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The 38 movies in the video store fall into the following thr

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The 38 movies in the video store fall into the following thr [#permalink]

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The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there?

Solution:
[Reveal] Spoiler:
I don't like drawing Venn diagrams because it is time consuming. I tend to use the formula:

(Total in Group 1) + (Total in Group 2) + (Total in Group 3) – (Overlap of 1 and 2) – (Overlap of 1 and 3) – (Overlap of 2 and 3) – [2 * (Overlap of 1, 2, and 3)] + (total in none of the groups) = Overall total

10 + 20 + 18 - 5 - 3 - 4 - 2(x) + 0 = 38.
=> 48 - 12 - 2x = 38
=> 36 - 2x = 38
=> x=-1

But the answer is:
X = 2


Where am I going wrong? I used the method suggested by Bunuel in this thread:
gmatclub dot com/forum/at-a-certain-resort-each-of-the-39-food-service-employees-133276.html

Last edited by Bunuel on 29 Sep 2013, 10:32, edited 1 time in total.
Renamed the topic and edited the question.

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Re: 3 sets overlap problem: Video store - action, drama, comedy [#permalink]

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New post 28 Sep 2013, 20:39
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saintforlife wrote:
The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there?


Hi Saint,

Check if this works for you, quite basic method though

Given........
Total = 38
A=10
D=20
C=18
AD=5
AC=3
DC=4
ALL=x (Assume action-drama-comedies be x)

At first we have to remove the movies that belong to all (i.e.action-drama-comedy) categories from every subset.

Total = 38
A=10 - x
D=20 - x
C=18 - x
AD only =5 - x
AC only =3 - x
DC only =4 - x
ALL=x

At second step we have to remove movies that belong to only two categories (AD only, AC only, DC only) from the main subsets (i.e A, D, C)

So we have that,

A only =(10 - x) - (5-x) - (3-x)
D only =(20 - x) - (5-x) - (4-x)
C only =(18 - x) - (3-x) - (4-x)
AD only =5 - x
AC only =3 - x
DC only =4 - x
ALL=x

So finally we have that,
Total = A only + D only + C only + AD only + AC only + DC only + ALL
38 = 2 + x + 11 + x + 11 + x + 5 - x + 3 - x + 4 - x + x
38 = 36 + x
x = 2

This method is just the algebraical version of venn diagram. IMO solving thru venn diagram would be much easier and faster though.

Hope that helps! :)
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Re: 3 sets overlap problem: Video store - action, drama, comedy [#permalink]

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New post 29 Sep 2013, 00:19
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saintforlife wrote:
Solution:
[Reveal] Spoiler:
I don't like drawing Venn diagrams because it is time consuming. I tend to use the formula:

(Total in Group 1) + (Total in Group 2) + (Total in Group 3) – (Overlap of 1 and 2) – (Overlap of 1 and 3) – (Overlap of 2 and 3) – [2 * (Overlap of 1, 2, and 3)] + (total in none of the groups) = Overall total

10 + 20 + 18 - 5 - 3 - 4 - 2(x) + 0 = 38.
=> 48 - 12 - 2x = 38
=> 36 - 2x = 38
=> x=-1

But the answer is:
X = 2


Where am I going wrong? I used the method suggested by Bunuel in this thread:
gmatclub dot com/forum/at-a-certain-resort-each-of-the-39-food-service-employees-133276.html


I agree that drawing venn diagram is a time taking thing. But you should be able to picturize the venn diagram in your mind to correctly understand the problem :)

As shown in the venn diagram below:
Attachment:
Venn_Diagram.png
Venn_Diagram.png [ 14.39 KiB | Viewed 3794 times ]


a = only action
b = only drama
c= only comedy

d = both action and drama but not comedy
e = both action and comedy but not drama
f = both drama and comedy but not action
g = all three

As per the question,
Both action and drama (including comedy) = d + g = 5
Both action and comedy (including drama) = e + g = 3
Both drama and comedy (including action) = f + g = 4

Action = a + d + g + e = 10
Drama = b + d + f + g = 20
Comedy = c + e + f + g = 18

As per your formula:
(Total in Action) + (Total in Drama) + (Total in Comedy) – (Overlap of A and D) – (Overlap of D and C) – (Overlap of A and C) – [2 * (Overlap of A, D, and C)] + (total in none of the groups) = Overall total
=> (a + d + g + e) + (b + d + f + g) + (c + e + f + g) – (d + g) – (e + g) – (f + g) – (2*g) + 0 = 38

Here you can see that you are adding g thrice but subtraction g 5 times (3 + 2)
So instead of subtracting 2g, you have to add “g” once as you have already added g thrice and subtracted thrice earlier

Hence the correct formula should be:
(a + d + g + e) + (b + d + f + g) + (c + e + f + g) – (d + g) – (e + g) – (f + g) + (g) + 0 = 38
=> 10 + 20 + 18 - 5 - 3 – 4 + g = 38
=> 48 – 12 + g = 38
=> 36 + g = 38
=> g = 38 – 36 = 2


Kudos plz if my reply helped. Lost all my kudos in getting G M A T C L U B Test :P

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Re: The 38 movies in the video store fall into the following thr [#permalink]

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New post 29 Sep 2013, 10:34
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The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there?


{Total} = {action} + {drama} + {comedy} - {action&drama+action&comedy+drama&comedy} + {action&drama&comedy}

38=10+20+18-(5+3+4)+{action&drama&comedy}

{action&drama&comedy}=2.

ADVANCED OVERLAPPING SETS PROBLEMS: advanced-overlapping-sets-problems-144260.html

Hope it helps.
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Re: The 38 movies in the video store fall into the following thr [#permalink]

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Re: The 38 movies in the video store fall into the following thr [#permalink]

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New post 20 Aug 2017, 17:02
Question for this: based on the wording of the question, I don't see how you can assume that the overlapping action & drama number of 5 (or the overlapping action & comedy # of 3, or the overlapping drama & comedy # of 4) can be (5-X), where X is the # for a video falling under all 3 categories.

The wording said: "Some movies are classified under more than one category: 5 are both action and drama ...." - to me, this clearly says that 5 fall under ACTION & DRAMA ; these 5 do not include any of the ones that are action & drama & comedy. Therefore, the 5 should just be 5, and not 5 - X.

...Idk if that made sense, does anyone follow?

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Re: The 38 movies in the video store fall into the following thr   [#permalink] 20 Aug 2017, 17:02
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