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

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Manager
Joined: 09 Nov 2012
Posts: 62
The 38 movies in the video store fall into the following thr  [#permalink]

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Updated on: 29 Sep 2013, 10:32
5
00:00

Difficulty:

(N/A)

Question Stats:

94% (01:40) correct 6% (04:49) wrong based on 42 sessions

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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:
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

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

Originally posted by saintforlife on 28 Sep 2013, 19:16.
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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Posts: 58176
Re: The 38 movies in the video store fall into the following thr  [#permalink]

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29 Sep 2013, 10:34
6
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.

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

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29 Sep 2013, 00:19
3
2
saintforlife wrote:
Solution:
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

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 [ 14.39 KiB | Viewed 6748 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

(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)

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

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28 Sep 2013, 20:39
2
1
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
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
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)
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: The 38 movies in the video store fall into the following thr  [#permalink]

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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?
Manager
Joined: 27 Oct 2017
Posts: 73
Re: The 38 movies in the video store fall into the following thr  [#permalink]

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05 Mar 2019, 13:51
Just curious to know, why we can't apply the formula below:

= action+drama+comedy-action&drama-action&comedy-drama&comedy-2*all
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Joined: 02 Jan 2019
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GPA: 3.3
Re: The 38 movies in the video store fall into the following thr  [#permalink]

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27 Mar 2019, 21:12
arorni wrote:
Just curious to know, why we can't apply the formula below:

= action+drama+comedy-action&drama-action&comedy-drama&comedy-2*all

I'm also wondering this.
Bunuel , can you explain why we don't multiply All by 2?
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Joined: 02 Sep 2009
Posts: 58176
Re: The 38 movies in the video store fall into the following thr  [#permalink]

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27 Mar 2019, 21:14
scubaVC wrote:
arorni wrote:
Just curious to know, why we can't apply the formula below:

= action+drama+comedy-action&drama-action&comedy-drama&comedy-2*all

I'm also wondering this.
Bunuel , can you explain why we don't multiply All by 2?

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

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21 Jun 2019, 08:11
daftypatty wrote:
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?

I know it's 2 years later but I just came across this and have the same exact question.
Re: The 38 movies in the video store fall into the following thr   [#permalink] 21 Jun 2019, 08:11
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