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Thread: Combination of Packages

  1. #1
    Senior Member harpazo's Avatar
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    Combination of Packages

    The weights of four packages are 1, 3, 5, and 7 pounds, respectively. Which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

    A. 9
    B. 10
    C. 12
    D. 13
    E. 14

    Seeking one or two hints.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Combination of Packages

    I would look at each given choice, and see if that weight can be made from the sum of some combination of the given numbers.

    9 = 5 + 3 + 1...so A is out.

    10 = 7 + 3...so B is out.

    Continue on...which choice isn't possible?
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  3. #3
    Senior Member harpazo's Avatar
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    Re: Combination of Packages

    Quote Originally Posted by MarkFL View Post
    I would look at each given choice, and see if that weight can be made from the sum of some combination of the given numbers.

    9 = 5 + 3 + 1...so A is out.

    10 = 7 + 3...so B is out.

    Continue on...which choice isn't possible?

    12 = 7 + 5
    So, 12 is out.

    13: 1 + 5 + 7
    So, 13 is out.

    The answer is 14. No combination of 1, 3, 5, and 7 produce a sum of 14.
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  4. #4
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    Re: Combination of Packages

    Quote Originally Posted by harpazo View Post
    The weights of four packages are 1, 3, 5, and 7 pounds, respectively. Which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

    A. 9
    B. 10
    C. 12
    D. 13
    E. 14
    Seeking one or two hints.
    Look at this expansion.
    Can you see why 14 is the correct answer?
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  5. #5
    Senior Member harpazo's Avatar
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    Re: Combination of Packages

    Quote Originally Posted by Plato View Post
    Look at this expansion.
    Can you see why 14 is the correct answer?
    I found the answer after playing with the question. The link you provided is too advanced for me.

    Keep in mind a few things about me:

    1. I am 53 years old.

    2. I majored in Sociology not math.

    3. I have not been a student in a formal class setting since the Fall of 1993.

    4. The highest math course I took as an elective was precalculus in the Spring 1993 semester. I got an A minus.
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    Re: Combination of Packages

    Quote Originally Posted by harpazo View Post
    I found the answer after playing with the question. The link you provided is too advanced for me. Keep in mind a few things about me:
    1. I am 53 years old.
    2. I majored in Sociology not math.
    3. I have not been a student in a formal class setting since the Fall of 1993.
    4. The highest math course I took as an elective was precalculus in the Spring 1993 semester. I got an A minus.
    Frankly my dear I can't give a damn about any of the above. YOU have chosen to post serious mathematical questions here.
    We here are a group of serious people here and we give you serious answers. The fact that one may not have the background experience to understand the provided help in no way is our concern. So don't ask a question if you are not prepared to understand the answer. Or if you don't understand the answer, say what it is it is that you don't understand. Do not blame us for your lack of understanding.
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Combination of Packages

    Quote Originally Posted by harpazo View Post
    ...The link you provided is too advanced for me...
    It's actually not too advanced for you, although it might seem to be at first glance an unorthodox approach to the problem. It's actually a very clever approach for finding all of the possible weight combinations in one calculation (and even how many ways there are to get a particular combination, represented by the coefficient of each term), but the actual mathematics involved is at the elementary algebra level (by elementary, I mean the algebra one typically learns prior to the calculus).

    Do you understand where the binomial coefficients come from in the binomial theorem, that they actually represent the number of ways to choose each term in the expansion?
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  8. #8
    Senior Member harpazo's Avatar
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    Re: Combination of Packages

    Moving on....
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