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    Question

    The greatest number of four digits which when divided by

    10, 12, 14 leave remainders 8, 10, 12 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 2). LCM of 10, 12 and 14 = 420 Largest 4-digit number = 9999 After dividing 9999 by 420 we will get the remainder as 339. Therefore, the number divisible by 420 = 9999 – 339 = 9660 If 2 is subtracted from the number 9660 the resulting number will follow the condition in the question and that number is 9658.

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