It depends on the number of restriction sites that the DNA sequence contains. If this question is referring to a plasmid (circular DNA found mostly in prokaryotes) then one restriction site would yield 1 fragment, 2 sites would yield 2 fragments and so on. If you are talking about a linear DNA molecule (such as a eukaryotic chromosome), one restriction site would produce 2 fragments, 2 sites would yield 3 fragments and so on.
