Question

Each child in a family has at least 4 brothers and 3 sisters. What is the smallest number of children the family might have?

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The Correct Option is C

The problem requires us to determine the smallest number of children in a family where each child has at least 4 brothers and 3 sisters.
Let's define:

• B: the number of boys in the family.
• G: the number of girls in the family.

Given conditions:

• Each child has at least 4 brothers, implying B ≥ 4.
• Each child has at least 3 sisters, implying G ≥ 3.

The total number of children, N, is therefore N = B + G.
Let's find the smallest N that satisfies these conditions:
If B = 4 (minimum number of boys), then there must be G = 3+1=4 girls (to meet the condition of each child having at least 3 sisters). Thus, N = 4 + 4 = 8.
Check:

• Each boy has 3 sisters and 3 brothers, which is not enough.

This configuration doesn't work.
Try B = 5:
G = 3 (to satisfy the condition of having at least 3 sisters), then N = 5 + 3 = 8.
Check:

• Each boy has 4 brothers and 3 sisters.
• Each girl has 5 brothers, which is more than enough.

To find the minimum, try B = 4 and G = 5, then N = 9.
Final Check:

• Boys have 4 brothers and 5 sisters.
• Girls have 4 brothers, which works.

Therefore, the smallest number of children the family might have is 9.