Results 1 to 5 of 5

Math Help - Problem Solving Question

  1. #1
    Member
    Joined
    Sep 2010
    Posts
    98
    Thanks
    1

    Problem Solving Question

    Does anyone know what the five digit number 5DDDD is when it is divisible by 6.

    What is the digit D?

    I have this so far...

    50000/6 = 8333.33 remaining

    51111/6 = 8518.5

    52222/6 = 8703.66 remaining

    53333/6 = 8888.83 remaining

    54444/6 = 9074

    55555/6 = 9259.166 remaining

    56666/6 = 94444.33 remaining

    Does this mean that 4 is the only digit of D that is divisible by 5DDD, because it is the only digits that goes into this problem evenly?


    I honestly do not know if this is right...these are just my ideas. Any help or ideas would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by matgrl View Post
    Does this mean that 4 is the only digit of D that is divisible by 5DDD, because it is the only digits that goes into this problem evenly?
    Exhaustive search is a valid method, but if you want to do that you will need to check 57777 through 59999 as well. (And indeed 54444 is the only solution.)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,713
    Thanks
    632
    Hello, matgrl!

    \text{A five-digit number of the form }N = 5DDDD\text{ is divisible by 6.}
    \text{What is the digit }D?

    As undefined pointed out, an exhaustive search is a valid approach.


    We can use some knowledge to aid in our search.

    Since N is divisible by 6, it is divisible by 2 and 3.

    Since N is divisible by 2, it must be an even number.
    . . An even number ends in an even digit: 0, 2, 4, 6, or 8.

    Since N is divisible by 3, the sum of its digits must be a multiple of 3.

    . . \begin{array}{ccc}D & N & \text{Digital sum} \\ \hline<br />
0 & 50000 & 5 \\ 2 & 52222 & 13 \\ 4 & 54444 & 21 \\ 6 & 56666 & 29 \\ 8 & 58888 & 37 \end{array}

    And we see that only 54444 is divisible by 6.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Sep 2010
    Posts
    98
    Thanks
    1
    I understand your chart and I think this is a great idea, but I have one question. How does54444 show that it is divisible by 6? The digitial sum is not an even number. What exactly does this digital sum show us?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by matgrl View Post
    I understand your chart and I think this is a great idea, but I have one question. How does54444 show that it is divisible by 6? The digitial sum is not an even number. What exactly does this digital sum show us?
    A positive integer is divisible by 3 if and only if its digital sum is divisible by 3. So you can actually repeat the digitial sum process iteratively (take the digital sum of the digital sum of the digital sum....) until you reach a single digit, if you wanted to.

    An integer is divisible by 6 if and only if it is divisible by 2 and it is divisible by 3.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem solving logartithm question
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 10th 2010, 11:55 PM
  2. 9th Grade Problem Solving Question
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 23rd 2009, 02:32 AM
  3. help with problem solving question
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 15th 2009, 01:25 AM
  4. A problem solving question I just don't get..
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 18th 2008, 01:53 PM
  5. A Problem Solving Question
    Posted in the Math Challenge Problems Forum
    Replies: 2
    Last Post: August 2nd 2006, 03:28 AM

Search Tags


/mathhelpforum @mathhelpforum