For an interview question: how would I write new "malloc" and "free" functions? I don't think "using new and delete" would be an acceptable answer or using something similar like LocalAlloc/HeapAlloc
Since this is for an interview question, it probably won't have a "right" answer, and they're more interested in your thought process, and your general knowledge surrounding the topic.
You should ask to clarify the requirements, or give a range of answers depending on the situation. Here are some issues to consider: