A company has two types of employees: full-time and part-time. Each full-time employee works 8 hours a day, and each part-time employee works 4 hours a day. What is the total number of hours worked by all employees in the company in one day? Statements: There are twice as many part-time employees as full-time employees in the company. The total number of employees in the company is 90.

Solution

Solution: From Statement 1: We know that the number of part-time employees is twice the number of full-time employees, but we don’t know the total number of employees in the company, so we cannot determine the total hours worked. Statement 1 alone is not sufficient. From Statement 2: We know the total number of employees is 90, but we don’t know the breakdown between full-time and part-time employees, so we cannot determine the total hours worked. Statement 2 alone is not sufficient. Combining Statements 1 and 2: Let the number of full-time employees be x. Then, the number of part-time employees is 2x. According to Statement 2, x + 2x = 90, so 3x = 90, which gives x = 30. Thus, there are 30 full-time employees and 60 part-time employees. The total hours worked in one day is (30 × 8) + (60 × 4) = 240 + 240 = 480 hours. Both statements together are sufficient. Correct Answer: (c) Both statements together are sufficient, but neither alone is sufficient.