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The rate of downloading is 1,200 KB / 3 minutes = <<1200/3=400>>400 KB/minute.
The remaining size of the file is 3,200 KB - 1,200 KB = <<3200-1200=2000>>2,000 KB.
Therefore, it will take 2,000 KB / 400 KB/minute = <<2000/400=5>>5 more minutes to finish downloading. Answer: \boxed{5}.