• e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Regular polygon X has r sides, and each vertex has...

This topic has 1 expert reply and 0 member replies

Regular polygon X has r sides, and each vertex has...

Post Sun Nov 05, 2017 4:53 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q?

    A. 2
    B. 160
    C. 176
    D. 178
    E. 179

    The OA is C.

    Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Tue Nov 07, 2017 5:44 pm
    LUANDATO wrote:
    Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q?

    A. 2
    B. 160
    C. 176
    D. 178
    E. 179

    The OA is C.

    Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
    If we want to find the maximum possible angle measure for the interior angles of Q, we first need to find the max possible angle measure for X, as Q will have 1/4 as many sides as X.

    Equation for finding the sum of all interior angles of a polygon with 'n' sides: (n-2) * 180
    Equation for finding the measure of each interior angle of a regular polygon with 'n' sides: (n-2)*180/n

    If the interior angles of X are integer values, then the greatest possible measure of each angle would be 179 degrees. (180 would be a straight line, and thus not a polygon.)
    To find the number of sides of a polygon with interior angles of 179, simply set the above equation to 179:
    (n-2)*180/n = 179
    (n-2) *180 = 179n
    180n - 360 = 179n
    -360 = -n
    n = 360

    So X can have at most 360 sides.

    If Q has 1/4 the number of sides as X, then Q, at most, can have 360/4= 90 sides.
    If n = 90, each interior angle would be (90-2)*180/90 = 88*180/90 = 88*2 = 176. The answer is C

    _________________
    Veritas Prep | GMAT Instructor

    Veritas Prep Reviews
    Save $100 off any live Veritas Prep GMAT Course

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

    Best Conversation Starters

    1 LUANDATO 157 topics
    2 lheiannie07 87 topics
    3 Roland2rule 75 topics
    4 ardz24 64 topics
    5 AAPL 58 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description EconomistGMATTutor

    The Economist GMAT Tutor

    163 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    133 posts
    3 image description Jay@ManhattanReview

    Manhattan Review

    128 posts
    4 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    121 posts
    5 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    100 posts
    See More Top Beat The GMAT Experts