Question

What was the revenue that a theater received from the sale of 400 tickets, some of which were sold at the full price and the remainder of which were sold at a reduced price?
(1) The number of tickets sold at the full price was $\frac{1}{4}$ of the total number of tickets sold.
(2)The full price of a ticket was $25.

• 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: (E)

Statements (1) and (2) together are not sufficient.

1. Since of the tickets were sold at full price, tickets were sold at a reduced price. However, the revenue cannot be determined from this information; NOT sufficient.
2. Although a full-priced ticket cost $25, the revenue cannot be determined without additional information; NOT sufficient.

• When both (1) and (2) are taken together, the revenue from full-priced tickets was 100 * $25=$2,500, but the cost of a reduced-priced ticket is still unknown, and the theater’s revenues cannot be calculated.
• The correct answer is E; both statements together are still not sufficient.