Suppose that the number 735383629 is modified by subtracting 1 from each odd digit. If all the digits of the newly formed number are subsequently sorted in ascending order from left to right, what will be the sum of the digits occupying the 2nd, 4th, 6th, and 7th positions from the left?

The correct option is 16.

Let us solve the problem step-by-step.

Step 1: Understand the original number
The given number is 735383629.

Step 2: Modify the digits
According to the problem, we need to subtract 1 from each odd digit (7, 3, 5, 3, 3, 9). Even digits (8, 6, 2) remain unchanged.

Let us modify each digit position by position from left to right:

1st digit: 7 (odd) → 7 - 1 = 6
2nd digit: 3 (odd) → 3 - 1 = 2
3rd digit: 5 (odd) → 5 - 1 = 4
4th digit: 3 (odd) → 3 - 1 = 2
5th digit: 8 (even) → 8
6th digit: 3 (odd) → 3 - 1 = 2
7th digit: 6 (even) → 6
8th digit: 2 (even) → 2
9th digit: 9 (odd) → 9 - 1 = 8

The newly formed number is 624282628.

Step 3: Sort the digits in ascending order
The digits of 624282628 are: 6, 2, 4, 2, 8, 2, 6, 2, 8.
Sorting these digits from left to right in ascending order gives:
2, 2, 2, 2, 4, 6, 6, 8, 8

Step 4: Identify digits at the specified positions
Now, let us find the digits occupying the 2nd, 4th, 6th, and 7th positions from the left in the sorted sequence (2, 2, 2, 2, 4, 6, 6, 8, 8):

1st position: 2
2nd position: 2
3rd position: 2
4th position: 2
5th position: 4
6th position: 6
7th position: 6
8th position: 8
9th position: 8

Digit at 2nd position = 2
Digit at 4th position = 2
Digit at 6th position = 6
Digit at 7th position = 6

Step 5: Calculate the required sum

$\text{Sum}=2+2+6+6=16$

Thus, the sum of the digits occupying the 2nd, 4th, 6th, and 7th positions from the left is 16.