Understanding the Problem

The question asks us to modify a given number, 7643185, based on specific rules for its digits. We need to add 1 to every odd digit and subtract 2 from every even digit. After performing these operations, we need to find the difference between the largest and smallest digit in the newly formed number.

Step-by-Step Digit Transformation

Let's break down the original number and apply the rules to each digit:

• The original number is 7643185.
• We will examine each digit individually.

Applying Rules to Digits

Here's how each digit changes:

• Digit 7: It is an odd digit. Applying the rule, we add 1: $7 + 1 = 8$.
• Digit 6: It is an even digit. Applying the rule, we subtract 2: $6 - 2 = 4$.
• Digit 4: It is an even digit. Applying the rule, we subtract 2: $4 - 2 = 2$.
• Digit 3: It is an odd digit. Applying the rule, we add 1: $3 + 1 = 4$.
• Digit 1: It is an odd digit. Applying the rule, we add 1: $1 + 1 = 2$.
• Digit 8: It is an even digit. Applying the rule, we subtract 2: $8 - 2 = 6$.
• Digit 5: It is an odd digit. Applying the rule, we add 1: $5 + 1 = 6$.

The New Number Formed

After applying the operations, the sequence of digits becomes:

8, 4, 2, 4, 2, 6, 6

Finding the Highest and Lowest Digits

Now, we look at the digits in the new sequence (8, 4, 2, 4, 2, 6, 6) to find the highest and lowest values:

• The highest digit in this new sequence is 8.
• The lowest digit in this new sequence is 2.

Calculating the Final Difference

The final step is to calculate the difference between the highest and lowest digits found:

Difference = Highest Digit - Lowest Digit

Difference = $8 - 2$

Difference = $6$

Conclusion

The difference between the highest and lowest digits in the number formed after applying the given operations is 6.