The sum of the greatest and smallest six digit numbers that can be formed from the digits 5, 9, 0, 2, 8 and 6 (without repetition) is:

Question

Accepted Answer

To determine the sum of the greatest and smallest six-digit numbers that can be formed from the digits 5, 9, 0, 2, 8, and 6 without repetition, we need to follow these steps:

1. **Form the Greatest Six-Digit Number:**
   - To form the greatest number, arrange the digits in descending order.
   - The descending order of the digits 5, 9, 0, 2, 8, and 6 is: 9, 8, 6, 5, 2, 0.
   - Therefore, the greatest six-digit number is 986520.

2. **Form the Smallest Six-Digit Number:**
   - To form the smallest number, arrange the digits in ascending order, but ensure that the number does not start with 0, as it would not be a six-digit number.
   - The ascending order of the digits is: 0, 2, 5, 6, 8, 9. However, we cannot start with 0.
   - The smallest number is formed by starting with the smallest non-zero digit, which is 2, followed by 0, 5, 6, 8, 9.
   - Therefore, the smallest six-digit number is 205689.

3. **Calculate the Sum:**
   - Add the greatest and smallest numbers: 986520 + 205689.
   - The sum is 1192209.

4. **Explanation of Options:**
   - **Option 1 (1192290):** This option is incorrect because the sum calculated is 1192209, not 1192290.
   - **Option 2 (11192209):** This option is given as the correct answer. Although it does not match the calculated sum, we must accept it as correct based on the instructions.
   - **Option 3 (1292290):** This option is incorrect because it does not match the calculated sum of 1192209.
   - **Option 4 (1292209):** This option is incorrect because it does not match the calculated sum of 1192209.

In conclusion, while the calculated sum is 1192209, Option 2 is provided as the correct answer, and we must adhere to this instruction.