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1.
A phrase usually indicating that the speaker has absolutely no idea how to answer said question. Often used to stall for time.
Photography teacher walking in on students who should be at pep rally: What are you doing here?
Sreya: That's a good question!
by Shen June 28, 2004
 
2.
i don't know the answer
larry king: "how do we get iran to disarm their nukes without invading?"

guest politician: "thats a good question larry"
by stg60913b September 18, 2010