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Thread: Another one I need help on.

  1. #1
    Trying to make mom and pop proud
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    Another one I need help on.

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    The attached JPEG corresponds to this question.

    If arc PQR above is a semicircle, what is the length of diameter PR?
    (1) a=4
    (2) b=1



    ANSWER: D (Either is sufficient)



    I kind of get it, but would like a thorough, clear explanation from all you smarties out there. Thanks!!

    Attached Thumbnails Attached Thumbnails Another one I need help on.-gmat-question-no.-7.jpg  

  2. #2
    An Urch Guru Pundit Swami Sage
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    Re: Another one I need help on.


  3. #3
    Trying to make mom and pop proud
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    Re: Another one I need help on.

    (pls draw a figure on your end as I can't draw a figure here )

    Let's say the centre of the circle is O and point where perpendicular from Q meets the diameter is M (so that QM = 2 as given in the figure)

    Construct a line connecting centre O and Q, which will equal to the radius of the circle = r.

    Statement - 1 : a = 4

    In triangle QOM, applying pythagoras,
    OQ^2 = MO^2+MQ^2
    Here, OQ = r
    MQ = 2
    and MO = 4-r

    Therefore, r^2 = (4-r)^2 + 2^2.... solving it gives you r = 2.5
    So I is SUFFICIENT
    ____________________________________

    In a similar fashion, b = 1 gives you following equation,
    r^2 = (r-1)^2 + 4.... solving it gives you r = 2.5
    So II is SUFFICIENT

    Hence, answer is D...

    Cheers...
    You never win the Silver, you lose the Gold!!!!

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