Hi Ana and PG,
What kind of hypothetical question would you come up with? I have tried this before and I couldn't think of anything for the life of me so I asked the director of the department, are you the hiring manager and can you tell me more about the position? I didn't send him my CV, I sent that to HR. But I got a phone call from him and he explained the position and asked me questions too (it actually ended up being like a phone interview).
I know it worked this time (sort of) but I just got lucky. I didn't really have anything intelligent to ask when i made that first contact. I'm wondering, what is a better way to approach this? Can you give some hypothetical questions that don't come across as desperate?