# What percent of a group of people are women…

## Solution:

An easy way to solve the problem is to set up a double set matrix. In our matrix we’ll have two main categories: gender and red hair. More specifically, our table will be labeled with:

1) Number of people who have red hair (RH)

2) Number of people who do not have red hair (No RH)

3) Number of Women

4) Number of Men

(To save room on our table headings we will use the abbreviations for the categories.)

Since we are asked “what percent” of the people are women with red hair, we can use the convenient number 100 as the total number of people in the group.

Thus, we know:

Total people = 100

Let’s fill all the information into a table.

Now we can consider the statements.

Statement One Alone:

Of the women in the group, 5 percent have red hair.

Since we do not know the number of women in the group, we can let the number of women in the group = w. Thus, 0.05w = the number of women in the group with red hair.

Let’s fill the information into the table.

The information provided is not enough to determine the percentage of people who are women with red hair. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

Of the men in the group, 10 percent have red hair.

Since we do not know the number of men in the group, we can let the number of men in the group = m. Thus, 0.1m = the number of men in the group with red hair.

Let’s fill the information into the table.

The information provided is not enough to determine the percentage of people who are women with red hair. Eliminate answer choice B.

Statements One and Two Together:

We know the following:

We see that with the information in the table we still cannot determine the values of w and m, and thus we cannot determine what percent of the group of people are women with red hair.