Question

In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?
(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master's degrees.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is A Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

1. It is given that 50 percent of the employees are college graduates. Here, it is now known that exactly 100 of the employees are college graduates. Thus, the total number of employees in the company is 200. It is also given that 60 percent of the employees are over 40 years old, which would be (0.60) * (200), or 120 employees. Since it is given that 30 percent of those over 40 have master’s degrees, then (0.30) * (120), or 36 employees are over 40 and have master’s degrees; SUFFICIENT.
2. There is no information regarding how many employees fall into any of the categories, and it thus cannot be determined how many employees there are in any category; NOT sufficient.

• The correct answer is A; statement 1 alone is sufficient.