Question

At a certain banquet, meals were served in only 2 locations. In the main dining room, 40 servings of eggplant parmesan and 60 servings of risotto were served. In the annex, 60 servings of eggplant parmesan and 30 servings of risotto were served. If each guest at the banquet was served exactly 1 serving of eggplant parmesan only, exactly 1 serving of risotto only, or exactly 2 servings, one of eggplant parmesan and the other of risotto, how many guests were at the banquet?

(1) In the main dining room, each of exactly 5 guests were served both eggplant parmesan and risotto; and in the annex, exactly 5 guests were served risotto only.
(2) The number of guests that were served eggplant parmesan only was the same in the 2 locations.
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

Using Statement (1), it's possible to compute the number of guests at the banquet as 95, proving it sufficient to determine the number of guests, whereas Statement (2) is not sufficient on its own as it lacks specific numbers for guests having each dish.

Step-by-step explanation:

To determine how many guests were at the banquet, we will use the information provided in the question and evaluate the sufficiency of each statement to find the answer.

In the main dining room, there were 40 servings of eggplant parmesan and 60 servings of risotto. In the annex, there were 60 servings of eggplant parmesan and 30 servings of risotto. It is mentioned that each guest had exactly one serving of each dish or one of each.

Analysis of Statement 1 :

In the main dining room, 5 guests had both dishes, so we subtract 5 servings from each of the 40 servings of eggplant parmesan and the 60 servings of risotto. This leaves us with 35 servings of eggplant parmesan and 55 servings of risotto. In the annex, 5 guests had only risotto, leaving us with 60 servings of eggplant parmesan and 25 servings of risotto. Using these figures, we can determine the number of guests who had eggplant parmesan alone, risotto alone, and one of each in both locations, which totals to 95 guests.

Analysis of Statement 2 :

Statement (2) tells us that the number of guests served eggplant parmesan only was the same in both locations. However, without knowing the specific number or the guests who had risotto only, this information alone is not enough to determine the total number of guests.

Since statement (1) provides us with complete information to calculate the number of guests, and statement (2) doesn't, the correct answer is that Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.