I thought I would just reply with a update on this issue although original post is a little old and security questions themselves will eventually likely be obsolete
This is a more rare issue and can be frustrating but actually is a very simple fix.
What you have to do is call Apple care/iOS (1-800-MY APPLE/1-800-692-7753)
What you will need to do is go to appleid.apple.com, sign in like you normally would with password, and when it brings you to answer security questions at the bottom of that menu click instead "generate temporary support pin"
Give it to the agent, then they will be required to verify one other piece of identity. It may need to be at least one correct answer to security questions, up to date credit card info on file (they never need the whole card number, legit apple care never asks for the entire CC number or pin etc), or other information depending on how much info you set up on your appleid.
If they are able to verify you they are able to reset your security questions, then you sign into appleid.apple.com again, but this it asks you to select new ones.
Another word of advice, write them down/type them and save them somewhere. It is not apple's fault you set up security features on your account then cant remember your own answers. Hope this helps for all of you having this problem.