Is there a better way to check an integer against multiple divisibility rules without nesting so many if-elses?

Problem:
Write a program to compute a score for an integer x. If x is zero or negative the score is −100. Otherwise we start with 0. If the x is a multiple of 3, add 3 to the score. After that if x is a multiple of 5, add 5 to the score. After that if x is between 100 and 200 (inclusive), add 50 to the score, else subtract 50 from the score. Now print the score.

My Question:
The solution below works, but I can't find a more concise way to write a program that solves the problem. I'm new to C but my understanding is that Switch Statements can't do logical comparisons, and that as soon as an If Statement is met, no further ones are checked.

Is there a way to check an integer against multiple rules without repeating the code blocks? - Thank you.

My Solution:

#include <stdio.h>

int main()
{
    int x;
    int score;

    scanf("%d", &x);

    if (x <= 0){
        score = -100;
    }
    else {
        score = 0;

        if (x % 3 == 0 && x % 5 == 0) {
            score += 8;
            if (x >= 100 && x <= 200) {
                score += 50;
            }
            else {
                score -= 50;
            }
        }

        else if (x % 3 == 0) {
            score += 3;
            if (x >= 100 && x <= 200) {
                score += 50;
            }
            else {
                score -= 50;
            }
        }

        else if (x % 5 == 0) {
            score += 5;
            if (x >= 100 && x <= 200) {
                score += 50;
            }
            else {
                score -= 50;
            }
        }

        else if (x >= 100 && x <= 200) {
            score += 50;
        }

        else {
            score -= 50;
        }
    }

    printf("%d", score);
    return 0;
}