(Untested) If the questions in the input are separated by blank lines:

# Read input a paragraph at a time
# and put carriage returns on output lines
local $/ = "\n\n";
local $\ = "\n";

# Read input, one question at a time
while (<>) {
  chomp;

  # Grab the question number
  my $number = /^(\d+\.)/;

  # Split the question into lines
  my @question = split /\n/;

  # The answer is the last line
  my $answer = pop @question;

  # Send the results to different output streams
  print OUT1 join("\n", @question);
  print OUT2 "$number $answer";
}
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