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

Overlapping sets question

This topic has 6 expert replies and 5 member replies
AndyMann Just gettin' started! Default Avatar
Joined
25 Jan 2013
Posted:
19 messages
Thanked:
2 times
Overlapping sets question Post Sat Jun 22, 2013 11:01 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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

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

    Enter our contest to win a free course.

    Thanked by: AndyMann
    GMAT Prep Now's comprehensive video course can be used 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
    Joined
    25 Jan 2013
    Posted:
    19 messages
    Thanked:
    2 times
    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.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    Thanked by: AndyMann, Gurpreet singh
    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
    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 video course along with Beat The GMAT's free 60-Day Study Guide

    Enter our contest to win a free course.

    Thanked by: AndyMann
    GMAT Prep Now's comprehensive video course can be used 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
    Joined
    25 Jan 2013
    Posted:
    19 messages
    Thanked:
    2 times
    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
    Joined
    12 May 2015
    Posted:
    518 messages
    Thanked:
    9 times
    Test Date:
    3 Oct
    Target GMAT Score:
    750
    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.

    Zoser Just gettin' started!
    Joined
    16 Jan 2017
    Posted:
    14 messages
    Post Wed Feb 08, 2017 11:11 am
    Quote:
    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.
    Hi Brent!

    As I understood, the question is asking for the fraction of the bottom right box (no Degree with No school). Can you explain why you included the three blue boxes and not just the bottom right?

    Post Wed Feb 08, 2017 11:33 am
    Zoser wrote:
    Quote:
    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.
    Hi Brent!

    As I understood, the question is asking for the fraction of the bottom right box (no Degree with No school). Can you explain why you included the three blue boxes and not just the bottom right?
    The question is asking for more than just the number of students in the bottom right.

    Here's the question: 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?

    So, the students in the top left box are those who BOTH received a degree in the applied sciences AND graduated from a school in one of six northeastern states.

    So, the students in the remaining 3 boxes are those who did NOT BOTH receive a degree in the applied sciences AND graduate from a school in one of six northeastern states. This is the value that question is asking us to determine.

    Does that help?

    Cheers,
    Brent

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

    Enter our contest to win a free course.

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Zoser Just gettin' started!
    Joined
    16 Jan 2017
    Posted:
    14 messages
    Post Wed Feb 08, 2017 1:13 pm
    Brent@GMATPrepNow wrote:
    Zoser wrote:
    Quote:
    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.
    Hi Brent!

    As I understood, the question is asking for the fraction of the bottom right box (no Degree with No school). Can you explain why you included the three blue boxes and not just the bottom right?
    The question is asking for more than just the number of students in the bottom right.

    Here's the question: 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?

    So, the students in the top left box are those who BOTH received a degree in the applied sciences AND graduated from a school in one of six northeastern states.

    So, the students in the remaining 3 boxes are those who did NOT BOTH receive a degree in the applied sciences AND graduate from a school in one of six northeastern states. This is the value that question is asking us to determine.

    Does that help?

    Cheers,
    Brent
    I believe so. But if the question is asking for the bottom right box, how would it be probably be phrased?

    Thanks
    Zoser

    GMAT/MBA Expert

    Matt@VeritasPrep GMAT Instructor
    Joined
    12 Sep 2012
    Posted:
    2120 messages
    Followed by:
    107 members
    Thanked:
    504 times
    Target GMAT Score:
    V51
    GMAT Score:
    780
    Most Active Expert Most Thanked Expert
    Post Fri Feb 17, 2017 2:06 am
    Zoser wrote:
    I believe so. But if the question is asking for the bottom right box, how would it be probably be phrased?

    Thanks
    Zoser
    "How many students neither received a degree in the applied sciences nor graduated from a school in one of six northeastern states?"

    _________________
    Don't trust anyone who doesn't type ².
    Very Happy

    Save $100 on any VP online 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!
    Post Fri Feb 17, 2017 10:37 am
    Hi All,

    This question can be solved by TESTing VALUES. Even before we read the prompt, the answer choices certainly appear to provide some context for what the perfect Value to TEST would be (probably 12 or 7, since the answer choices are all fractions with one or the other of those numbers as the denominator). Once we read through the information involving the two fractions, it seems pretty clear that we should be TESTing 12...

    IF...
    N = 12 graduates
    1/3 = 4 received a degree in applied sciences
    1/4 (of those 4) = 1 graduated from a school in a northeastern state

    We're asked for the number of people who did NOT receive a degree in applied sciences and graduate from one of those states. Since 1 of the 12 fit BOTH descriptions, 11 of the 12 do NOT. TESTing N = 12 leads to just one matching answer...

    Final Answer: A

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com


    Best Conversation Starters

    1 Mo2men 21 topics
    2 neeti2711 16 topics
    3 ziyuenlau 14 topics
    4 REINE 8 topics
    5 vikkimba17 8 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    84 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    82 posts
    3 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    81 posts
    4 image description Matt@VeritasPrep

    Veritas Prep

    80 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    70 posts
    See More Top Beat The GMAT Experts