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Math Help - Logic problem

  1. #1
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    Question Logic problem

    Difficult logic test. Sorry if offtopic.

    -Alex


    QUESTIONS 51 to 56

    A university is arranging five new advanced-level courses, one each in Anthropology, Botany, Chemistry, Drama, and Economics. To teach the five courses, the university has hired three new professors, Karanoff, Largent, and Marakowski, who teach no other courses at the university. Each professor will teach at least one course. The courses will be held in exactly five rooms in the same building, numbered consecutively 101 through 105, each of which will accommodate one and only one of the courses. No course is taught by a professor lacking training in that subject in which one of the other two is trained. The following conditions must be met:
    Karanoff is trained in Anthropology.
    Any professor who is trained in Botany is also trained in Chemistry.
    Economics must be held in room 104.
    Chemistry must be held in either room 101 or 102.
    Marakowski will teach in room 102.

    51.Which one of the following could be a complete and accurate list of the assignments of professors to courses?
    a)Karanoff: Anthropology and Economics; Largent: Drama; Marakowski: Chemistry and Botany
    b)Karanoff: Anthropology and Botany; Largent: Economics; Marakowski: Chemistry and Drama
    c)Karanoff: Botany and Chemistry; Largent: Economics; Marakowski: Anthropology and Drama
    d)Karanoff: Anthropology; Largent: Drama, Botany, and Chemistry; Marakowski: Economics
    e)Karanoff: Anthropology, Botany, and Chemistry; Largent: does not teach; Marakowski: Drama and Economics

    52.Each of the following is a pair of courses both of which Marakowski could teach EXCEPT:
    a)Botany in Room 101 and Drama in Room 102
    b)Botany in Room 101 and Drama in Room 105
    c)Chemistry in Room 102 and Economics in Room 104
    d)Botany in Room 102 and Economics in Room 104
    e)Drama in Room 102 and Economics in Room 104

    53.If Karanoff teaches Anthropology and exactly two other courses, which one of the following could be false?
    a)Karanoff teachers in Room 101.
    b)Karanoff does not teach Economics.
    c)Largent teachers exactly one course.
    d)Marakowski teachers Botany.
    e)Marakowski does not teach Economics.

    54.If Botany is held in Room 102, which one of the following must be true?
    a)Karanoff teaches in Room 101.
    b)Largent does not teach in Room 101.
    c)Karanoff teachers Economics.
    d)Largent teachers Economics.
    e)Marakowski teachers Economics.

    55.Assume the rule that Karanoff is trained in Anthropology is revoked but all other rules still apply; if Marakowski teachers exactly one course and Largent teachers Economics and at most one other course, each of the following could be false EXCEPT:
    a)Karanoff teachers in Room 101.
    b)Largent teachers Anthropology.
    c)Karanoff teachers exactly two courses.
    d)Karanoff teachers Drama.
    e)Marakowski teachers Drama.

    56.Which of the following is the complete and accurate list of all of the courses that could be held in Room 102?
    a)Botany
    b)Drama
    c)Botany and Chemistry
    d)Botany, Chemistry, and Drama
    e)Anthropology, Botany, Chemistry, and Drama
    Last edited by Alexandre1981; September 3rd 2008 at 07:58 PM.
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  2. #2
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    Your logic problem can be approached in two ways:

    • By formalizing the problem and then by using propositional or predicate calculus go through it and in this case it is a problem of symbolic logic ,or
    • By answering the questions of the problem without formalizing it and in that case you run the risk of very easily making wrong conclusions.And in this case although we may implicitly use logic it is not a problem of logic,but simply a problem in a certain department in a certain University.
    • And then again if the forum tries to formalize the problem it Will be a very tedious procedure and long winded.
    • So if you go back to your sources and get the formalization or at least a hind then we can start rolling
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  3. #3
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    Thank you for your response.
    Unfortunately, no additional data is available. This series of tests were part of an admission exam. I doubt many people have been able to solve this, in the very limited time. If any at all.
    I may be able to post the responses, if there is interest.
    Regards,
    Alex
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  4. #4
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    Quote Originally Posted by Alexandre1981 View Post
    Difficult logic test. Sorry if offtopic.

    -Alex


    QUESTIONS 51 to 56

    A university is arranging five new advanced-level courses, one each in Anthropology, Botany, Chemistry, Drama, and Economics. To teach the five courses, the university has hired three new professors, Karanoff, Largent, and Marakowski, who teach no other courses at the university. Each professor will teach at least one course. The courses will be held in exactly five rooms in the same building, numbered consecutively 101 through 105, each of which will accommodate one and only one of the courses. No course is taught by a professor lacking training in that subject in which one of the other two is trained. The following conditions must be met:
    Karanoff is trained in Anthropology.
    Any professor who is trained in Botany is also trained in Chemistry.
    Economics must be held in room 104.
    Chemistry must be held in either room 101 or 102.
    Marakowski will teach in room 102.
    A,B,C,D,E : courses
    K,L,M : teachers
    1,2,3,4,5 : rooms

    (Teacher T not trained in subject S AND there is another teacher trained in S) => T doesn't teach S.
    K is trained in A.
    Trained in B => Trained in C.
    E <=> 4.
    C <=> 1 or 2.
    M <=> 2.

    Note that you gotta make the difference between "trained" and "teach"

    51.Which one of the following could be a complete and accurate list of the assignments of professors to courses?
    a)Karanoff: Anthropology and Economics; Largent: Drama; Marakowski: Chemistry and Botany
    b)Karanoff: Anthropology and Botany; Largent: Economics; Marakowski: Chemistry and Drama
    c)Karanoff: Botany and Chemistry; Largent: Economics; Marakowski: Anthropology and Drama
    d)Karanoff: Anthropology; Largent: Drama, Botany, and Chemistry; Marakowski: Economics
    e)Karanoff: Anthropology, Botany, and Chemistry; Largent: does not teach; Marakowski: Drama and Economics
    e) is obviously false since it is said
    Each professor will teach at least one course.
    The other ones are possible (there is not enough restrictive conditions, so it's quite normal...)

    52.Each of the following is a pair of courses both of which Marakowski could teach EXCEPT:
    a)Botany in Room 101 and Drama in Room 102
    b)Botany in Room 101 and Drama in Room 105
    c)Chemistry in Room 102 and Economics in Room 104
    d)Botany in Room 102 and Economics in Room 104
    e)Drama in Room 102 and Economics in Room 104
    a) is not possible since C is in 1 or 2.
    The others are possible...

    53.If Karanoff teaches Anthropology and exactly two other courses, which one of the following could be false?
    a)Karanoff teaches in Room 101.
    b)Karanoff does not teach Economics.
    c)Largent teaches exactly one course.
    d)Marakowski teaches Botany.
    e)Marakowski does not teach Economics.
    Any of them can be false, except c), because once again, every teacher teaches at least one course.

    54.If Botany is held in Room 102, which one of the following must be true?
    a)Karanoff teaches in Room 101.
    b)Largent does not teach in Room 101.
    c)Karanoff teaches Economics.
    d)Largent teaches Economics.
    e)Marakowski teaches Economics.
    "if B is held in 2", from the sentence "C is held in 1 or 2", we can conclude that C is held in 1.
    From the sentence "M teaches in 2", we can conclude that M teaches B(otany)
    But this doesn't help answering the question. (or I can't see it)

    55.Assume the rule that Karanoff is trained in Anthropology is revoked but all other rules still apply; if Marakowski teaches exactly one course and Largent teachers Economics and at most one other course, each of the following could be false EXCEPT:
    a)Karanoff teaches in Room 101.
    b)Largent teaches Anthropology.
    c)Karanoff teaches exactly two courses.
    d)Karanoff teaches Drama.
    e)Marakowski teaches Drama.
    Huh


    56.Which of the following is the complete and accurate list of all of the courses that could be held in Room 102?
    a)Botany
    b)Drama
    c)Botany and Chemistry
    d)Botany, Chemistry, and Drama
    e)Anthropology, Botany, Chemistry, and Drama
    The courses will be held in exactly five rooms in the same building, numbered consecutively 101 through 105, each of which will accommodate one and only one of the courses.
    So c), d) and e) are not possible.

    -------------------------------------------------------
    What's worrying me is this difference between trained and teach. That's why I post to show you my reasoning and to say that I'm very interested in the correction
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  5. #5
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    Quote Originally Posted by Moo View Post
    What's worrying me is this difference between trained and teach. That's why I post to show you my reasoning and to say that I'm very interested in the correction
    Standard university practice is if a person is not trained in a discipline then that person will not teach a course in that area.
    This acts as negative condition.
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  6. #6
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    Hi,
    These are the answers divulged:

    51-A
    52-A
    53-D
    54-B
    55-A
    56-D

    -Alex
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  7. #7
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    Hi Alex

    I did tell you that the risk of making mistakes is very easy.

    For example for 51 you say that the correct answer is " a",but this is wrong because "d" is also correct.

    From the statements:

    1) no course is taught by professor lacking training,in that subject in which one of the other two is trained.

    2)Karanoff is trained in Anthropology.

    We can conclude Largent and Marakowski do not teach Anthropology,hence ......................"c" is wrong...............................

    From 1 and the statement :

    3) Any professor who is trained in Botany is also trained in Chemistry

    we can conclude ................"b" is wrong............................................

    Also ..................................."e" is wrong..........................................
    For the reason that was pointed out correctly by Moo

    So we are left with ......................."a" and "d"..............................being correct

    in 52 i can make no meaning coming out of it
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  8. #8
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    Quote Originally Posted by Plato View Post
    Standard university practice is if a person is not trained in a discipline then that person will not teach a course in that area.
    This acts as negative condition.
    I could be wrong (the wording is confusing), but it seems to me the statement

    "No course is taught by a professor lacking training in that subject in which one of the other two is trained."

    is saying that if none of the 3 professors is trained in a subject, then any one of them can teach it. But so long as at least one professor is trained in the subject, then the teacher of the course must be trained in it.
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