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Overlapping sets question

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AndyMann Just gettin' started! Default Avatar
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Overlapping sets question Post Sat Jun 22, 2013 11:01 am
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    Will really appreciate if anyone can help to solve this question using Double set matrix method.

    In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

    (A) 11N/12
    (B) 7N/12
    (C) 5N/12
    (D) 6N/7
    (E) N/7

    OA: A

    Thanks a lot,
    Andy

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    Post Sat Jun 22, 2013 11:05 am
    AndyMann wrote:
    Will really appreciate if anyone can help to solve this question using Double set matrix method.

    In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

    (A) 11N/12
    (B) 7N/12
    (C) 5N/12
    (D) 6N/7
    (E) N/7

    OA: A

    Thanks a lot,
    Andy
    Here's the Double Matrix method step-by-step:

    Note: This technique can be used for most questions featuring a population in which each member has two criteria associated with it.
    Here, the criteria are:
    - degree (applied sciences or not)
    - school location (northeastern state or not)

    In 1997, N people graduated from college.


    1/3 of them received a degree in the applied sciences


    Of those (1/3)N students, 1/4 graduated from a school in one of six northeastern states.

    In other words, (1/12)N students have a degree in applied sciences and graduated from a northeastern school.

    Which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?
    If the box that has (1/12)N students in it represents the students with a degree in applied sciences and graduated from a northeastern school, then the remaining boxes (shaded in blue) must represent the students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.


    Since all 4 boxes must add to N (the total number of students), the 3 shaded boxes must add to (11/12)N.

    Answer = A

    Cheers,
    Brent

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

    Then try these additional practice questions that can be solved using the Double Matrix Method:
    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
    - http://www.beatthegmat.com/ds-quest-t187706.html
    - http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
    - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
    - http://www.beatthegmat.com/ds-french-japanese-t222297.html

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    AndyMann Just gettin' started! Default Avatar
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    Post Sat Jun 22, 2013 11:25 am
    Dear Brent,

    Thanks so much for your prompt reply. Your answers are always so concise and helpful.

    I am still little confused with the wording of the question. It says to find "who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states"; Is this not pointing to the box in the double matrix for "Not AS" and "Not NES"?

    I am trying to get my head around it that why it's the sum of the 3 blue boxes.

    Thanks,
    Andy

    Post Sat Jun 22, 2013 11:28 am
    AndyMann wrote:
    Will really appreciate if anyone can help to solve this question using Double set matrix method.

    In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

    (A) 11N/12
    (B) 7N/12
    (C) 5N/12
    (D) 6N/7
    (E) N/7

    OA: A
    Let N = the LCM of the denominators in the problem = 3*4 = 12.
    The number who received a degree in the applied sciences = (1/3)12 = 4.
    Of the 4 who received a degree in the applied sciences, the number who graduated in one of the NE states = (1/4)4 = 1.
    Since only 1 person both received a degree in the applied sciences and graduated in one of the NE states, the number who did NOT do both = 12-1 = 11. This is our target.

    Now we plug N=12 into the answers to see which yields our target of 11.
    A quick scan of the answer choices reveals that only A works:
    (11N)12 = (11*12)/12 = 11.

    The correct answer is A.

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    Post Sat Jun 22, 2013 11:58 am
    AndyMann wrote:
    Dear Brent,

    Thanks so much for your prompt reply. Your answers are always so concise and helpful.

    I am still little confused with the wording of the question. It says to find "who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states"; Is this not pointing to the box in the double matrix for "Not AS" and "Not NES"?

    I am trying to get my head around it that why it's the sum of the 3 blue boxes.

    Thanks,
    Andy
    Good question.
    The top-left box refers to students who both received a degree in the applied sciences and graduate from a school in one of six northeastern states.

    So, the other 3 boxes refer to students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

    The box you're referring to ("Not AS" and "Not NES") is for students who neither received a degree in the applied sciences not graduated from a school in one of six northeastern states.
    This is just one of the boxes that meet the criteria of not both receiving a degree in the applied sciences and graduate from a school in one of six northeastern states.

    Also, notice that the top-right box, also meets the criteria of not both receiving a degree in the applied sciences and graduate from a school in one of six northeastern states.

    The bottom-left box also meets the criteria of not both receiving a degree in the applied sciences and graduate from a school in one of six northeastern states.

    I hope that helps.

    Cheers,
    Brent

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

    Thanked by: AndyMann
    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!
    AndyMann Just gettin' started! Default Avatar
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    Post Sat Jun 22, 2013 12:12 pm
    Awesome! Thanks for the explanations Mitch and Brent.

    Brent,the concept is very nicely explained. Much appreciate. Thanks a lot!

    Cheers,
    Andy

    nikhilgmat31 GMAT Destroyer! Default Avatar
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    Post Thu Oct 08, 2015 4:01 am
    Mitch,
    This statement in question seems very confusing.

    "Number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states"

    Whether it says number of people who both didn't received applied science degree & nor graduated from NE states.

    or
    number of people who both didn't received applied science degree and people who are not graduated from NE states.

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