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suneja Group Title

if x represents the sum of all the positive 3-digit nos that can be constructed using each of the distinct non zero digits a,b,c exactly once, wat is the largest integer by wic x must be divisible?

  • one year ago
  • one year ago

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  1. suneja Group Title
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    no its 222

    • one year ago
  2. matricked Group Title
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    see it is clear for the sum of all 3-digited number is always divisible by 111

    • one year ago
  3. matricked Group Title
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    total no. of 3 digited nos as per ur question is 504 do u need the highest integer which divides the sum of all 504 numbers? or something else..

    • one year ago
  4. matricked Group Title
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    if i am not wrong the sum of all 3 digited numbers is 279720 with each of the distinct non zero digits a,b,c exactly once it is divisible by integers greater than 222

    • one year ago
  5. matricked Group Title
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    ?? r u there

    • one year ago
  6. suneja Group Title
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    how did u gt tis?? .. bit confused

    • one year ago
  7. matricked Group Title
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    see in any order the each digit 1 through 9 will appear as many as(8X7) times in the unit , tenth and hundredth place

    • one year ago
  8. matricked Group Title
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    now the sum of 1 through 9=45 hence required sum of all reqd + 3digited number is=45*56*(100+10+1)=279720

    • one year ago
  9. matricked Group Title
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    i hope it is clear to u or point where i am making mistake

    • one year ago
  10. suneja Group Title
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    see u might be rite but its jst not helping.... no offense but see its 3digit no so it shud be 9X8X7 Possibilities

    • one year ago
  11. matricked Group Title
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    yes u r correct that is total 504 numbers possible

    • one year ago
  12. suneja Group Title
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    k then

    • one year ago
  13. matricked Group Title
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    now each of the digits appear 504 /9 =56 times in each column

    • one year ago
  14. matricked Group Title
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    do u agree

    • one year ago
  15. suneja Group Title
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    k

    • one year ago
  16. matricked Group Title
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    now can u guess the sum total of each of the three columns

    • one year ago
  17. matricked Group Title
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    will it not be 56*(1+2+3....+9)=56*45=2520

    • one year ago
  18. matricked Group Title
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    am i correct...

    • one year ago
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