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pythagoras123

The numbers 82, 90 and 168 are divided by a positive integer (a non-zero whole number), leaving remainders. If the sum of the three remainders is 25, what is the positive integer?

  • one year ago
  • one year ago

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  1. integralsabiti
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    we should also know the remainders.

    • one year ago
  2. FoolForMath
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    I am getting 21.

    • one year ago
  3. integralsabiti
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    @FoolForMath wanna see your solution pls.

    • one year ago
  4. beknazar23
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    82 = n*x + a 90 = m*x + b 168 = k*x + c a+b+c = 25 x - ?

    • one year ago
  5. integralsabiti
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    three equasions and 7 variables

    • one year ago
  6. beknazar23
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    you should add theses 3 equations, then you'll get: 340 = x*(n+m+k)+ 25, replace n+m+k = c(some positive integer like x) 315 = x*c

    • one year ago
  7. FoolForMath
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    The numbers were small, i simply calculated one by one. The general problem is interesting. I need think about it.

    • one year ago
  8. beknazar23
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    my equation helps to reduce the candidate numbers: x = 3,5,7,21 only. because, there are only integer number. then you'll put these candidate numbers one-by-one

    • one year ago
  9. integralsabiti
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    @beknazar23 s solution is good enough.

    • one year ago
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