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Math Help - largest remainder.

  1. #1
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    largest remainder.

    Good morning,
    having trouble with this one.

    what is the largest possible remainder when a two-digit number
    is divided by the sum of its digits?
    a)13, b)14, C)15, D)16, E)17

    How would I approach this one please?
    algebra? explanation if possible
    Thanks
    Cody, Perth
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    The largest sum is 18 for the number 99. The largest remainder can be 17, but in fact the remainder is 9: 99=18*5+9

    For the numbers 98 and 89 the sum is 17 and the remainders are 13 and 5.

    For 79 the sum is 16 and the remainder is 15. This is the largest remainder that can be obtained.
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  3. #3
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    Thank you Red Dog,
    so I had the answer correct,
    I was just wondering about the methodology,
    I was just testing all numbers back from 99
    so this seems the correct way to do it.
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