Discussion

Which digit should come in place of * in the number 8*9632 to make it divisible by 11?

Answer: A

A number is divisible by 11 if the difference of the sums of alternating digits is 0 or a multiple of 11.

Let's sum the digits in odd positions (from the right): 2 + 6 + * = 8 + *.

Let's sum the digits in even positions (from the right): 3 + 9 + 8 = 20.

The difference is \(|(8 + *) - 20| = |* - 12|\).

We need \(|* - 12|\) to be 0 or a multiple of 11.

If \(* - 12 = -11\), then \(* = 1\). Since * must be a single digit, this is a valid solution.

If \(* - 12 = 0\), * would be 12 (not a digit). If \(* - 12 = 11\), * would be 23 (not a digit).

So, the required digit is 1.

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