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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  [#permalink]

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12 Sep 2015, 12:30
5
8
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:25) correct 38% (02:22) wrong based on 217 sessions

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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
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Joined: 02 Sep 2009
Posts: 59712
Re: At a certain wedding, the bar served only beer and wine. If 320 people  [#permalink]

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13 Sep 2015, 03:32
2
1
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

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.

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Re: At a certain wedding, the bar served only beer and wine. If 320 people  [#permalink]

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15 Sep 2015, 06:10
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.
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Posts: 59712
Re: At a certain wedding, the bar served only beer and wine. If 320 people  [#permalink]

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15 Sep 2015, 06:31
2
1
shikarikutta wrote:
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.

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:
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

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Re: At a certain wedding, the bar served only beer and wine. If 320 people  [#permalink]

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15 Sep 2015, 09:52
1
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.
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Re: At a certain wedding, the bar served only beer and wine. If 320 people  [#permalink]

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16 May 2016, 09:42
Bunuel wrote:
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

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.

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
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Posts: 59712
Re: At a certain wedding, the bar served only beer and wine. If 320 people  [#permalink]

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16 May 2016, 10:32
nipunjain14 wrote:
Bunuel wrote:
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

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.

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

No, (2) says the same number of people drank only beer as drank both beer and wine: {Only Beer} = {Beer} - {Both}.
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Re: At a certain wedding, the bar served only beer and wine. If 320 people  [#permalink]

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12 Sep 2019, 05:07
1
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.

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

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

Re: At a certain wedding, the bar served only beer and wine. If 320 people   [#permalink] 12 Sep 2019, 05:07
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