Welcome! Check out our free B-School Guides to learn how you compare with other applicants.
Login or Register

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

This topic has 2 expert replies and 2 member replies

Top Member

vinni.k Really wants to Beat The GMAT!
Joined
17 Apr 2011
Posted:
278 messages
Thanked:
5 times
Test Date:
2016
Target GMAT Score:
700+
GMAT Score:
620
Most Active Member
A wagon wheel with a circumference of 14π has seven straigh Post Tue Jan 29, 2013 8:17 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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
    Attachments

    This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    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

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Enter our contest to win a free course.

    Thanked by: vinni.k, sana.noor, Halimah_O
    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    hemant_rajput GMAT Destroyer!
    Joined
    22 Apr 2012
    Posted:
    447 messages
    Followed by:
    13 members
    Thanked:
    45 times
    Test Date:
    25/08/2014
    GMAT Score:
    700
    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

    _________________
    I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

    Thanked by: vinni.k

    Top Member

    vinni.k Really wants to Beat The GMAT!
    Joined
    17 Apr 2011
    Posted:
    278 messages
    Thanked:
    5 times
    Test Date:
    2016
    Target GMAT Score:
    700+
    GMAT Score:
    620
    Most Active Member
    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!

    _________________
    Manhattan Prep

    All of our instructors have 99th percentile scores and expert teaching experience.
    Sign up for a FREE TRIAL, and learn why our students love us!

    Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

    Best Conversation Starters

    1 Mo2men 21 topics
    2 neeti2711 19 topics
    3 ziyuenlau 13 topics
    4 Anaira Mitch 9 topics
    5 Donna@Stratus 9 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    88 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    88 posts
    3 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    83 posts
    4 image description Matt@VeritasPrep

    Veritas Prep

    80 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    73 posts
    See More Top Beat The GMAT Experts