## In a certain office, 50 percent…

## Solution:

We are given that 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If we let T = the total number of employees we can create the following equations:

0.5T = number of employees who are college graduates

0.6T = number of employees who are over 40 years old

We are next given that 30 percent of those over 40 have master’s degrees. We must remember that 0.6T represents the number of employees who are over 40 years old. Thus, we can create the following equation:

0.3(0.6T) = number of employees over 40 with a master’s degree

0.18T = number of employees over 40 with a master’s degree.

If we can determine a value for T, we can determine the number of employees over 40 with a master’s degree.

**Statement One Alone: **

Exactly 100 of the employees are college graduates.

Using the information in statement one, we know that 0.5T = 100. So T = 200, and there are 0.18T = 0.18 x 200 = 36 employees over 40 who have master’s degrees. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and D.

**Statement Two Alone: **

Of the employees forty years old or less, 25 percent have master’s degrees.

Because T represents the number of total employees and 0.6T represents the number of employees who are over 40 years old, we know that T – 0.6T = 0.4T represents the total number of employees forty years old or less. Let’s now create an equation using the information in statement two.

0.25(0.4T) = number of employees with a master’s degree.

We see that we are unable to determine a value for T and thus we are unable to determine the number of employees over 40 with a master’s degree. Statement two is not sufficient to answer the question.

**Answer:** A