If there are 3 girls in a family where each boy has as many sisters as brothers and each girl has twice as many brothers as sisters, how many boys are there?

• A. 3
• B. 5
• C. 4
• D. 6

Answer: (C)

Think about how many brothers and sisters each person has and translate that into simple counts. Let b be the number of boys and g be the number of girls. For a boy, the number of brothers is b − 1 and the number of sisters is g, and the statement that these are equal means g = b − 1. For a girl, the number of brothers is b and the number of sisters is g − 1, and the statement that brothers are twice as many as sisters means b = 2(g − 1). We’re told there are 3 girls, so g = 3. Plugging into the second equation gives b = 2(3 − 1) = 4. This also satisfies the first equation since 3 = 4 − 1. Therefore there are 4 boys.