'P' is the only daughter of 'R'. 'R' is a grandmother of 'Q'. The name of Q's…

Solution:

• Given: P is the only daughter of R.

• R is the grandmother of Q, so one of R's children is the parent of Q.

• P is the only daughter of R, so the child of R who is the parent of Q must be P.

• S is the sister of Q, so S is also a child of P.

Answer: S is a daughter of P.

Note: The standard interpretation of this puzzle assumes the parent of Q who is a child of R is the female child (P). Under that reading, S must be P's daughter.