Question

n a family gathering there are 2 males who are grandfathers and 4 males who are fathers. In the same gathering there are 2 females who are grandmothers and 4 females who are mothers. There is at least one grandson or a granddaughter present in this gathering. There are 2 husband-wife pairs in this group. These can either be a grandfather and a grandmother, or a father and a mother. The single grandfather (whose wife is not present) has 2 grandsons and a son present. The single grandmother (whose husband is not present) has 2 grand daughters and a daughter present. A grandfather or a grandmother present with their spouses does not have any grandson or granddaughter present.
What is the minimum number of people present in this gathering?

• A. 10
• B. 12
• C. 14
• D. 16

Hint:

Optimise by overlapping roles where allowed by conditions to minimise headcount.

Answer 1

The Correct Option is C

Count distinct individuals: - 2 grandparents pairs = 4 people.
- 1 single grandfather + 3 grandchildren (2 grandsons, 1 son) = 4 more, but sons can be fathers already counted.
- 1 single grandmother + 3 grandchildren (2 granddaughters, 1 daughter) = 4 more, but daughters may be mothers already counted.
By optimising overlaps, total = 14.