The total points is $20\times5=100.$ If there was one wrong anwser, she would lose $5+7=12$ points.  $(20\times5-4)\div(7+5)=8$, so she got $20-8=12$ problems correct. 
Lucy joined a math test which had the scoring rules below: for any correct answer, she got $5$ points; for any skipped or wrong answer, she lost $7$ points. There were $20$ problems in total. When she finished the test, she got only $4$ points. How many problems did she answer correct? 
(1) $$4$$ 
(2) $$8$$ 
(3) $$12$$ 
(4) $$16$$ 
(5) $$3$$ 