Since 1 dozen is equal to 12 then 2 dozens of cups is equal to 2 x 12 = <<2*12=24>>24 cups.
So, Liezl prepared a total of 24 cups x 4 sets = <<24*4=96>>96 paper cups.
A total of 5 + 30 = <<5+30=35>>35 paper cups were not used.
Hence, 96 - 35 = <<96-35=61>>61 paper cups were used.
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