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Math Help - 2 problems

  1. #1
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    2 problems

    I was trying to help my sister study for the SATs and I came across two problems that i didn't know how to do. Here they are:


    Consider a positive odd integer n. Let X = twice the number of factors of n, and let Y = the number of factors of 2n. Which of the following must be true?
    A)X = 4
    B)X > Y
    C)Y > X
    D)X = Y
    E)There is not enough information to solve the problem



    Let the expectal(x) be defined for all x as the smallest prime number that is greater than x/2. What is the value of:
    expectal(8.1)expectal(5.2)


    Thanks in advance!!
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  2. #2
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    Quote Originally Posted by PensFan10 View Post
    I was trying to help my sister study for the SATs and I came across two problems that i didn't know how to do. Here they are:


    Consider a positive odd integer n. Let X = twice the number of factors of n, and let Y = the number of factors of 2n. Which of the following must be true?
    A)X = 4
    B)X > Y
    C)Y > X
    D)X = Y
    E)There is not enough information to solve the problem
    The answer is D)X = Y

    When you multiply an odd number by two, the number of it's factors doubles

    Try a few examples and you should see why.
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  3. #3
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    Quote Originally Posted by PensFan10 View Post
    I was trying to help my sister study for the SATs and I came across two problems that i didn't know how to do. Here they are:


    Consider a positive odd integer n. Let X = twice the number of factors of n, and let Y = the number of factors of 2n. Which of the following must be true?
    A)X = 4
    B)X > Y
    C)Y > X
    D)X = Y
    E)There is not enough information to solve the problem!!
    Well let n have r factors these are all odd, so each of these is a factor of 2n, and so is 2 times any of them and these are different from any of the factors of n, so Y>=X.

    Now all the factors of 2n are or the form f, where f is a factor of n, or 2f, where again f is a factor of n (since n is odd) So X>=Y

    Together these twi inequalities imply that X=Y.

    RonL
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  4. #4
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    Let the expectal(x) be defined for all x as the smallest prime number that is greater than x/2. What is the value of:
    expectal(8.1)expectal(5.2)
    The first skill is dividing by 2.

    8.1/2 = 4.05
    5.2/2 = 2.6

    The next skill is identifying prime numbers.

    8.1/2 = 4.05 ==> 5
    5.2/2 = 2.6 ==> 3

    Now what?
    Last edited by TKHunny; July 30th 2008 at 11:09 AM. Reason: Missed a word and deleted #1
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by PensFan10 View Post
    Let the expectal(x) be defined for all x as the smallest prime number that is greater than x/2. What is the value of:
    expectal(8.1)expectal(5.2)
    What is the smallest prime graeter than 4.05?

    And the smallest prime greater than 2.6?

    RonL
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  6. #6
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    Okay

    Thanks for all the help. It all makes sense now
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