Directions: Answer the question based on the procedure described below.

Consider the sequence of digits "264185397". If every digit located at an odd position is incremented by 1, and the resulting digits are then sorted in descending order from left to right, what will be the product of the fourth digit from the left end and the fourth digit from the right end of the newly formed sequence?

The correct answer is 30.

Step-by-step explanation:

Step 1: Identify the given digit sequence and position indices.
The original sequence of digits is: 264185397.
Let's list each digit along with its position from left to right:
- 1st position (odd): 2
- 2nd position (even): 6
- 3rd position (odd): 4
- 4th position (even): 1
- 5th position (odd): 8
- 6th position (even): 5
- 7th position (odd): 3
- 8th position (even): 9
- 9th position (odd): 7

Step 2: Apply the modification rule.
Every digit at an odd position is incremented by 1, while digits at even positions remain unchanged:
- 1st position: 2 + 1 = 3
- 2nd position: 6 (unchanged)
- 3rd position: 4 + 1 = 5
- 4th position: 1 (unchanged)
- 5th position: 8 + 1 = 9
- 6th position: 5 (unchanged)
- 7th position: 3 + 1 = 4
- 8th position: 9 (unchanged)
- 9th position: 7 + 1 = 8

The new sequence of digits in their original order becomes:
3, 6, 5, 1, 9, 5, 4, 9, 8

Step 3: Sort the resulting digits in descending order.
Arranging all 9 digits from highest to lowest gives:
9, 9, 8, 6, 5, 5, 4, 3, 1

Step 4: Identify the specified positions and find their product.
- The 4th digit from the left end is 6.
- The 4th digit from the right end (which is the 6th digit from the left end) is 5.

Now, calculate the product of these two digits:

$6\times 5=30$

Thus, the required product is 30.