The sum of the successor of the greatest 3-digit number and the predecessor of the smallest 3-digit number is

1. 1000

2. 1100

3. 1101

4. 1099

The greatest 3-digit number = 999.

Successor of 999 = 999 + 1 = 1000.

The smallest 3-digit number = 100.

Predecessor of 100 = 100 - 1 = 99.

Sum = 1000 + 99 = 1099.

Hence, option 4 is the correct option.