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Lê Quốc Trần Anh Coordinator

11/01/2018 at 09:46
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How many positive integers not exceeding $2001$ are multiples of $3$ or $4$ but not $5$?




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  • ...
    Phan Thanh Tinh Coordinator 11/01/2018 at 11:13

    From 1 to 2001 :

    The number of multiples of 3 is : (2001 - 3) : 3 + 1 = 667

    The number of multiples of 4 is : (2000 - 4) : 4 + 1 = 500

    The number of common multiples of 3 and 5 is : 

    (1995 - 15) : 15 + 1 = 133

    The number of common multiples of 4 and 5 is :

    (2000 - 20) : 20 + 1 = 100

    The number of common multiples of 3 and 4 is :

    (1992 - 12) : 12 + 1 = 166

    The number of common multiples of 3, 4 and 5 is :

    (1980 - 60) : 60 + 1 = 33

    The answer is :

    (667 - 133) + (500 - 166 - 100 + 33) = 801

    Multiples of 3 Multiples of 4 Multiples of 5

    Lê Quốc Trần Anh selected this answer.
  • ...
    FA Liên Quân Garena 12/01/2018 at 12:26

    From 1 to 2001 :

    The number of multiples of 3 is : (2001 - 3) : 3 + 1 = 667

    The number of multiples of 4 is : (2000 - 4) : 4 + 1 = 500

    The number of common multiples of 3 and 5 is : 

    (1995 - 15) : 15 + 1 = 133

    The number of common multiples of 4 and 5 is :

    (2000 - 20) : 20 + 1 = 100

    The number of common multiples of 3 and 4 is :

    (1992 - 12) : 12 + 1 = 166

    The number of common multiples of 3, 4 and 5 is :

    (1980 - 60) : 60 + 1 = 33

    The answer is :

    (667 - 133) + (500 - 166 - 100 + 33) = 801


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