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ANSWER: A = 3.

If you write 3 between the hundreds and ones digit which make 3-digit number  $132, then divide the same by eleven members, the answer is whole number.

$ 132 ÷ 11 = $12  ⇒  the amount to be equally paid by each member

But if you write other numbers from 0 to 9 (except 3, of course), and divide the 3-digit number by 11, the result will have repeating decimals.