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Math Help - Impossible Question?

  1. #1
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    Impossible Question?

    Ok I just had my Probability exam today, this was a national standard in New Zealand and there was one question that left me wondering whether or not it was possible to answer or if the NZQA (New Zealand Qualifications Authority) had made a mistake. I wasn't the only one who was confused by this either..

    Anyway the question was essentially:
    There are 30 people on a tour bus.
    22 passengers were male
    8 passengers were over 30 y/o
    1 passenger was a male Australian over 30 y/o
    3 passengers were male Australians 30 y/o or under
    All female Australians passengers were over 30 y/o
    There were 2 male passengers over 30 y/o but not Australian
    10 passengers were Australians
    Calculate the probability that a randomly selected passenger was an Australian female over 30 y/o


    The problem was that there are 4 out of the 10 Australians were male therefore the other 6 Australian passengers were female. These women are all over 30 y/o but the problem is that there are only 8 passengers over 30 y/o and in the constraints there's the 1 Australian male over 30 y/o and the 2 non-Australians who were over 30 y/o so
    8-2-1= 5 ≠6

    SO anyone have a solution??
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Impossible Question?

    I agree with you - there is a logical inconsistency here. If we number the statements 1 through 8, starting with statement #1 being "there are 30 people on a tour bus," then we know that there 8 passengers > 30 years old (from #3), and that among them there is 1 Australian male (from #4), 2 non-Australian males (#7), and 6 Australian females (from #6 combind with #8). So - either the answer involves hermaphroditic bus riders or there is an error in the problem statement.
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  3. #3
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    Re: Impossible Question?

    Thanks for that, it's concerning that there'd be this sort of mistake in an exam (in New Zealand everyone who takes this level of Statistics and Modelling takes the same exam at the same time so this probably would've affected tens of thousands of students.)
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    Super Member Quacky's Avatar
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  5. #5
    MHF Contributor ebaines's Avatar
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    Re: Impossible Question?

    Occasionally errors creep into the standardized tests here in the US as well. One of my faviorite examples involved not a clerical error but one where the person who wrote the problem got it wrong, and so did all the reviewers! It went something like this:

    Imagine a triangular equilateral pyramid of side length A and a square pyramid whose triangular faces all also have side length A. Now imagine that one face of the triangular pyramid is lined up with one of the triangular faces of the square pyramid, and the two pyramids are glued together. How many surfaces does the combined shape have?

    A) 5
    B) 7
    C) 8
    D) 9
    E) None of the above

    The "obvious" answer is 7, and that was what the examiners thought was correct, based on the concept that if a 4-sided object and 5-sided object are glued together thereby obscuring one side of each then that leaves 7 edges exposed. But that's not correct. Can anyone tell me the correct answer?
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  6. #6
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    Re: Impossible Question?

    Well if you glued the triangular pyramid to the square face of the square pyramid you'd get 8 faces?? maybe..? depending how you positioned it on the square face. Or is it because when you line up the 2 triangular faces some of the other faces don't have a different angle so they combine to become one face across both pyramids?
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  7. #7
    Super Member Quacky's Avatar
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    Re: Impossible Question?

    I think reiddu's logic is right - I count 6 because two other faces will connect. Unless there's even more to this.
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  8. #8
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    Re: Impossible Question?

    it seems to me, that 2 of the faces of the tetrahedron will become co-planar with 2 of the sides of the pyramid, leaving just 5 faces (2 of the "fused faces", the base of the pyramid, the opposite side of the pyramid from the "glued side, and the base of the tetrahedron).
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    Re: Impossible Question?

    Quote Originally Posted by Deveno View Post
    it seems to me, that 2 of the faces of the tetrahedron will become co-planar with 2 of the sides of the pyramid, leaving just 5 faces (2 of the "fused faces", the base of the pyramid, the opposite side of the pyramid from the "glued side, and the base of the tetrahedron).
    That's what I meant, just unable to express it as articulately as you did haha
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  10. #10
    Super Member Quacky's Avatar
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    Re: Impossible Question?

    I thought the angles wouldn't work out, but then I saw a diagram, and yeah I guess that works too
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  11. #11
    MHF Contributor ebaines's Avatar
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    Re: Impossible Question?

    Quote Originally Posted by Deveno View Post
    it seems to me, that 2 of the faces of the tetrahedron will become co-planar with 2 of the sides of the pyramid, leaving just 5 faces (2 of the "fused faces", the base of the pyramid, the opposite side of the pyramid from the "glued side, and the base of the tetrahedron).
    Correct - 5 it is! The people who conceived the test didn't think about the possibility of the sides aligning. It came to light when a really bright kid who thought he had aced the math SAT exam received a score of 780 (a score of 800 is perfect, and 780 is 1 wrong) - he sued the testing company for the answer key and that's when it all came out. The testing company ended up scoring everyone who responded with an answer of either 5 or 7 as correct.
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  12. #12
    Super Member Quacky's Avatar
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    Re: Impossible Question?

    But I feel like that isn't sufficient. It knocks the confidence of the candidate when they get confused by an apparently simple question. They probably spent longer on this question than was sufficient and as a result didn't have the necessary time to complete more challenging questions. And the nervousness may well have thrown them off.
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