Each family in a locality has at most two adults, and no family has fewer than…
2019
Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is
Answer: B. 3 — Let F = number of families, A = adults, B = boys, G = girls. The given conditions are A > B > G > F, with A ≤ 2F (at most two adults per family) and B + G ≥…
- A.
4
- B.
3
- C.
2
- D.
5
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Correct answer: B
Let F = number of families, A = adults, B = boys, G = girls. The given conditions are A > B > G > F, with A ≤ 2F (at most two adults per family) and B + G ≥ 3F (no family has fewer than 3 children).
Since A > B > G > F are four distinct integers, we need A ≥ F + 3. Combined with A ≤ 2F, this forces 2F ≥ F + 3, i.e. F ≥ 3.
Check F = 3: take A = 6, B = 5, G = 4. Then A ≤ 2F = 6 ✓, the chain 6 > 5 > 4 > 3 holds ✓, and children B + G = 9 = 3F satisfies B + G ≥ 9 ✓. Every condition is met.
F = 2 fails: A ≤ 4, but A > B > G > 2 needs A ≥ 5 — a contradiction. So the minimum possible number of families is 3.