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Explanation:

The age of Nadeem is a two-digit number. When squared yields a three-digit number whose last digit is Y. Y is a prime number.
Using statement 1:
When a number is squared :
The last digit of the number can be :
1, 2, 3, 4, 5, 6, 7, 8, 9. When squared the last digit can be :
For a number ending with 1: 1
For a number ending with 2: 4
For a number ending with 3: 9
For a number ending with 4: 6
For a number ending with 5: 5
For a number ending with 6: 6
For a number ending with 7: 9
For a number ending with 8: 4
For a number ending with 9: 1
The only possible prime number is 5.
Hence the last digit of X is 5 and Y is 5.
Using statement 2 : Y = X/3.
This alone cannot be sufficient to determine the possibilities for Y and X.
Combining both the statements :
Since Y = 5, then the value of X = 15.
The age is equal to 15.