I recently had to prepare a lesson on "Talk, speak, say, or tell" for one of my TEFL classes, because my non-native Engish speaking students were heartily confused by the choice. I admit that I had to put a lot of thought into the preparation, because this is one of those points that seems simple until you have to define it.

This is an extract from my lesson on the difference between "talk" and "speak", although as I always find myself saying, "there are exceptions":

 “Speak” is used to mean the mechanical act of forming words from sounds: using the teeth, tongue, palate, and lungs to make words, but not necessarily sense.
“Talk” however is much more about using those words to express thoughts and ideas: to have a conversation, to communicate with spoken words.
So, I learn to speak French in order to talk to my Gallic neighbours.
Consider these examples as illustrations of my point:
>“Speak up! We can’t hear you.” ( Failure of mechanical process).
>“Don’t speak with your mouth full!” (A visual affront, not an aural one).
>“Sit down, we have to talk.” (The verbal content is important here).

In your example, "they were talking about the exam" is correct for the subject of a conversation, but it could be argued that a misheard tannoy announcement about the school timetable, for example, could be explained as "they were speaking about the exam" (heard but not attended to, so no communication).

Hope this helps!

jaylang