If 320 people attended the wedding and 200 attendees drank

Question

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

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} 
 120 = {Beer} - {Both} + {Neither} 
{Neither} = ?

(1) There were the same number of beer drinkers as nondrinkers:
 {Beer} = {Neither}  
 120 = {Neither} - {Both} + {Neither} 
 120 = 2*{Neither} - {Both} . 
Two unknowns. Not sufficient.

(2) The same number of people drank only beer as drank both beer and wine:
 {Beer} - {Both} = {Both} 
 {Beer} = 2*{Both} 
 120 = 2*{Both} - {Both} + {Neither} 
 120 = {Both} + {Neither} . 
Two unknowns. Not sufficient.

(1)+(2) We have that  120 = 2*{Neither} - {Both}  and  120 = {Both} + {Neither} . We have two unknowns and two linear equation, thus we can solve. Sufficient.

Answer: C.

Hope it's clear.

aceacharya · Answer

I Option A gives us that the no. of people who drink beer is the same as non-drinkers. So there are 160 beer drinker and same no. of non drinkers. We cannot judge the no. of people who neither drink beer or wine as all of these 160 non-beer drinkers could have wine, thereby leaving 0 people who dont have both drinks. NOT SUFFICIENT

II Option B gives us that there are the same no. of only beer drinkers as the no. of drinker of both beer and wine. But, there could be 10 people who drink only beer or there could be 120 and the same no. of people drinking both the beverages

Both taken together gives us that there are 160 people who drink beer. Out of them 80 drink only beer so the other 80 drink both beer and wine. So the no. of guys drinking neither is 320-(160+200-80) So the correct answer will be C

fameatop · Answer

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.

As per Set theory, we can write - 
 Total no of Attendees= No of people drinking only Wine+ No of people drinking only BEER - No of people drinking both Wine & Beer + No of people drinking None 
320= 200 + Beer only - Both + None
120 = Beer only - Both + None ----- (Equation 1)

We need to find the value of  NONE   
Statement 1- Beer only = None
By using this info & equation 1 we can not find the value of None.
 Thus Insufficient

Statement 1- Beer only = Both
By using this info & equation 1 we can find the value of None.
 Thus Sufficient

So the answer for this question has to be B.

Hope this detailed explanation will help many.

Fame

atalpanditgmat · Answer

Your equation is wrong as indicated by red part.....Make sure of it
Correct one is:
Total = Beer dinker + wine drinker - both + Neither

fameatop · Answer

I think, I am too tired. Pardon for the mistake

atalpanditgmat · Answer

I am confused becasue of the wording of the first statement. What does non drinker mean? Is it the one who does not drink beer or it is referring to the people who drink neither of the drink.

Interpretation of this statement in different ways gives two different answer....

Someone shed some light....

Regards
Atal Pandit

atalpanditgmat · Answer

Your solution is awesome..... Could you elaborate the red part?

Bunuel · Answer

The second statement states that  {Beer} - {Both} = {Both}  thus  {Beer} = 2*{Both} . Now, substitute  {Beer} = 2*{Both}  into  120 = {Beer} - {Both} + {Neither}  to get  120 = 2*{Both} - {Both} + {Neither} .

Hope it's clear.

madzstar · Answer

could you solve it for me please so i can see how this works out

Bunuel · Answer

Sum the equations:  240 = 3*{Neither}  -->  {Neither} = 80 .

Hope it helps.

cg0588 · Answer

Hi Bunuel - for Statement (2), it sounds like Beer = Both. Can you explain why this is not true?

Bunuel · Answer

Check here: if-320-people-attended-the-wedding-and-200-attendees-drank-153185.html#p1227863

EgmatQuantExpert · Answer

Presenting the matrix approach to the solution

Question statement

Question statement tells us that total number of attendees are 320 out of which 200 drank wine i.e. the remaining 120 either drank only beer or did not drink at all.

Statement- I

Statement-I tells us that number of attendees who drank beer and number of attendees who did not drink anything were same. Let's assume them as x and populate the rest of the matrix.

We see that we do not get any relation through which we can find the value of x. Hence st-I is insufficient to answer the question

Statement-II

St-II tells us that same number of people drank only beer as both beer and wine. Let's assume the number of people as y and populate the rest of the matrix.

We see that we do not get any relation through which we can find the value of y. Hence st-II is insufficient to answer the question.

Combining Statement- I & II

Considering the matrix of statement-I and using the information given in st-II we get the equation as 120 - x = 2x - 120 which gives us x = 80 i.e number of attendees who drank neither beer nor wine.

Thus combining both the statements is sufficient to answer the question.

Hope this helps

Regards
Harsh

Regards Harsh

Harley1980 · Answer

Hello  reto . 
In "overlapping sets" tasks you should pay big attention on words 'exactly' and 'only'

Beer drinkers are all people who drink beer and also wine. Some of them drink beer only and some of them both beer and wine.
Statement 2 says that 'beer only' drinkers equal to people who drink wine and beer.

Let's write some facts about this task:

Total people = 320
Beer = 80
Wine 200
Beer and wine = 40
Neither = 80

Beer only = Beer - both = 80 - 40 = 40
Wine only = Wine - both = 200 - 40 = 160

So when statement says that beer equal to neither we can write it as: beer = 80 = neither = 80
and when statement says beer ONLY equal to both we can write it as: beer only = 40 = both = 40
and from this statement we can infer that beer(80) - both(40) = beer only = 40

Does that make sense?

Arindamad · Answer

Total 320 people are there
200 people drink wine
Let x no. of people drink both wine and beer

Case 1: There were the same number of beer drinkers as nondrinkers.
Let beer drinkers be a and hence non drinkers be a too

Therefore total (200-x)+(a-x)+a=320
=> 2a-2x=120
Not sufficient

Case 2:The same number of people drank only beer as drank both beer and wine.
Taking variables from above
Let the number of people drink both beer and wine and only beer be y

and the number of people who do not drink anything be s

200 - y + y + s = 320
s = 120

Hence B

kpstudies · Answer

I was hung up on this problem for a long time and asking myself this same question. This post is 5 years old but for those that may be in my shoes and revisiting:

The term "Beer = Both" is meaning "ALL beer" = both. think of "all beer" as one whole circle of a venn diagram. The correct way is to consider those who drank ONLY beer = drank both. So the whole circle of the venn diagram would be ALL that drank Beer = those that ONLY Beer + those that drank Both

so ONLY Beer = Both
ALL Beer = Both + Both, or (2)Both

Plug that in to your equation of 
120=ALL Beer - Both + Neither
120=(2)Both - Both + Neither
120= Both + Neither

As you can see. we still can't solve for "both" or "neither".

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If 320 people attended the wedding and 200 attendees drank

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