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Honestly I don't understand "If two people each said they drink either all three types of beverage or only liquor "
I don't understand how to represent the "either ... or".

Can you please explain?
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Bunuel
A marketing company doing a survey at a local nightspot asked 44 drinkers about their alcohol preferences. 10 people said they drink only wine, while 4 people said they only drink wine and hard liquor. One-fourth of all the people said they only drink beer, and there was no one that said they only drink beer and wine. If two people each said they drink either all three types of beverage or only liquor and the rest of the people drink only beer and liquor, how many people said they drink don't drink wine?

A. 34
B. 28
C. 23
D. 20
E. 11

We can use the formula:

Total = #(W only) + #(L only) + #(B only) + #(W & L only) + #(W & B only) + #(L & B only) + #(W & L & B) + #(None)

44 = 10 + 2 + 11 + 4 + 0 + #(L & B only) + 2 + 0

44 = 29 + #(L & B only)

15 = #(L & B only)

The people who don’t drink wine are “L only”, “B only” and “L & B only”; so the number of them is:

2 + 11 + 15 = 28

Answer: B
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Bunuel
A marketing company doing a survey at a local nightspot asked 44 drinkers about their alcohol preferences. 10 people said they drink only wine, while 4 people said they only drink wine and hard liquor. One-fourth of all the people said they only drink beer, and there was no one that said they only drink beer and wine. If two people each said they drink either all three types of beverage or only liquor and the rest of the people drink only beer and liquor, how many people said they drink don't drink wine?

A. 34
B. 28
C. 23
D. 20
E. 11
Deconstructing the Question
This is a 3-set Venn Diagram problem involving Wine (W), Liquor (L), and Beer (B).
Total People = 44.

Given Data:
1. Only Wine = 10.
2. Only Wine and Liquor (but not Beer) = 4.
3. Only Beer = \(\frac{1}{4}\) of Total = \(\frac{1}{4} \times 44 = 11\).
4. Only Beer and Wine (but not Liquor) = 0.
5. "Two people each said they drink either all three... or only liquor":
This implies: All Three = 2 AND Only Liquor = 2.

Step 1: Calculate the Missing Group
The only remaining group is "Only Beer and Liquor".
Let's sum the known groups:
Sum = (Only W) + (Only W&L) + (Only B) + (Only B&W) + (All 3) + (Only L)
Sum = \(10 + 4 + 11 + 0 + 2 + 2 = 29\).

The "Rest" (Only Beer and Liquor) = Total - Sum
Rest = \(44 - 29 = 15\).

Step 2: Calculate "Not Wine"
The question asks for the number of people who don't drink wine.
We sum all regions strictly outside the Wine circle:
1. Only Beer = 11
2. Only Liquor = 2
3. Only Beer and Liquor = 15

Total Not Wine = \(11 + 2 + 15 = 28\).

Answer: B
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