Quizzes core is built using the Backbone JS framework. To work, it uses the PUT and DELETE request method for HTTP requests.
If you encounter problem with adding/removing your quiz questions/answers/results, you have probably blocked the DELETE and/or PUT methods on your server.
The easiest way to allow Backbone working properly, is to insert the below condition into the .htaccess file on your server.
If this not an option on your server, please contact with your server provider to check other possible solutions.
order deny,allow allow from all