Question

At a family reunion were the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But not as many people attended as it sounds. How many people were there?

• A. 5
• B. 10
• C. 15
• D. 7

Hint:

Most of the roles overlap: one person can be a father, a son, and a son-in-law all at once. Try to build the smallest possible three-generation family that covers every role listed.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The list of roles sounds like a huge gathering, but many of these roles belong to the same real people wearing different "hats" at once. We need to find the smallest family that can genuinely produce every role on the list.

Step 2: Key Formula or Approach:
Build the family from the top generation down, and check that every listed role is covered by someone already placed, instead of adding a brand new person for each role.

Step 3: Detailed Explanation:
Start with a grandfather and a grandmother. This already covers "one grandfather" and "one grandmother".
The grandparents have one son, who is married. This son is a father to his own children, and one of the "two fathers"; he is also one of the "two sons" (a son to his parents).
The son's wife is the "daughter-in-law" to the grandparents, and she is also a mother to her own children, covering one of the "two mothers".
The grandfather is automatically this wife's father-in-law, and the grandmother is automatically her mother-in-law, covering "one father-in-law" and "one mother-in-law" without adding anyone new.
The son and his wife have three children: one boy and two girls. The boy is the "one brother" to his sisters, and also the second of the "two sons". The two girls are the "two sisters" to their brother, and also the "two daughters".
These three children are also the "three grandchildren" of the grandfather and grandmother, and together with the son of the grandparents they make up the "four children" (the son is a child of the grandparents, and the three kids are children of the son and his wife).

Step 4: Final Answer:
The complete family needed is: grandfather, grandmother, their son, their daughter-in-law, and the couple's three children (one son and two daughters).
That is \(2 + 2 + 3 = 7\) distinct people, and every role in the list is accounted for.
\[ \boxed{7} \]