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
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­Can someone please explain how this can be performed using either the double matrix or the Venn diagram method?
chetan2u Bunuel gmatophobia
 

In that real sense of venn Diagram, we cannot solve it because there is no overlap in the guests at Annex and main dining room.

But we can have separate venn diagrams for Main dining room and separate for Annex.­

1) Main dining room: the two circles, one for eggplant parmesan and one for risotto, would have three parts, only E, only R and both.
Both or overlap will be 5, so only E = 40-5 or 35 and only R = 6-5 or 55. Total 35+5+55 or 95

2) Annex: Again the two circles, one for eggplant parmesan and one for risotto, would have three parts, only E, only R and both.
Only R will be 5, so Not (only R) that is Both + only E = 60. Total 5+60 or 65

Combined 95+65 = 160.
 
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Here's a simplified way to consider the problem. We know the number of dishes but we don't know the number of guests. Why not? Because we don't know who had double meals. Otherwise, the number of dishes and the number of guests will be the same.

(1) tells us that the first room had 5 double meals, so all the rest were single servings and we can count accordingly. It also tells us that the second room had only 5 single-R meals. That means all the rest of the R were double meals. So once again, we know the number of double meals and all the rest are singles. SUFFICIENT.

(2) just tells us that our single-E meals match in both rooms, but it doesn't give any numbers to work with. This would only be useful if we wanted to combine with (1), butit was already sufficient, so there's no need to consider that. INSUFFICIENT.
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Do we assume that when a dish is served, it's consumed? I took the total serves as the total dish availability and tried finding guests which just made me go round and round in the question.

­The question solely focuses on the dishes served and does not mention whether they were consumed. Therefore, whether the dishes were consumed or not is irrelevant for this question.
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