Question
What is the maximum value of (a + b) if '5a346b8' 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.
'b8' 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, (5 + a + 3 + 4 + 6 + 8 + 8) = (34 + a) must be divisible by 3.
So, 'a' = 2, 5 or 8
Since, we have to find maximum value, so 'a' = 8.
Therefore, required value = 8 + 8 = 16
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