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Math Help - Need Help with numbers

  1. #1
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    Need Help with numbers

    Here is the problem. I just have no clue on how to solve this without spending hours writing them all out.

    Find the number of four-digit positive integers divisible by either 3 or 7.
    Last edited by ceasar_19134; September 28th 2006 at 02:38 PM.
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  2. #2
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    Quote Originally Posted by ceasar_19134 View Post
    Find the number of four-digit positive integers divisible by either 3 or 7.[
    Assume that by “four-digit positive integers” you mean 1000-9999.
    The number of integers 1-9999 divisible by 3 is floor(9999/3)=3333.
    The number of integers 1-999 divisible by 3 is floor(999/3)=333.
    Therefore, the number of integers 1000-9999 divisible by 3 is 3333-333=3000.

    The number of integers 1-9999 divisible by 7 is floor(9999/7)=1428.
    The number of integers 1-999 divisible by 7 is floor(999/7)=142.
    Therefore, the number of integers 1000-9999 divisible by 7 is 1286.

    The number of integers 1000-9999 divisible by 21 is 429.

    The number of integers 1000-9999 divisible by 3 or 7 is 3000+1286-429=3857.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by ceasar_19134 View Post
    Here is the problem. I just have no clue on how to solve this without spending hours writing them all out.
    ing
    Find the number of four-digit positive integers divisible by either 3 or 7.
    There are 9000 four digit numbers 3000 of them are divisible by 3 and 1286 of
    them are divisible by 7, and 429 are divisible by both (that is by 21).

    Therefore 3000+1286-429 are divisible by either 3 or 7 (the 429 are
    subtracted because these are the numbers divisible by both 3 and 7 and so
    will have been counted in both the 3000 and 1286).

    You will need to check that I have the number of four digit numbers
    divisible by 3, 7 and 21 correct!

    RonL
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ceasar_19134 View Post
    Here is the problem. I just have no clue on how to solve this without spending hours writing them all out.
    ing
    Find the number of four-digit positive integers divisible by either 3 or 7.
    I am confused on something here. The mathematical "or" statement is true when both statements are true. So shouldn't we be including rather than excluding any 4 digit number that is divisible by both 3 and 7? (ie if it is divisible by 21) I realize that using "English" rules "either/or" statements do mean one or the other, not both. Which should we be using here?

    (This kind of question has always bugged me.)

    -Dan
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    If |A| stands for the number of elements in set A, then |AuB|=|A|+|B|-|A^B|.
    We subtract off those elements that we have counted twice.
    Both of us did subtract the number of multiples of 21.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by topsquark View Post
    I am confused on something here. The mathematical "or" statement is true when both statements are true. So shouldn't we be including rather than excluding any 4 digit number that is divisible by both 3 and 7? (ie if it is divisible by 21) I realize that using "English" rules "either/or" statements do mean one or the other, not both. Which should we be using here?

    (This kind of question has always bugged me.)

    -Dan
    Ah! The blind are beginning to see. You only subtracted it once. I get it now. Thanks!

    -Dan
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