In a family where every boy has as many sisters as brothers, and every girl has twice as many brothers as sisters, how many total brothers and sisters are there?

• A. 3 boys and 4 girls.
• B. 5 boys and 3 girls.
• C. 4 boys and 4 girls.
• D. 4 boys and 3 girls.

Answer: (D)

The key idea is to translate the sibling-count conditions into simple equations and solve for how many boys and how many girls exist.

Let the number of boys be b and the number of girls be g. For a boy, the number of sisters is g and the number of brothers is b minus one (since he isn’t counted as his own brother). The condition that a boy has as many sisters as brothers gives g = b − 1.

For a girl, the number of brothers is b and the number of sisters is g minus one. The condition that a girl has twice as many brothers as sisters gives b = 2(g − 1).

Now solve the system:

From g = b − 1, we get b = g + 1. Substitute into b = 2(g − 1):

g + 1 = 2g − 2 → 3 = g, so g = 3.

Then b = g + 1 = 4.

So there are 4 boys and 3 girls, for a total of 7 children. Check: each boy has 3 sisters and 3 brothers, so they’re equal. Each girl has 4 brothers and 2 sisters, and 4 is twice 2, so the condition for girls holds as well.