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      Question

      Find the largest four-digit number which when divided

      by 6, 10, 15, and 18, leaves a remainder 1, 5, 10, and 13 respectively.
      A 9,980 Correct Answer Incorrect Answer
      B 9,985 Correct Answer Incorrect Answer
      C 9,875 Correct Answer Incorrect Answer
      D 9,965 Correct Answer Incorrect Answer

      Solution

      Here we can see that the difference (5) between numbers and remainder is same along all four numbers. 6 = 2 × 3
      10 = 2 × 5
      15 = 3 × 5
      18 = 2 × 3² LCM of (6, 10, 15, 18) = 2 × 3² × 5
      = 90 Largest four-digit number which is a multiple of 90 = 9,990 So, the required number = 9990 − 5 = 9,985

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