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Prblem Solving

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RiyaR Rising GMAT Star Default Avatar
31 May 2014
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Prblem Solving Post Tue Sep 16, 2014 9:59 am
Elapsed Time: 00:00
    Of the z students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
    (A) z + w - x - y
    B) z - w - x - y
    (C) z - w - x + y
    (D) w + x + y - z
    (E) w - x - y - z

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    Post Tue Sep 16, 2014 10:36 am
    This question is from set theory,

    The general rule states that

    Total = Type A + Type B - Both Type A and B + None

    Applying the same to the mentioned question

    Total = Z
    Type A = Students studying french = X
    Type B = Students studying german = Y
    Both = Students studying french and german = W
    None = Students studying neither = N

    Z = X + Y - W + N

    Therefore N = Z + W -X -Y

    Ans : A

    Experts , correct me if I am wrong Smile

    Post Thu Sep 18, 2014 11:08 am
    RiyaR wrote:
    Of the z students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
    (A) z + w - x - y
    B) z - w - x - y
    (C) z - w - x + y
    (D) w + x + y - z
    (E) w - x - y - z
    We can also use the Double Matrix Method here. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.

    Here, we have a population of zstudents, and the two characteristics are:
    - studying French or not studying French
    - studying German or not studying German

    So, we can set up our diagram as follows:

    Note: I placed a star in the bottom right box to remind me that this is the value we are trying to determine.

    Now, if there are z students ALTOGETHER, and x of them are studying French, then the number of students NOT studying French = z - x.
    Similarly, if there are z students ALTOGETHER, and y of them are studying German, then the number of students NOT studying German = z - y.
    So, we can add that information to the diagram.

    w are studying both French and German
    When we add this information to our diagram, we get the following:

    When we examine the TOP 2 BOXES, we see that they add to x. So, the TOP-RIGHT box must be x - w

    Finally, we know that the two HIGHLIGHTED boxes below must add to z - y.

    So, the BOTTOM-RIGHT box must equal (z - y) - (x - w)

    (z - y) - (x - w) = z - y - x + w

    Answer: A
    NOTE: This type of question is VERY COMMON on the GMAT, so be sure to master the technique.

    To learn more about the Double Matrix Method, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

    Once you’re familiar with this technique, you can attempt these additional practice questions:

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