A nice idea would be an array of hashes, which is an alternative to the excellent two-array solution hardburn explained you.

use strict;

open(QUESTIONS, '<', 'questions.txt') or die $!;
open(ANSWERS, '<', 'answers.txt') or die $!;

my @quiz;
while(my $question = <QUESTIONS>) {
    my $answer = <ANSWERS>;
    chomp ($question);
    chomp ($answer);
    push @quiz, {
        'q' => $question,
        'a' => $answer,
    };
}

close(QUESTIONS);
close(ANSWERS);

my $nquestions = scalar(@quiz);
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You can then access to the elements as follows:

for my $i(0..$nquestions-1) {
    print $quiz[$i]{'q'}."\n";
    print $quiz[$i]{'a'}."\n";
}
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Michele.