A wagon wheel with a circumference of 14π has seven straigh

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vinni.k Master | Next Rank: 500 Posts
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A wagon wheel with a circumference of 14π has seven straigh

Post Tue Jan 29, 2013 8:17 am
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    A wagon wheel with a circumference of 14π has seven straight spokes that originate at the center of the wheel. If the distance between consecutive spokes on the wheel’s circumference is equivalent, what is the perimeter of each sector of the circle bounded by consecutive spokes?

    A) 14 + 2π
    B) 7π
    C) 14π
    D) 14 + 4π
    E) 7 + 7π

    Answer is A

    Thanks & Regards
    Vinni
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    Post Tue Jan 29, 2013 8:27 am
    vinni.k wrote:
    A wagon wheel with a circumference of 14π has seven straight spokes that originate at the center of the wheel. If the distance between consecutive spokes on the wheel’s circumference is equivalent, what is the perimeter of each sector of the circle bounded by consecutive spokes?

    A) 14 + 2π
    B) 7π
    C) 14π
    D) 14 + 4π
    E) 7 + 7π

    Answer is A

    Thanks & Regards
    Vinni
    I'm assuming that 14π is the same as 14(pi).
    (the "π" looks like a lower case N in my browser)

    We know the circumference of any circle is 2(pi)r.
    So, if the circumference of the wagon wheel is 14(pi), then it's radius (r) must be 7.

    Also, if the total circumference of the wagon wheel is 14(pi), then each of the seven arcs (divided by spokes) must have length 2(pi)

    So, the perimeter of each sector must be 7 + 7 + 2(pi), which equals 14 + 2(pi) = A

    Cheers,
    Brent

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    hemant_rajput Master | Next Rank: 500 Posts
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    Post Tue Jan 29, 2013 8:30 am
    circumference of wagon wheel = 14*PI = 2*PI*radius

    so radius = 7

    Now you want to find perimeter of each sector of the circle bounded by consecutive spokes.



    this is equal to (left spoke)radius + arc of circle(sector arc) + (right spoke)radius

    (7) + (14*PI/7) + (7)

    14 + 2*PI

    answer is A

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    vinni.k Master | Next Rank: 500 Posts
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    Post Tue Jan 29, 2013 10:41 am
    Thank you.

    Regards
    Vinni

    Post Tue Jan 29, 2013 11:50 am
    Brent and Hemant are both correct, but there's a way that you could quickly guess on this problem.

    When we're looking for the perimeter of one section, we know we're going to have 2 straight pieces (2 spokes), and one curved piece (the edge of the wheel). We know that the circumference of the wheel is in terms of pi, so any piece of that circumference will also be something*pi.

    However, those straight pieces (the spokes) won't have a pi. So if we're adding 2 spokes + 1 curved piece, we know the answer has to be "something + something*pi." We could eliminate B and C.

    We know that the GMAT likes to include trap answers, so looking at 14 or 7... you can bet that 7 is the trap answer for people who only counted 1 spoke, not 2. Now looking at 2pi or 4pi, 4pi is probably the trap for people who accidentally counted 2 curved pieces instead of 1.

    So if we just had to quickly guess, we'd guess A here. And we'd be right!

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