If (XY)^2 = PQX, where each letter represents a distinct digit, then

From the equation given in the question stem, we can infer that PQX is a 3-digit perfect square.
Hence, the highest value for PQX = 961 and so the possible values for X can only be 1, 2 or 3 since making X = 4 (or higher) will make \((XY)^2\) a four digit perfect square.

Since the unit digit of the perfect square is X, X cannot be 2 or 3 since no perfect square ends with a 2 or 3. Therefore, X = 1.

\((11)^2\) = 121 and \((19)^2\) = 361 are the only two squares that satisfy the constraints. Since each letter represents a distinct digit, 121 can be ruled out.
The value of PQX = 361 and hence P+Q = 9.

The correct answer option is E.

Hope that helps!
Aravind B T