:D What an excellent question and a very important one as well.
You are correct that the particle KA at the end of a sentence asks a question. So, the phrase *Anata wa * is either incorrect, or missing some words and of course the *KA* if it is a question.
The answer is that in this context, it is incomplete. I'd like to introduce to you the Japanese way of speaking which is - dropping all understood words between the speaker and the listener.
Sayaka: O namae wa nan desu ka?
Kenny: Watashi no namae wa Kenī desu, *anata wa?*
In English, this would be:
_Sayaka: What is you name?_
_Kenny: My name is Kenny, *yours is?*_
Just as you do in English - _*yours is?*_ without any intonation at the end is simply stating a fact - like "yours is the big one" however, when it is said with a rising intonation _*yours IS?*_ - then it is clearly asking a question.
In the example above, *Anata wa?* - _*"Yours is?"*_ has dropped the words _*"what"*_ and *_"name"*_ - that's *namae* and *nan desu ka?*
So, the complete version would be something like:
*__Anata __no namae __wa__ nan desu ka?*
You will often hear Japanese people speak with sentences that consists of just an action word, such as:
*_Iku?_* - which literally translates to _*"Go?"*_ but may ask the questions "Are you going?"
I hope this helped to clarify the confusion.
Gambatte kudasai! May your learning be enjoyable! :lol: