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

Prblem Solving

This topic has 1 expert reply and 1 member reply
RiyaR Rising GMAT Star Default Avatar
31 May 2014
98 messages
Followed by:
2 members
1 times
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

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

    Easy Problem Solving questions
    - http://www.beatthegmat.com/the-aam-aadmi-party-t272242.html
    - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

    Medium Problem Solving questions
    - http://www.beatthegmat.com/probability-question-t273360.html
    - http://www.beatthegmat.com/posted-speed-limit-t272374.html
    - http://www.beatthegmat.com/motel-t271938.html
    - http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
    - http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
    - http://www.beatthegmat.com/ds-french-japanese-t222297.html

    Difficult Problem Solving questions
    - http://www.beatthegmat.com/ratio-problem-t268339.html
    - http://www.beatthegmat.com/overlapping-sets-question-t265223.html
    - http://www.beatthegmat.com/fractions-t264254.html
    - http://www.beatthegmat.com/overlapping-sets-t264092.html
    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

    Easy Data Sufficiency questions
    - http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
    - http://www.beatthegmat.com/ds-quest-t187706.html

    Medium Data Sufficiency questions
    - http://www.beatthegmat.com/sets-matrix-ds-t271914.html
    - http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
    - http://www.beatthegmat.com/a-manufacturer-t270331.html
    - http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

    Difficult Data Sufficiency questions
    - http://www.beatthegmat.com/double-set-matrix-question-t271423.html
    - http://www.beatthegmat.com/sets-t269449.html
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3[img]

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

    GMAT Prep Now's 35-hour (500+ videos) course is 100% FREE. Use our free course in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

    Best Conversation Starters

    1 NandishSS 28 topics
    2 fiza gupta 20 topics
    3 Mo2men 11 topics
    4 Anaira Mitch 10 topics
    5 gabrielrc 7 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Rich.C@EMPOWERgma...


    113 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    91 posts
    3 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    80 posts
    4 image description Jay@ManhattanReview

    Manhattan Review

    66 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    65 posts
    See More Top Beat The GMAT Experts