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Math Help - divisor and remainder

  1. #1
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    divisor and remainder

    (1) what is the sum of all 3 digit numbers that leave a remainder of 2 when divided by 3 ?



    (2) How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ?
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) The least number is 101=3\cdot 33+2
    The greatest number is 998=3\cdot 332+2
    You have to calculate \sum_{k=33}^{332}(3k+2)

    2) The least number is 103=7\cdot 14+5
    The greatest number is 999=7\cdot 142+5
    How many numbers are from 14 to 142?
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