E is the sister-in-law of B. A and C are sisters. D is the daughter of B. H is the nephew of C. A is the paternal grandmother of D. F is the brother-in-law of C. G is the son of H. B has no siblings. There are two married couples in the family. C is not married.
How many female members are there in the family?
Correct Answer :
Five
Solution :
The correct answer is Five.
Let's analyze the relationships step-by-step to construct the family tree and determine the gender of each member:
1. "A is the paternal grandmother of D." and "D is the daughter of B."
Since D is the daughter of B, B must be D's parent. For A to be the paternal grandmother of D, A must be the mother of D's father. This implies B is the father of D (male), and A is B's mother (female).
Thus:
- A is female.
- B is male.
- D is female (since she is B's daughter).
- A is B's mother.
2. "A and C are sisters."
Since A and C are sisters, C is also female. Since C is not married, she has no husband.
3. "B has no siblings."
Since B has no siblings, he is an only child of A.
4. "There are two married couples in the family." and "E is the sister-in-law of B."
B is married because he has a daughter, D, and there are married couples. Since B has no siblings, his sister-in-law E cannot be the wife of B's sibling. Thus, E must be the sister of B's spouse, or B's wife herself cannot be E (E is the sister-in-law). Let's look closer. A sister-in-law can also be the wife's sister. Since B has no siblings, E must be B's wife's sister. This means B's wife is female, and E is also female.
Wait, is there another possibility? Let's check: B is married to someone (let's call her W). E is the sister-in-law of B, which means E is W's sister. So E is female.
Wait, who is B married to? Let's check the remaining clues.
5. "F is the brother-in-law of C."
Since A and C are sisters, and C is unmarried, the brother-in-law of C must be the husband of her sister A. Therefore, F is married to A.
This gives us the first married couple: F (male) and A (female). F is B's father.
6. "H is the nephew of C." and "G is the son of H."
Since H is a nephew of C, H must be the son of C's sister A (since A is C's sister and C has no other siblings mentioned, or B is the only child of A, wait).
Let's re-evaluate: "B has no siblings." If A is B's mother, and B is an only child, then A's only child is B. But H is the nephew of C. Since A and C are sisters, the nephew of C must be the son of C's sister, which is A. Thus, H must be A's son. But B has no siblings. How can both B and H be sons of A if B has no siblings? This means B and H must be the same person! No, "H is the nephew of C. G is the son of H." If H is the nephew of C, and B has no siblings, could H be the nephew through another sibling? But only A and C are mentioned. Let's see: if H is B, then H (B) is the nephew of C, which fits perfectly because B is the son of A, and A is C's sister! Therefore, H is B.
Let's verify: H is the nephew of C. Since B is the son of A, and A is the sister of C, B is indeed the nephew of C. Thus, H and B are the same person (male).
Then, G is the son of H (B), which means G is male, and G is the brother of D.
7. "E is the sister-in-law of B."
Since B is married, and has no siblings, E is the sister of B's wife. This makes E female. But who is B's wife? We need a second married couple. The first couple is F and A. The second couple must be B and his wife. Let's find B's wife. The text mentions "E is the sister-in-law of B." The wife of B is female. E, being the sister-in-law, is also female.
Let's list all family members and their genders:
1. A: Female (sister of C, wife of F, mother of B)
2. C: Female (sister of A, unmarried)
3. F: Male (husband of A, father of B)
4. B (also referred to as H): Male (husband of his wife, father of D and G)
5. B's wife: Female (mother of D and G)
6. E: Female (sister-in-law of B, i.e., sister of B's wife)
7. D: Female (daughter of B)
8. G: Male (son of B/H)
Let's count the female members:
- A (Female)
- C (Female)
- B's Wife (Female)
- E (Female)
- D (Female)
Thus, there are exactly five female members in the family (A, C, B's wife, E, and D).
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