Solution: If the number of people who failed in the initial test is X, then the number of people who passed the initial test is (3X+ 14).

There are (3X+ 14+33) people who passed the second interview and (X-33) people who failed.

Column equation

3X+ 14+33=(X-33)×5

3X+47=5X- 165

3X+47+ 165=5X

5X-3X=2 12

2X=2 12

X= 106

Then, the number of people who passed the preliminary examination is: 106×3+ 14=332.

106+332=438 students participated in the competition.