Question
What is the highest possible sum of (m + n) if the
number '9m813n2' is divisible by 12?Solution
ATQ,
A number is divisible by 12 if it is divisible by both 3 and 4.
A number is divisible by 4 when the last two digits of the number are divisible by 4.
'n2' is divisible by 4 when 'n' = 0, 2, 4, 6, or 8.
Since we have to find the maximum value, so 'n' = 8.
A number is divisible by 3 when the sum of its digits is divisible by 3.
So, (9 + m + 8 + 1 + 3 + 8 + 2) = (31 + m) must be divisible by 3.
So, 'm' = 2, 5, or 8.
Since we have to find the maximum value, so 'm' = 8.
Therefore, required value = 8 + 8 = 16 .
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