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      Question

      Find the smallest positive integer which when divided by

      5, 7 and 9 leaves a remainder 4 in each case.
      A 319 Correct Answer Incorrect Answer
      B 335 Correct Answer Incorrect Answer
      C 365 Correct Answer Incorrect Answer
      D 440 Correct Answer Incorrect Answer

      Solution

      If N leaves remainder 4 when divided by 5, 7, 9, then N тИТ 4 is divisible by all 5, 7, 9. LCM(5,7,9): 5 = 5 7 = 7 9 = 3┬▓ LCM = 5 ├Ч 7 ├Ч 3┬▓ = 5 ├Ч 7 ├Ч 9 = 315 So N тИТ 4 = 315k тЗТ N = 315k + 4 Smallest positive N when k = 1: N = 315 ├Ч 1 + 4 = 319 Check: 319 ├╖ 5 тЖТ remainder 4 319 ├╖ 7 тЖТ 7├Ч45 = 315, remainder 4 319 ├╖ 9 тЖТ 9├Ч35 = 315, remainder 4 Answer: 319.

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