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

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.

Show Spoiler

Attachment:

2024-01-24_14-51-07.png [ 107.1 KiB | Viewed 9427 times ]

Show Answer

Official Answer

A

Pro tip: Combine official questions for familiarity with GMAT Club Tests for analytics and tougher Focus-level practice so the real exam feels manageable. Explore →

chetan2u · Accepted Answer

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

DmitryFarberMPrep · Answer

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.

mustafa87 · Answer

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

chetan2u · Answer

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.

AdjustedEbitdad · Answer

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.

Bunuel · Answer

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.

KarishmaB · Answer

Use both double set matrix and Venn diagram to understand what is given. For the meals and locations, use a double set matrix. Screenshot 2025-02-04 at 11.02.57 AM.png For people, who got eggplant or risotto or both, use a Venn diagram. (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. In Dining - 5 were served both so put in overlap region. Then from matrix we can see that 35 were served only eggplant and 55 were served only risotto. Add those to the Venn diagram regions as shown. In Annex - 5 were served risotto only. Add 5 to the risotto only region. Then from matrix we can see that 25 were served both. Put 25 in overlap region. If 25 were served both in annex, it means 35 were served only eggplant in annex. Add it to the eggplant only region. Screenshot 2025-02-04 at 11.09.38 AM.png Total number of people = 35 + 35 + 5 + 25 + 55 + 5 = 160 Sufficient alone (2) The number of guests that were served eggplant parmesan only was the same in the 2 locations. Gives us no info to put in the Venn diagram. It is just a bait to make us pick (C). Not sufficient alone. Answer (A)

NEYR0N · Answer

I solved this with double set matrix. statement 1, suff.

can I get some feedback.  KarishmaB ,  chetan2u

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.