Analysis: 1: Choose any student, the score of each of the 30 questions is odd (5, 1,-1), and the sum of the 30 odd questions must be even, that is, the score of the 30 questions is even, plus the basic score 15, it becomes odd, that is, arbitrary.

2: 2003 students took part in the competition, among which 2002 students can be divided into 100 1 group and two students in the first group. Their scores will add up to even numbers, because we know that odd numbers+odd numbers = even numbers, 100 1 multiplied by even numbers will also be even numbers, plus the rest.