ToString() and AddString() method without using .Net Collections
ListOfString = null; is useless, fields get initialized to default(T) which is null for reference types. So you can drop the constructor.

For simple initializations you can use inline initializers. e.g.

private string ListOfString = "";

You're hiding ToString() instead of overriding it.
You're ignoring empty input strings, the spec doesn't require that. Curiously you're not ignoring null input strings.
Using a string as accumulator leads to quadratic runtime since it has to create a new string which contains all current data for each append.

Use StringBuilder.Append in Add instead. Don't return a string from Add, else you lose the performance advantage. Call stringBuilder.ToString() in your ToString operation. This has linear runtime.
You're returning null if no value has ever been added. I'd expect the empty string instead.


I don't know what they meant by calling your code "not detailed enough". You could add documentation for corner cases, possibly in the form of unit tests. For my observations 3 and 5 it's not clear if your code is behaving like you intended. Documentation and/or unit tests would have clarified your intent.