CAT 2004 — QA Question 14
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 & solution
- A
4
- B
5
- C
2
3
Let f be the number of families.
∴ The number of adults ≤ 2f, children ≥ 3f
Also, adults > boys > girls > families
If f = 2, the minimum possible number of girls and boys is 3 and 4.
Thus, number of children = 3 + 4 = 7 and number of adults ≤ 4
But as adults can be equal to boys, f cannot be 2.
If f = 3, minimum possible number of girls and boys = 4 and 5.
Thus number of children = 9 and number of adults ≤ 6
This is possible. Thus the minimum number of families in the locality = 3.
Hence, option (d).