Data Sufficiency: Geometry & Equations

Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below: A. Statement I alone is sufficient to answer the question. B. Statement II alone is sufficient to answer the question. C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question. D. Either Statement I or Statement II alone is sufficient to answer the question. E. Neither Statement I nor Statement II is necessary to answer the question.

Let PQRS be a quadrilateral. Two circles O1 and O2 are inscribed in triangles PQR and PSR respectively. Circle O1 touches PR at M and circle O2 touches PR at N. Find the length of MN. I. A circle is inscribed in the quadrilateral PQRS. II. The radii of the circles O1 and O2 are 5 and 6 units respectively.

Given below is an equation where the letters represent digits. $(PQ) \cdot (RQ) = XXX$. Determine the sum of $P + Q + R + X$. I. $X = 9$. II. The digits are unique.