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    Question

    A six-digit number 4c68d2 is divisible by 12. Find the

    sum of all possible values of 'c' for the largest possible value of 'd'.
    A 12 Correct Answer Incorrect Answer
    B 15 Correct Answer Incorrect Answer
    C 18 Correct Answer Incorrect Answer
    D 20 Correct Answer Incorrect Answer

    Solution

    ATQ, A number is divisible by 12 when it is divisible by 3 and 4 both. A number is divisible by 4 when its last two digits are divisible by 4. Here 'd2' is divisible by 4 for 'd' = 0, 2, 4, 6, and 8. Largest possible value of 'd' = 8. A number is divisible by 3 when the sum of its digits is divisible by 3. Sum of digits of 4c6882 = 4 + c + 6 + 8 + 8 + 2 = 28 + c. So, possible values of 'c' = 2, 5, and 8. Therefore, the required sum = 2 + 5 + 8 = 15.

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