A family consists of six members P, Q, R, X, Y and Z. Q is the son of R but R is not the mother of Q. P and R are a married couple. Y is the brother of R. X is the daughter of P. Z is the brother of P. How many female members are there in this family?

Introduction / Context:
This problem asks you to count how many female members are present in a six member family using only relationship clues. To answer correctly, you must determine the gender of each person by using words like son, brother, daughter and the fact that P and R form a married couple.

Given Data / Assumptions:

• Members are P, Q, R, X, Y and Z.
• Q is the son of R, and R is not the mother of Q.
• P and R are a married couple.
• Y is the brother of R.
• X is the daughter of P.
• Z is the brother of P.
• We assume a heterosexual married couple and standard meanings for son, daughter, brother and sister.

Concept / Approach:
The idea is to classify each family member as male or female using the relationship words. Then, once everyone is classified, we simply count the females. The phrase "R is not the mother of Q" is crucial, because it implies that R is the father, and therefore P must be the wife and female spouse in the married couple.

Step-by-Step Solution:
Step 1: Q is the son of R, so Q is male. R is a parent, but the next statement says R is not the mother of Q.Step 2: If R is not the mother of Q but is a parent, then R must be the father. Hence R is male.Step 3: P and R are a married couple. Since R is male, P must be female as the wife in a standard family structure.Step 4: Y is the brother of R, so Y is male.Step 5: X is the daughter of P. Daughter implies female, so X is female.Step 6: Z is the brother of P, so Z is male.Step 7: Summarise genders: P (female), Q (male), R (male), X (female), Y (male), Z (male).Step 8: Count the females. P and X are female. Thus there are exactly two female members in the family.

Verification / Alternative check:
Place the members into a quick table. Married couple: P (wife, female) and R (husband, male). Children: Q is the son of R and therefore male, X is the daughter of P and therefore female. Siblings: Y is brother of R and male, Z is brother of P and also male. The final gender count is four males (Q, R, Y, Z) and two females (P, X). This matches the count of two female members.

Why Other Options Are Wrong:
A count of 1 would ignore either P or X as female, which contradicts the explicit daughter relation. Counts of 3, 4 or 5 would require us to treat some person marked as brother or son as female, which again contradicts given data. Only the count of 2 is consistent with all the gender clues.

Common Pitfalls:
One common mistake is to misinterpret "R is not the mother of Q" and assume that R might still be female, but the wording clearly separates the parental role and the gender, forcing R to be the father. Another error is to forget to count X as female in the final tally. Writing down each person with an M or F next to their name usually prevents such mistakes.

Final Answer:
There are 2 female members in the family.