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Question: There are more adults than boys, more boys than girls, more girls than families. If no family has fewer than 3 children, then what is the least number of families that there could be?

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Question:
There are more adults than boys, more boys than girls, more girls than families.
If no family has fewer than 3 children, then what is the least number of families that there could be?

Options:
(1) 4
(2) 3
(3) 2
(4) 1

1 Answer

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by (19.9k points)

Key Information:

  1. More adults than boys:

    • The number of adults must be greater than the number of boys.

  2. More boys than girls:

    • The number of boys must be greater than the number of girls.

  3. More girls than families:

    • The number of girls must be greater than the number of families.

  4. Each family has at least 3 children:

    • This means the sum of boys and girls in each family is at least 3.

Step 1: Understanding the Problem

We need to minimize the number of families while satisfying all conditions. This requires choosing the smallest possible values for adults, boys, girls, and families.

Step 2: Assume the Least Number of Families

Let’s start with the smallest possible number of families and verify if the conditions hold.

Case 1: 1 Family

  • If there is 1 family, there must be at least 3 children (boys + girls).
  • The number of girls must be greater than the number of families, so girls = 2 (greater than 1).
  • The number of boys must be greater than the number of girls, so boys = 3 (greater than 2).
  • The number of adults must be greater than the number of boys, so adults = 4 (greater than 3).

All conditions are satisfied with 1 family.

Step 3: Verify for Other Cases

If there are more families (e.g., 2 or more), the conditions can still hold, but the problem asks for the least number of families, so we stick with the minimum.

Final Answer:

(4) 1

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