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Math Help - Three digit number problem?

  1. #1
    Junior Member
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    Three digit number problem?

    Q-> K is a three digit number such that the ratio of the number to the sum of digits is least?what is the difference between the hundred and tens digit of K?
    a) 9
    b) 8
    c) 7
    d) None of these

    Q-> In the above question what can be said about the difference between the tens and unit digit?
    a) 0
    b) 1
    c) 2
    d) None of these

    Q-> For the above question for how many values of K will the ratio be highest?
    a) 9
    b) 8
    c) 7
    d) None of these.

    Any help would be appreciated.

    Thanks,
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  2. #2
    Super Member Gamma's Avatar
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    Iowa City, IA
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    I think for a and b the number you are looking for is 199. I knew you needed 1 for the first digit and 9 for the last because the idea is to make the number as small as possible while keeping the digits as large as possible. Basically increasing the hundreds spot hurts you 100 fold up top for each one increase, while only decreasing the ratio marginally. Conversely for the ones digit. For the middle digit to be honest I just tried the different possibilities, nothing fancy.

    Not sure about c) sorry its late here and I gotta hit the sack.
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  3. #3
    Junior Member
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    For third question.
    I think below are the possible number with highest ratio.
    100:1,200:2,300:3,400:4,500:5,600:6,700:7,800:8,90 0:9.

    Hence answer should be 9.

    Any correction would be appreciated.

    Thanks
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  4. #4
    Super Member Gamma's Avatar
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    beautiful, like I said, I was getting very sleepy and wasn't thinking. That has to be correct the way the question is worded.
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