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Somewhat tricky calculation: 2² - 4² + 6² - 8² + ...

This topic has 4 expert replies and 0 member replies

Somewhat tricky calculation: 2² - 4² + 6² - 8² + ...

Post Tue May 02, 2017 5:46 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =

    A) -40
    B) -110
    C) -220
    D) -440
    E) -880

    Answer: C

    Source: www.gmatprepnow.com
    Difficulty level: 650 -700

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    Post Tue May 02, 2017 6:37 am
    Brent@GMATPrepNow wrote:
    2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =

    A) -40
    B) -110
    C) -220
    D) -440
    E) -880

    Answer: C

    Source: www.gmatprepnow.com
    Difficulty level: 650 -700
    Fun one. If we group the terms into pairs, a pattern emerges: 2² - 4² = -12; 6² - 8² = -28; 10² - 12² = -44
    Each successive term is 16 less than the previous term. We'll have 5 pairs, so 5 terms: -12, -28, -44, -60, -76. We could just add them here and get -220 or C

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    Post Tue May 02, 2017 6:39 am
    Time Saver:

    In an evenly spaced set, the mean = median = (high + low)/2
    First term = -12
    Last term = -76

    Mean (average) = (-12+-76)/2 = -44
    There are 5 terms.
    Average * # terms = (-44) * 5 = -220

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    Post Tue May 02, 2017 10:38 am
    Brent@GMATPrepNow wrote:
    2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =

    A) -40
    B) -110
    C) -220
    D) -440
    E) -880

    Answer: C

    Source: www.gmatprepnow.com
    Difficulty level: 650 -700
    Another approach:

    2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² = (2² - 4²) + (6² - 8²) + (10² - 12²) + (14² - 16²) + (18² - 20²)
    = (2 - 4)(2 + 4) + (6 - 8)(6 + 8) + (10 - 12)(10 + 12) + (14 - 16)(14 + 16) + (18 - 20)(18 + 20)
    = (-2)(2 + 4) + (-2)(6 + 8) + (-2)(10 + 12) + (-2)(14 + 16) + (-2)(18 + 20)
    = -2(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)
    = -2(2)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
    = (-4)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
    = (-4)(55)
    = -220

    Answer: C

    Cheers,
    Brent

    _________________
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    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

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    Post Wed May 03, 2017 8:38 am
    Brent@GMATPrepNow wrote:
    Brent@GMATPrepNow wrote:
    2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =

    A) -40
    B) -110
    C) -220
    D) -440
    E) -880

    Answer: C

    Source: www.gmatprepnow.com
    Difficulty level: 650 -700
    Another approach:

    2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² = (2² - 4²) + (6² - 8²) + (10² - 12²) + (14² - 16²) + (18² - 20²)
    = (2 - 4)(2 + 4) + (6 - 8)(6 + 8) + (10 - 12)(10 + 12) + (14 - 16)(14 + 16) + (18 - 20)(18 + 20)
    = (-2)(2 + 4) + (-2)(6 + 8) + (-2)(10 + 12) + (-2)(14 + 16) + (-2)(18 + 20)
    = -2(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)
    = -2(2)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
    = (-4)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
    = (-4)(55)
    = -220

    Answer: C

    Cheers,
    Brent
    Nice difference of squares action there. Elegant solution, Brent.

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