Question

At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is $\dfrac{2}{5}.$ What fraction of the people in the room are married men?

$\dfrac{1}{3}$

$\dfrac{3}{8}$

$\dfrac{2}{5}$

$\dfrac{5}{12}$

$\dfrac{3}{5}$

Solution:

WLOG, let there be $5$ women in the room. Then there are $5 \cdot \dfrac{2}{5} = 2$ single women.

This means that there are $5 - 2 = 3$ married women, which is also the number of married men.

There are a total of $5 + 3 = 8$ people in the room. The fraction of married men is $\dfrac{3}{8}.$

Thus, B is the correct answer.

2004 AMC 8 Problem 22

Solution:

Problem 22 in Other Years