There are a huge number of ways to do this, but any form of storage that you are familiar with will work - a Database is probably just the most appropriate because it also allows you to store and / or manage the responses in a simple and structured manner. If you don't use a database, then the question storage is trivial, but storing the responses and relating them back to the user responding and the question they are responding to becomes quite complex.
However, the simplest way to store the questions is just to use a straight text file, and separate the question and the answer by a '|' character. You then keep Q&A pairs together by having each on a separate line, and process them with something like:
string[] qAndA = File.ReadAllLines(pathToQAndAFile);
foreach (string pair in qAndA)
{
string[] pairs = pair.Split('|');
if (pairs.Length == 2)
{
string question = pairs[0];
string answer = pairs[1];
...
}
}