In a group of 5 families, every family has a certain number of children, such…
2024
In a group of 5 families, every family has a certain number of children, such that the number of children forms an arithmetic progression with a common difference of one, starting with two children in the first family. Despite the objection of their parents, every child in a family has three times as many pets to look after as the number of offspring in the family. What is the total number of pets in the entire group of five families?
- A.
27
- B.
99
- C.
165
- D.
270
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Correct answer: D
Solution: compute the total number of pets across the five families.
Children per family:
The families have 2, 3, 4, 5 and 6 children respectively.
Pets per family:
Each child in a family with n children looks after 3n pets, so the family's total pets = n × (3n) = 3n².
Compute each family's total:
For 2 children: 3·2² = 3·4 = 12 pets
For 3 children: 3·3² = 3·9 = 27 pets
For 4 children: 3·4² = 3·16 = 48 pets
For 5 children: 3·5² = 3·25 = 75 pets
For 6 children: 3·6² = 3·36 = 108 pets
Total pets = 12 + 27 + 48 + 75 + 108 = 270
Answer: 270 pets.