Question

On a company-sponsored cruise, $\frac{2}{3}$ of the passengers were company employees and the remaining passengers were their guests. If $\frac{3}{4}$ of the company-employee passengers were managers, what was the number of company-employee passengers who were NOT managers?
(1) There were $690$ passengers on the cruise.
(2) There were $230$ passengers who were guests of the company employees.

• 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

Answer: (D)

Each statement alone is sufficient.

1. From this, since of the passengers were company employees, then passengers were company employees. Then, since of the company employees were managers, so of the company employee were not managers. Therefore, company employees were not managers; SUFFICIENT.
2. If 230 of the passengers were guests, then this represents of the cruise passengers. Therefore, there were 230 * 3 = 690 passengers altogether, 690 - 230 = 460 of whom were company employees. Since of the company employees were not managers, of the passengers who were company employees were not managers; SUFFICIENT.

• The correct answer is D; each statement alone is sufficient.