Question
Find the maximum value of (a + b) if '1a624b0' is
divisible by 12.Solution
A number is divisible by 12 if it divisible by both 3 and 4. A number is divisible by 4 when last two digits of the number is divisible by 4. 'b0' is divisible by 4 when 'b' = 0, 2, 4, 6 or 8. Since, we have to find maximum value, so 'b' = 8. A number is divisible by 3 when sum of its digit is divisible by 3. So, (1 + a + 6 + 2 + 4 + 8 + 0) = (21 + a) must be divisible by 3. So, 'a' = 0, 3, 6 or 9. Since, we have to find maximum value, so 'a' = 9. Therefore, required value = 9 + 8 = 17
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