Shortcut Trick
Identify the four target digits: first two (6, 3) and last two (2, 7).
Original sum of these four digits = 6 + 3 + 2 + 7 = 18.
Since 2 is added to every digit (even and odd), total increase for 4 digits = 4 × 2 = 8.
New sum = Original sum + Total increase = 18 + 8 = 26.
∴ The correct answer is 26.
Alternate Method
Given Number: 6345127
Operation: Add 2 to each even digit and add 2 to each odd digit (effectively adding 2 to every digit).
⇒ New first digit: 6 + 2 = 8
⇒ New second digit: 3 + 2 = 5
⇒ New sixth digit: 2 + 2 = 4
⇒ New seventh digit: 7 + 2 = 9
⇒ New first two digits: 8, 5
⇒ New last two digits: 4, 9
⇒ Required Sum = (8 + 5) + (4 + 9)
⇒ Required Sum = 13 + 13 = 26
∴ The correct answer is 26.
Additional Information
Digit Manipulation Property
When a constant k is added to n specific digits of a number, the total sum of those digits increases by exactly n × k.
Parity Preservation
Adding an even number (like 2) to any digit preserves its parity (even remains even, odd remains odd).
Sum of Digits (Digital Root)
Changing individual digits affects the total sum of digits directly; this is often used in divisibility tests for 3 and 9.