There are six persons 1, 2, 3, 4, 5 and 6. Person 3 is the sister of 6. Person 2 is the brother of the husband of 5. Person 4 is the father of 1 and the grandfather of 6. There are two fathers, three brothers and one mother in the group. Which of the following is the group of brothers?

Introduction / Context:
This question describes a small group of six people and gives several family relationships among them. You are told that in this group there are exactly two fathers, three brothers and one mother. The task is to determine which triple of persons are the three brothers.

Given Data / Assumptions:

• The persons are 1, 2, 3, 4, 5 and 6.
• Person 3 is the sister of 6, so 3 is female and 6 is a sibling of 3.
• Person 2 is the brother of the husband of 5, so 2 is male and 5 is female.
• Person 4 is the father of 1 and the grandfather of 6. This implies that 4 is male and that 1 is the parent of 6.
• There are exactly two fathers, three brothers and one mother in the group.
• We assume a single nuclear family structure to connect these relationships.

Concept / Approach:
First we identify the generations: 4 is the oldest generation as the father of 1 and grandfather of 6. Person 1 is the parent of 6 and hence in the middle generation. Person 5 is female and married to someone; her husband, together with 2 as his brother, will help identify the brothers. The idea is to work out who the two fathers are and then see which three males are brothers according to the family structure.

Step-by-Step Solution:
Step 1: From "4 is the father of 1 and grandfather of 6", we know 4 is male and 1 is the child of 4. Since 4 is also the grandfather of 6, 1 is a parent of 6.Step 2: Person 3 is the sister of 6. So 3 and 6 are siblings and both are children of 1 and 1 spouse.Step 3: There is one mother in the group, and that role naturally fits person 5, who is female and has a husband.Step 4: If 5 is the mother of 3 and 6, then her husband must be 1, who is already known to be the parent of 6. Thus 1 is male, husband of 5, and father of 3 and 6.Step 5: Person 2 is the brother of the husband of 5. Since the husband of 5 is 1, person 2 is the brother of 1. So 1 and 2 are brothers.Step 6: Person 6 is also the son of 1 and 5, and since 3 is specified as his sister, 6 is male. Thus 6 is another brother in the younger generation.Step 7: The two fathers in the group are 4 (father of 1) and 1 (father of 3 and 6). The three brothers are persons 1, 2 and 6.

Verification / Alternative check:
Summarise the structure. Oldest generation: 4 (father of 1) and his spouse (not explicitly in the group). Middle generation: 1 and 2 are brothers, with 1 married to 5, the only mother. Youngest generation: 3 (sister) and 6 (brother) are children of 1 and 5. The brothers across the family are 1 and 2 in the parent generation, and 6 in the children generation. Thus the exact set of three brothers is 1, 2 and 6.

Why Other Options Are Wrong:
Option a includes 3, who is explicitly described as a sister, not a brother. Option b includes 3 again, which cannot be correct. Option c includes 4, who is the father of 1 and not a brother in the sense intended by the question. Option e includes 4, but 4 is a father and grandfather, not part of the trio of brothers. Only option d groups persons 1, 2 and 6, which matches the analysis.

Common Pitfalls:
Many learners misread the phrase "there are three brothers in the group" as meaning three men of the same generation who are all brothers to each other. In fact, the question simply counts people who are brothers to someone. It is entirely possible for one brother to belong to the parent generation and another to the child generation, as long as the relationship statements support it.

Final Answer:
The group of brothers is 1, 2 and 6.