At a certain wedding, the bar served only beer and wine. If 320 people

Question

At a certain wedding, the bar served only beer and wine. If 320 people attended the wedding and 200 attendees drank wine, how many attendees drank neither beer nor wine?

(1) There were the same number of beer drinkers as nondrinkers.

(2) The same number of people drank only beer as drank both beer and wine

Bunuel · Accepted Answer

At a certain wedding, the bar served only beer and wine. If 320 people attended the wedding and 200 attendees drank wine, how many attendees drank neither beer nor wine?

{Total} = {Wine} + {Beer} - {Both} + {Neither}
320 = 200 + {Beer} - {Both} + {Neither}
{Neither} = ?

(1) There were the same number of beer drinkers as nondrinkers --> {Beer} = {Neither} --> 320 = 200 + {Neither} - {Both} + {Neither}. We need {Both} to answer the question. Not sufficient.

(2) The same number of people drank only beer as drank both beer and wine --> {Beer} - {Both} = {Both} --> 320 = 200 + {Both} + {Neither}. We need {Both} to answer the question. Not sufficient.

(1)+(2) We can solve for {Neither} the two equations we got above. Sufficient.

Answer: C.

shikarikutta · Answer

Hi, I have a doubt regarding the question statement.
The question states that 200 people drank wine.
I think there are two ways of interpreting this, one that 200 people drank only wine or, second that 200 people drank wine and some of them drank both beer and wine. 
Using either of the above interpretation, the answer changes.

Bunuel · Answer

It cannot be the first case. 200 drank wine does not mean that 200 drank only wine. You should familiarize yourself with the standard GMAT language/wording: Theory on Overlapping Sets: advanced-overlapping-sets-problems-144260.html how-to-draw-a-venn-diagram-for-problems-98036.html All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45 All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

At a certain wedding, the bar served only beer and wine. If 320 people attended the wedding and 200 attendees drank wine, how many attendees drank neither beer nor wine?

(1) There were the same number of beer drinkers as nondrinkers.

(2) The same number of people drank only beer as drank both beer and wine
 
Transforming the original condition and the question, we have 2by2 question and below table.

We have 4 variables (a,b,c,d) and 2 equations (a+b+c+d=320, a+b=20) in the table. In order to match the number of variables and equations, we need 2 more equations and since there is 1 each in 1) and 2), C has high probability of being the answer. It turns out that C actually is the answer.

Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

nipunjain14 · Answer

Can you please explain the highlighted part?
Should the highlighted part not be :
{Beer} = {Both} as it says same number drank beer as did both

Bunuel · Answer

No, (2) says the same number of people drank   only   beer as drank both beer and wine: {Only Beer} = {Beer} - {Both}.

exc4libur · Answer

B+W-both+ø=Total…B+200-both+ø=320…B-both+ø=120

(1) There were the same number of beer drinkers as nondrinkers:  B=ø…ø-both+ø=120…2ø-both=120  insufic.
(2) The same number of people drank only beer as drank both beer and wine: 
 both=only.beer…B=both+only.beer=2both…(2both)-both+ø=120…both+ø=120  insufic.

(1&2):   2ø-both=120… both+ø=120…3ø=240…ø=80  sufic.

Answer (C)

Basshead · Answer

Bunuel , I'm getting 40 for neither beer nor wine. Can you let me know what is wrong with my solution?

Thank you.

mehro023 · Answer

Hi, I can try to help. What Statement I means is that number of non-drinkers of both beer and wine are the same as the number of beer drinkers overall. Hence you cannot assume 160 beer drinkers and 160 only non-beer drinkers. The non drinkers include those who do not drink wine too. Let me know if it makes sense and I can try elaborating further.

-K

Bunuel · Answer

For (1) we are given that {Beer} = {Neither}. So, 160's in you table are not correct. It should be y for Beer/Total and y for No wine/No beer.

CEdward · Answer

At a certain wedding, the bar served only beer and wine. If 320 people attended the wedding and 200 attendees drank wine, how many attendees drank neither beer nor wine?

(1) There were the same number of beer drinkers as non-drinkers.

This is saying B = Non-beer = 160

Insufficient (we are looking for neither beer nor wine)

(2) The same number of people drank only beer as drank both beer and wine

This is saying (B + W) = (B + No Wine) ---> x = x

200 - x + 120 - x = 320 - 2x <--- Neither (what we want)

Unknown variable, one equation

Insufficient.

Combo pack: 
320 - 2x = 160 
Sufficient.

bumpbot · Answer

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At a certain wedding, the bar served only beer and wine. If 320 people

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At a certain wedding, the bar served only beer and wine. If 320 people

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