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      Question

      The greatest number of four digits which when divided by

      8, 10, 12 leave remainders 5, 7, 9 respectively is:
      A 9658 Correct Answer Incorrect Answer
      B 9763 Correct Answer Incorrect Answer
      C 9957 Correct Answer Incorrect Answer
      D 9897 Correct Answer Incorrect Answer

      Solution

      The difference between divisor and the corresponding remainder is equal (i.e 3). LCM of 8, 10 and 12 = 120 Largest 4-digit number = 9999 After dividing 9999 by 120 we will get the remainder as 39. Therefore, the number divisible by 120 = 9999 – 39 = 9960 If 3 is subtracted from the number 9960 the resulting number will follow the condition in the question and that number is 9957.

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