Unit's Digit — XAT Previous-Year Questions

Nadeem’s age is a two-digit number X, squaring which yields a three-digit number,whose last digit is Y. Consider the statements below:

Statement I: Y is a prime number
Statement II: Y is one-third of X

To determine Nadeem’s age uniquely:

X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers (408X)⁶³ and (789Y)⁸⁵ are the same. What will be the possible value(s) of (X + Y)?

Example: If M = 3 then the digit at unit's place of the number (2M) is 3 (as the number is 23) and the digit at unit's place of the number (2M)² is 9 (as 23² is 529).