If there are 56 people attending a birthday party which of the followi

The number of women and the number of men must be integer.

A. \(\text{the ratio of women to men} = \frac{\text{women}}{\text{men}}=10 : 9\implies \frac{\text{women}}{\text{all}}=\frac{10}{19}\implies \text{women}=56 \times \frac{10}{19}\)

56 isn't divisible by 19, so eliminate this choice.

B. \(\frac{\text{woman}}{\text{all}}=\frac{11}{15}\).

56 isn't divisible by 15, so eliminate this choice.

C. \(\frac{\text{woman}}{\text{all}}=\frac{30}{31}\).

56 isn't divisible by 31, so eliminate this choice.

D. \(\frac{\text{woman}}{\text{all}}=\frac{1}{8} \implies \text{woman}=56 \times \frac{1}{8}=7 \implies \text{men}=49\).

This choice is the correct answer.

E. \(\frac{\text{woman}}{\text{all}}=\frac{2}{25}\).

56 isn't divisible by 25, so eliminate this choice.