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Thread: Value of n

  1. #1
    Senior Member harpazo's Avatar
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    Value of n

    When 10 is divided by the positive integer n, the remainder is (n - 4). What could be the value of n?

    10/n

    Remainder = n - 4

    Is the equation set up (10/n) = n - 4?
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    Re: Value of n

    Quote Originally Posted by harpazo View Post
    When 10 is divided by the positive integer n, the remainder is (n - 4). What could be the value of n?

    10/n

    Remainder = n - 4

    Is the equation set up (10/n) = n - 4?
    No, the dividend divided by a divisor equals a quotient, plus any remainder.

    Or, put another way, the divisor multiplied by the quotient, plus the remainder, equal the dividend.

    Here, 10 is the dividend, n is the divisor, the remainder is (n - 4), but the quotient is not explicitly given.

    I'll call the quotient Q.

    n*Q + (n - 4) = 10

    n*Q + n = 14

    n(Q + 1) = 14


    $\displaystyle n \ = \ \dfrac{14}{Q + 1}$


    This should help you determine the value(s) for n.
    Last edited by greg1313; Nov 28th 2018 at 08:29 AM.
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    Senior Member harpazo's Avatar
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    Re: Value of n

    Quote Originally Posted by greg1313 View Post
    No, the dividend divided by a divisor equals a quotient, plus any remainder.

    Or, put another way, the divisor multiplied by the quotient, plus the remainder, equal the dividend.

    Here, 10 is the dividend, n is the divisor, the remainder is (n - 4), but the quotient is not explicitly given.

    I'll call the quotient Q.

    n*Q + (n - 4) = 10

    n*Q + n = 14

    n(Q + 1) = 14


    $\displaystyle n \ = \ \dfrac{14}{Q + 1}$


    This should help you determine the value(s) for n.
    To find n, I need to know Q. How do I find Q?
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    Re: Value of n

    Quote Originally Posted by harpazo View Post
    To find n, I need to know Q. How do I find Q?
    Suppose you start out with the interval $\displaystyle \ 1 \le n \le 10 $.

    For usual division, the remainder is non-negative, so $\displaystyle \ (n - 4) \ge 0$.

    Or, $\displaystyle \ \ n \ge 4$.

    If 10 is divided by an n in this interval, the quotient would be in this interval: $\displaystyle \ 1 \le Q \le 10 $.

    (Q + 1) must be positive and divide 14. So, candidates for Q are 1 and 6. But, a Q-value of 6 makes an n-value of 2,
    and we already stated that $\displaystyle \ \ n \ge 4$.

    Check out what happens if Q = 1.
    Last edited by greg1313; Nov 29th 2018 at 01:11 PM.
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    Senior Member harpazo's Avatar
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    Re: Value of n

    Quote Originally Posted by greg1313 View Post
    Suppose you start out with the interval $\displaystyle \ 1 \le n \le 10 $.

    For usual division, the remainder is non-negative, so $\displaystyle \ (n - 4) \ge 0$.

    Or, $\displaystyle \ \ n \ge 4$.

    If 10 is divided by an n in this interval, the quotient would be in this interval: $\displaystyle \ 1 \le Q \le 10 $.

    (Q + 1) must be positive and divide 14. So, candidates for Q are 1 and 6. But, a Q-value of 6 makes an n-value of 2,
    and we already stated that $\displaystyle \ \ n \ge 4$.

    Check out what happens if Q = 1.
    If Q is 1, then n is 7. So, the answer is 7.
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    Re: Value of n

    Quote Originally Posted by harpazo View Post
    If Q is 1, then n is 7. So, the answer is 7.
    Yes. Quick check: When you divide 10 by 7, you get a remainder of 3, which is 7-4.
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    Senior Member harpazo's Avatar
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    Re: Value of n

    Quote Originally Posted by Debsta View Post
    Yes. Quick check: When you divide 10 by 7, you get a remainder of 3, which is 7-4.
    Thank you for your help and patience.
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    Re: Value of n

    how about $n=14$ ?
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    Re: Value of n

    Quote Originally Posted by Idea View Post
    how about $n=14$ ?
    An interesting thought....

    -Dan
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    Re: Value of n

    Quote Originally Posted by Idea View Post
    how about $n=14$ ?
    Are you saying to let n = 14 for n = 14/(Q + 1)?


    n = 14/(Q + 1)

    14 = 14/(Q + 1)

    14(Q+ 1) = 14

    14Q + 14 = 14

    14Q = 14 - 14

    14Q = 0

    Q = 0/14

    Q = 0

    When Q = 0, then we have:

    n = 14/(Q + 1)

    n = 14/(0 + 1)

    n = 14/1

    n = 14
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    Re: Value of n

    Quote Originally Posted by harpazo View Post
    Are you saying to let n = 14 for n = 14/(Q + 1)?


    n = 14/(Q + 1)

    14 = 14/(Q + 1)

    14(Q+ 1) = 14

    14Q + 14 = 14

    14Q = 14 - 14

    14Q = 0

    Q = 0/14

    Q = 0

    When Q = 0, then we have:

    n = 14/(Q + 1)

    n = 14/(0 + 1)

    n = 14/1

    n = 14
    yes that's how we check and see that n=14 is a solution

    10 divided by n=14 gives a quotient Q=0 and remainder = 10 = n - 4

    the same way that

    10 divided by n=7 gives Q=1 and remainder = 3 = n - 4
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    Re: Value of n

    Quote Originally Posted by Idea View Post
    yes that's how we check and see that n=14 is a solution

    10 divided by n=14 gives a quotient Q=0 and remainder = 10 = n - 4

    the same way that

    10 divided by n=7 gives Q=1 and remainder = 3 = n - 4
    Very good. Interesting reply. Interesting question.
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