Hey I tried this [basically] from my iPhone 4S. I've experienced similar issues like this since first using my AppleID waaay back in the day as they say, especially since iPhone [1] & every time it has to do with a little quirk with your Apple ID & payment Info. Here's what I did on my iPhone 4S but is same with almost ALL iPhones & iPods & fundamentally the same w/the iPad as well & all Apple devices using iTunes. It's one of those things so simple it's complicated-for us veterans anyways & for those of you newer to this just know it's fundamentally the same-just a little bit different as far as the interface of getting to it from each different yet great Apple device:). Anyways, here's what I did on my iPhone, hope this helps;
1) click on settings
2) go to Store Settings -or- Apple Store Settings
3) click on "View Apple ID"
a) enter your AppleID password when prompted
4) now click on payment method
5) select "None" as described above
b) then select "save" or "done"
6) back-out completely now like your going to use your iPhone/device as usual
7) locate your App Store App & select/open it
8) search for & select a free app you like -or- a paid one, doesn't matter yet
9) enter your Apple ID password when prompted & it will AGAIN take you to the 3 questions thingy (technical term;))
10) choose your 3 questions & their answers accordingly
11) now I left the rescue email or whatever it's called if otherwise blank but I don't think it matters as my friend entered hers while we did this together on our separate accounts & in the end both ways worked. Again I doubt it has anything to do with that-it's about some kinda scrub in the system needed or whatever (scrub sounds good/appropriate/like I actually know what I'm talking about;) -which I think I do here actually however;))
12) Hit "Done" on keyboard pop-up thingy (that tech term again;))
a) then hit "Done" or "Save" at top left of window/screen &
If you DL'd a free app;
A pop-up will say you can now DL the App "Such-n-So" (or whatever it's name is)
a) go back into settings & re-enter your cc info under Payment Method in App Store Settings in Settings & Voila! Good as new!
If you DL'd a paid App or selected to do so I should say;
A pop-up will ask you to enter your payment method CC info
a) enter your cc info again & confirm your billing address info & stuff at bottom in case different than your Apple ID one then enter your cc billing address info & if same as Apple ID one then confirm it anyway;)
Voila! A pop-up will say thank you...yada yada! & your App DL will begin as usual.
Hope this helps- I'm as positive as I can be after experiencing similar but never really major situations like this since it all began. Best of luck to you all!