Number Transformation and Sum Calculation

The problem asks us to modify a given number, $6134527$, based on specific rules for its digits and then find the sum of the first and last digits of the newly formed number.

Digit Transformation Process

The rules are:

• Add 1 to each odd digit.
• Add 2 to each even digit.

Let's apply these rules to the number $6134527$:

• Digit $6$ (even): $6 + 2 = 8$
• Digit $1$ (odd): $1 + 1 = 2$
• Digit $3$ (odd): $3 + 1 = 4$
• Digit $4$ (even): $4 + 2 = 6$
• Digit $5$ (odd): $5 + 1 = 6$
• Digit $2$ (even): $2 + 2 = 4$
• Digit $7$ (odd): $7 + 1 = 8$

New Number Formation

Combining the transformed digits, the new number formed is $8246648$.

Sum of First and Last Digits

Identify the first and last digits of the new number $8246648$:

• First digit = $8$
• Last digit = $8$

Calculate the sum:

Sum = First digit + Last digit

Sum = $8 + 8$

Sum = $16$