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Closest to 1/2?

This topic has 6 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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Closest to 1/2?

Post Mon Jul 03, 2017 8:37 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    How do you calculate these fast?

    Which of the following fractions is closest to 1/2?
    A) 4/7
    B) 5/9
    C) 6/11
    D) 7/13
    E) 9/16

    D

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    Post Mon Jul 03, 2017 10:09 pm
    AbeNeedsAnswers wrote:
    How do you calculate these fast?

    Which of the following fractions is closest to 1/2?
    A) 4/7
    B) 5/9
    C) 6/11
    D) 7/13
    E) 9/16

    D
    There can be few approaches to doing this faster. It depends on you at which approach you are comfortable. I am putting up my approach.

    We have to find out which of the following number is closest to 1/2.

    A number (1/2 + |a|) is closer to 1/2 than a number (1/2 + |b|) is closer to 1/2 if |a| < |b|.

    Note that in the given fraction 1/2, the numerator '1' is half of the denominator '2,' so we would try to make the numerator half of the denominator with the given fractions in the options.

    Let's take all the given fractions in the options.

    A) 4/7 = (3.5 + 0.5)/7 = 3.5/7 + 0.5/7 = 1/2 + 1/14
    B) 5/9 = (4.5 + 0.5)/9 = 4.5/9 + 0.5/9 = 1/2 + 1/18; since 1/18 < 1/14, 5/9 is relatively closer to 1/2, thus option A is ruled out.
    C) 6/11 = (5.5 + 0.5)/11 = 5.5/11 + 0.5/11 = 1/2 + 1/22; since 1/22 < 1/18, 6/11 is relatively closer to 1/2, thus option B is ruled out.
    D) 7/13 = (6.5 + 0.5)/13 = 6.5/13 + 0.5/13 = 1/2 + 1/26; since 1/26 < 1/18, 7/13 is relatively closer to 1/2, thus option C is ruled out.
    E) 9/16 = (8 + 1)/16 = 8/16 + 1/16 = 1/2 + 1/16; since 1/16 > 1/26, 7/13 is relatively close to 1/2, thus option E is ruled out.

    The correct answer: D

    Hope this helps!

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    Post Mon Jul 03, 2017 10:22 pm
    AbeNeedsAnswers wrote:
    How do you calculate these fast?

    Which of the following fractions is closest to 1/2?
    A) 4/7
    B) 5/9
    C) 6/11
    D) 7/13
    E) 9/16

    D
    Another approach: Calculate the values in decimals. Though it is time-consuming, it is not necessarily always.

    Convert all the fractions in percents.

    Thus, 1/2 = (1/2)*100% = 50%.

    Let's take all the options.

    A) 4/7 = (4/7)*100% = (400/7)% = (57.1...)%
    B) 5/9 = (5/9)*100% = (500/9)% = (55.55...)%. Since 55.55...% is relatively closer to 50% than 57.1...% is, Option A is ruled out.
    C) 6/11 = (6/11)*100% = (600/11)% = (54.5...)%. Since 54.5...% is relatively closer to 50% than 55.55...% is, Option B is ruled out.
    D) 7/13 = (7/13)*100% = (700/13)% = (53....)%. Since 53...% is relatively closer to 50% than 54.5..% is, Option C is ruled out.
    E) 9/16 = (9/16)*100% = (900/16)% = (56...)%. Since 56...% is NOT relatively closer to 50% than 53...% is, Option E is ruled out.

    The correct answer: D

    Hope this helps!

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    -Jay
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    Post Mon Jul 03, 2017 10:44 pm
    AbeNeedsAnswers wrote:
    How do you calculate these fast?

    Which of the following fractions is closest to 1/2?
    A) 4/7
    B) 5/9
    C) 6/11
    D) 7/13
    E) 9/16
    Since (1/2)(2) = 1, the correct fraction -- when multiplied 2 -- will be closest to 1.

    A: (4/7)(2) = 8/7, which is 1/7 from 1.
    B: (5/9)(2) = 10/9, which is 1/9 from 1.
    C: (6/11)(2) = 12/11, which is 1/11 from 1.
    D: (7/13)(2) = 14/13, which is 1/13 from 1.
    E: (9/16)(2) = 18/16 = 9/8, which is 1/8 from 1.

    When multiplied by 2, the option in blue yields the smallest distance from 1.

    The correct answer is D.

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    Post Tue Jul 04, 2017 6:36 am
    AbeNeedsAnswers wrote:
    How do you calculate these fast?

    Which of the following fractions is closest to 1/2?
    A) 4/7
    B) 5/9
    C) 6/11
    D) 7/13
    E) 9/16

    D
    We can use a property of fractions that says "the greater the denominator, the smaller the value of the fraction"
    For example, 3/14 is smaller than 3/13 because 14 is greater than 13

    Now let's check the answer choices...

    A) 4/7
    3.5/7 = 1/2. So, 4/7 is 0.5/7 away from 1/2
    Since 0.5/7 = 1/14, we can say that 4/7 is 1/14 away from 1/2

    B) 5/9
    4.5/9 = 1/2. So, 5/9 is 0.5/9 away from 1/2
    Since 0.5/9 = 1/18, we can say that 5/9 is 1/18 away from 1/2

    C) 6/11
    Using the same logic, we can say that 6/11 is 1/22 away from 1/2

    D) 7/13
    Likewise, 7/13 is 1/26 away from 1/2

    E) 9/16
    And 9/16 is 1/16 away from 1/2

    Of the BLUE fractions, 1/26 is the SMALLEST
    So, the correct answer is D

    Cheers,
    Brent

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    Post Wed Jul 05, 2017 12:52 am
    AbeNeedsAnswers wrote:
    How do you calculate these fast?

    Which of the following fractions is closest to 1/2?
    A) 4/7
    B) 5/9
    C) 6/11
    D) 7/13
    E) 9/16

    D
    You don't! Smile

    Look for the pattern. If the numerator is half the denominator, rounded up, the fraction gets smaller the larger the numerator gets:

    2/3 = .66666666...
    3/5 = .6
    4/7 = .571428...
    5/9 = .55555555...
    etc.

    You don't even need to calculate 4/7 (or any that come after) - approximation should do the trick.

    Thanked by: gmatdestroyer13
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    Post Wed Jul 05, 2017 12:54 am
    As an aside, if you remember your calculus from high school, the pattern here points to a limit: (n + 1) / (2n + 1) approaches 1/2 as n approaches ∞. (In other words, the longer we follow this pattern, the closer we get to 1/2, though we can never *quite* get there.)

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