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In a certain group of 50 people, how many are doctors

This topic has 3 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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In a certain group of 50 people, how many are doctors

Post Mon Jul 31, 2017 6:39 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In a certain group of 50 people, how many are doctors who have a law degree?
    (1) In the group, 36 people are doctors.
    (2) In the group, 18 people have a law degree.

    Official Guide question
    Answer: E

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    Post Mon Jul 31, 2017 6:59 am
    jjjinapinch wrote:
    In a certain group of 50 people, how many are doctors who have a law degree?
    (1) In the group, 36 people are doctors.
    (2) In the group, 18 people have a law degree.

    Official Guide question
    Answer: E
    Target question: How many are doctors who have a law degree?

    Given: There are 50 people

    When I scan the two statements, I see that we have the ingredients for applying the [size=150]Double Matrix method[/size]
    This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
    Here, we have a population of 50 people, and the two characteristics are:
    - Doctor or NOT a doctor
    - Has law degree or doesn't have law degree

    So, we can set up our double matrix as follows:

    NOTE: I have placed a star in the box that represents doctors who have a law degree, since this is what the target question is asking us about

    Statement 1: In the group, 36 people are doctors.
    If the group has 50 people, and 36 are doctors, we can conclude that there are 14 non-doctors in the group.
    Let's add this information to our matrix:


    As you can see, there's no way to determine the value that must go in the starred box.
    As such, statement 1 is NOT SUFFICIENT

    Statement 2: In the group, 18 people have a law degree
    If 18 of the 50 people have a law degree, than the remaining 32 people do NOT have a law degree.
    Let's add this information to our matrix:


    As you can see, there's no way to determine the value that must go in the starred box.
    As such, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    When we combine the two statements, we get the following:


    There are several ways to complete this matrix. Here are two cases:

    case a:

    In this case, there are 10 doctors with law degrees.

    case a:

    In this case, there are 5 doctors with law degrees.
    Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

    Answer: E

    This question type is VERY COMMON on the GMAT, so be sure to master the technique.

    To learn more about the Double Matrix Method, watch this 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/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

    Medium Problem Solving questions
    - http://www.gmatprepnow.com/module/gmat-word-problems/video/920
    - 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/at-least-100-students-at-a-certain-high-school-study-japanes-t274669.html
    - http://www.beatthegmat.com/prblem-solving-t279424.html

    Difficult Problem Solving questions
    - http://www.gmatprepnow.com/module/gmat-word-problems/video/946
    - 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.gmatprepnow.com/module/gmat-word-problems/video/943
    - 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
    - https://youtu.be/dsCeqF9Kbk8
    - http://www.beatthegmat.com/double-set-matrix-question-t271423.html
    - https://youtu.be/dOZ9KM1m5Hs
    - http://www.beatthegmat.com/sets-t269449.html
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

    Cheers,
    Brent

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    Post Mon Jul 31, 2017 11:47 pm
    jjjinapinch wrote:
    In a certain group of 50 people, how many are doctors who have a law degree?

    (1) In the group, 36 people are doctors.
    (2) In the group, 18 people have a law degree.

    Official Guide question
    Answer: E
    Given that there are 50 people. We have to find out how many are doctors who have a law degree.

    Statement 1: In the group, 36 people are doctors.

    No information about the number of people with the law degree. Insufficient.

    Statement 2: In the group, 18 people have a law degree.

    No information about the number of doctors. Insufficient.

    Statement 1 & 2 combined:

    Case 1: There are 50 - 36 = 14 non-doctors, and all have law degree, thus doctors with law degree = 18 - 14 = 4.

    Case 2: There are 50 - 36 = 14 non-doctors, and none have law degree, thus doctors with law degree = 18.

    No unique answer. Insufficient.

    The correct answer: E

    Hope this helps!

    Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

    -Jay
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    Post Wed Aug 09, 2017 11:14 am
    jjjinapinch wrote:
    In a certain group of 50 people, how many are doctors who have a law degree?
    (1) In the group, 36 people are doctors.
    (2) In the group, 18 people have a law degree.

    Official Guide question
    Answer: E
    We have a group of 50 people and need to determine how many of those people are doctors with a law degree.

    We can use the following formula:

    total = # of doctors + # of lawyers - # both + # neither

    50 = # of doctors + # of lawyers - # both + # neither

    Statement One Alone:

    In the group, 36 people are doctors.

    So, we have:

    50 = 36 + # of lawyers - # both + # neither

    24 = # of lawyers - # both + # neither

    We cannot determine the number of people who are both. Statement one alone is not sufficient to answer the question.

    Statement Two Alone:

    In the group, 18 people have a law degree.

    So, we have:

    50 = # of doctors + 18 - # both + # neither

    32 = # of doctors - # both + # neither

    We cannot determine the number of people who are both. Statement two alone is not sufficient to answer the question.

    Statements One and Two Together:

    Using statements one and two, we have:

    50 = 36 + 18 - # both + # neither

    -4 = - # both + # neither

    # both = 4 + # neither

    We still cannot determine the number of “both” since we don’t know the number of “neither.”

    Answer: E

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