

  • C.

    -50

  • D.

    -5050

  • E.

    50

Answer:C

We group the addends in pairs: 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 + \dots + 99 - 100 =(1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + (9 - 10) + (11 - 12) + (13 - 14) + (15 - 16) + \dots + (99 - 100) We find that when calculating each of the expressions within the parentheses, the result always  is  one, and there are fifty parentheses.  (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + (9 - 10) + (11 - 12) + (13 - 14) + (15 - 16) + \dots + (99 - 100)=(-1) \times 50

So the result of the original expression is -50.

Related Problems
Problem 1 AMC 8 Daily Practice - Calculation Tricks by Grouping
Problem 3 AMC 8 Daily Practice - Calculation Tricks by Grouping
Problem 4 AMC 8 Daily Practice - Calculation Tricks by Grouping
Problem 5 AMC 8 Daily Practice - Calculation Tricks by Grouping
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