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fast way to solve??

This topic has 7 expert replies and 1 member reply
boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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fast way to solve??

Post Mon Apr 25, 2016 2:31 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

    A) 0
    B) 2/15
    C) 2/5
    D) 9/20
    E) 5/6

    Answer: A

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    Post Mon Apr 25, 2016 3:46 pm
    boomgoesthegmat wrote:
    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

    A) 0
    B) 2/15
    C) 2/5
    D) 9/20
    E) 5/6

    Answer: A
    One option is to rewrite each fraction with the same denominator (a bit of work).

    Another option is to convert each fraction to a decimal.
    To do so, we need to know some BASE CONVERSIONS.

    Let's use this chart

    For example, if we know that 1/7 ≈ 0.14, then 2/7 ≈ 0.28
    Likewise, if 1/6 ≈ 0.17, then 5/6 ≈ 0.83 [since 5/6 = 1 - 1/6 ≈ 1 - 0.17 ≈ 0.83]

    So....
    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 = 0.33 + 0.5 - 0.83 + 0.2 + 0.25 - 0.45
    = 0 + 0
    = 0
    = A

    For more on converting fractions to decimals see this video: https://www.gmatprepnow.com/module/gmat-arithmetic/video/1066

    Cheers,
    Brent

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    Post Mon Apr 25, 2016 4:13 pm
    Hi boomgoesthegmat,

    Many GMAT questions are essentially just about pattern-matching. While this prompt includes 6 fractions with different denominators, you do NOT need to calculate a "giant" common denominator to get the correct answer. In that same way, you actually don't have to do a lot of math at all to get to the correct answer. By 'grouping' the fractions into sets of 3, a pattern emerges...

    1/3 + 1/2 --> the common denominator is 6....and THAT is the denominator of the next fraction....-5/6

    1/3 + 1/2 =
    2/6 + 3/6 =
    5/6

    5/6 - 5/6 = 0 so the first three fractions "cancel out"

    With the next 3 fractions, we have....

    1/5 + 1/4 --> the common denominator is 20....and THAT is the denominator of the next fraction....-9/20

    1/5 + 1/4 =
    4/20 + 5/20 =
    9/20

    9/20 - 9/20 = 0 so the last three fractions "cancel out"

    In the end, we have.... 0 + 0 = 0

    Final Answer: A

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    Thanked by: boomgoesthegmat
    Post Mon Apr 25, 2016 4:25 pm
    boomgoesthegmat wrote:
    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

    A) 0
    B) 2/15
    C) 2/5
    D) 9/20
    E) 5/6

    Answer: A
    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20

    = 1/60 * 60(1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20)

    = 1/60 * (20 + 30 - 50 + 12 + 15 - 27)

    = 1/60 * 0

    = 0.

    The correct answer is A.

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    Post Mon Apr 25, 2016 8:12 pm
    boomgoesthegmat wrote:
    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

    A) 0
    B) 2/15
    C) 2/5
    D) 9/20
    E) 5/6

    Answer: A
    The easiest and the most efficient way to calculate this is by taking the LCM
    However, we can be a bit creative in grouping the terms.
    Group the terms in the following way

    (1/3 + 1/2) - 5/6 + (1/5 + 1/4) - 9/20 = 5/6 - 5/6 + 9/20 - 9/20 = 0
    Option A

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    Post Wed Apr 27, 2016 2:16 pm
    One more solution for you!

    If we have

    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 = x

    We can multiply both sides by 60 to clear the denominators.

    20 + 30 - 50 + 12 + 15 - 27 = 60x

    50 - 50 + 27 - 27 = 60x

    0 = 60x

    0 = x

    Thanked by: boomgoesthegmat
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    Post Wed Apr 27, 2016 2:27 pm
    Matt@VeritasPrep wrote:
    One more solution for you!

    If we have

    1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 = x

    We can multiply both sides by 60 to clear the denominators.

    20 + 30 - 50 + 12 + 15 - 27 = 60x

    50 - 50 + 27 - 27 = 60x

    0 = 60x

    0 = x
    Sweet!!

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    Post Thu Apr 28, 2016 2:43 pm
    Brent@GMATPrepNow wrote:
    Sweet!!
    Math never gets old, does it? Smile

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    Post Thu Apr 28, 2016 4:49 pm
    Matt@VeritasPrep wrote:
    Brent@GMATPrepNow wrote:
    Sweet!!
    Math never gets old, does it? Smile
    Agreed. It's one of the oldest subjects, and it never gets old!

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