If the digit in the unit’s place of the square of an integer is x, then the sum of all possible distinct values of x is:

Formula used:

Unit digit of a square depends on the unit digit of the number being squared.

Possible unit digits of a number: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Unit digits of their squares: 0, 1, 4, 9, 6, 5, 6, 9, 4, 1

Calculation:

List of distinct unit digits of squares: {0, 1, 4, 9, 6, 5}

⇒ Sum of distinct values = 0 + 1 + 4 + 9 + 6 + 5

⇒ Sum = 25

∴ The correct answer is option (1).