Quiz in WPLMS requires configuration in the wordpress in order to work properly. Note that we're saving Quiz answers as comments to Questions. In order for quiz to work smoothly confirm the following pointers :
1. Verify Comment moderation settings in WP Admin -> settings -> Discussion as given in documentation
http://vibethemes.com/envato/wplms/documentation/quick-installation-guide.html#important
2. Verify that each of question in the quiz has comments enabled in the Discussion metabox in question edit screen in WP Admin. By default it is enabled.
3. If even after confirming above settings this Quiz is not saving the answers, try disabling Site Tracking in BuddyPress components from WP Admin -> Settings -> BuddyPress -> Components.