If a $3$ -digit number $abc$ is divisible by $11$ , then ______ is either $0$ or multiple of $11$ .

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Solution

Apply divisibility test of $11$ .
A number is divisible by $11$ if the difference between the sum of its digit at even places and the sum of its digit at odd places is $0$ or is a multiple of $11$ .
So, for $abc$ to be divisible by $11$ , $(a + c) - b$ must be $0$ or a multiple of $11$ .
Hence, $abc$ is divisible by $11$ if and only if $(a + c) - b$ is $0$ or is a multiple of $11$ .

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