Why is this code false? But it actually fufills everything?

Scanner input = new Scanner(System.in);
		ArrayList<Integer> numList = new ArrayList<Integer>();

		for (int i = 0; i < 20; i++) {
			String s = input.nextLine();
			numList.add(Integer.parseInt(s));
		}

		ArrayList<Integer> divBy3 = new ArrayList<Integer>();
		ArrayList<Integer> divBy2 = new ArrayList<Integer>();
		ArrayList<Integer> divBy3And2 = new ArrayList<Integer>();

		for (int i = 0; i < numList.size(); i++) {
			int x = numList.get(i); // gets number index position through each loop

			if(x % 3 == 0 && x % 3 != 1 && x % 2 == 0 && x % 2 != 1) {
				divBy3And2.add(x);}
			else if (x % 3 == 0) {
				divBy3.add(x);
			}else if (x % 2 == 0) {
				divBy2.add(x);
			}
		}
		System.out.print("Divisible by 3: ");
		printList(divBy3);
		System.out.print("\nDivisible by 2: ");
		printList(divBy2);
		System.out.print("\nDivisible by 2 and 3: ");
		printList(divBy3And2);
	}

	public static void printList(List<Integer> list) {

		for (Integer x : list) {
			System.out.print(x + " ");
		}

	}

}