At a certain banquet, meals were served in only 2 locations. In the

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?

Too much of information. Let us simplify it.
Main Dining Room(MDR): 40 Eggplant Parmesan(E) + 60 Risotto(R)
Annex(A): 60E + 30R
No guest were served more than one of any items. 1E or 1R or 1(E+R)..Nothing but overlapping set.
If we know any of the above three at MDR and A, we can get all answers.


(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.
The statement gives the information required. So should be SUFFICIENT.
MDR: 5 * 1(E+R), so remaining got 1E or 1R.....40-5 or 35 got 1E and 60-5 or 55 got 1R. Total guest = 5+35+55 = 95
A: 5 * 1(R), so remaining got 1E or 1(E+R).....30-5 or 25 got 1(E+R) and 60-25 or 35 got 1E. Total guest = 5+25+35 = 65
Total = 95+65 = 160
Sufficient

(2) The number of guests that were served eggplant parmesan only was the same in the 2 locations.
We do not the value it could be as small as 0 or as big as the entire strength of Es at a location, that is 40.
Different answers possible.
Insufficient


A