If 1 is added to every even digit and 1 is subtracted from every odd digit in the number 45289654, then what will be the sum of the 3rd digit from the left and 3rd digit from the right end?
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Digit Modification Rules Explained
The question involves a number, 45289654, and requires modifying its digits based on whether they are even or odd. After modification, we need to find the sum of specific digits.
The rules for modification are:
- Add 1 to every even digit.
- Subtract 1 from every odd digit.
Processing the Number 45289654
Let's apply these rules to each digit of the number 45289654:
- The first digit is 4 (even): $4 + 1 = 5$.
- The second digit is 5 (odd): $5 - 1 = 4$.
- The third digit is 2 (even): $2 + 1 = 3$.
- The fourth digit is 8 (even): $8 + 1 = 9$.
- The fifth digit is 9 (odd): $9 - 1 = 8$.
- The sixth digit is 6 (even): $6 + 1 = 7$.
- The seventh digit is 5 (odd): $5 - 1 = 4$.
- The eighth digit is 4 (even): $4 + 1 = 5$.
After applying the modifications, the new number becomes 54398745.
Identifying Key Digits
The question asks for the sum of the 3rd digit from the left and the 3rd digit from the right in the modified number (54398745).
Let's identify these digits:
- The digits from the left are: 5, 4, 3, 9, 8, 7, 4, 5. The 3rd digit from the left is 3.
- The digits from the right are: 5, 4, 7, 8, 9, 3, 4, 5. The 3rd digit from the right is 7.
Calculating the Sum of Digits
Now, we need to find the sum of the two identified digits: the 3rd digit from the left (3) and the 3rd digit from the right (7).
The sum is calculated as:
Sum = (3rd digit from left) + (3rd digit from right)
Using mathematical notation:
Sum = $3 + 7 = 10$
Final Result
The sum of the 3rd digit from the left and the 3rd digit from the right of the modified number is 10.
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