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saintforlife
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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The 38 movies in the video store fall into the following three categories: 10 action; 20 drama; 18 comedy
5 are both action and drama; 3 are both action and comedy; 4 are both drama and comedy
How many action-drama-comedies are there?

38=10+20+18-5-3-4
38=36
38-36=ADC

Answer -> 2
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Bunuel KarishmaB


What about the well known formula for the union of all three.

Let X be the number of movies in all three section (the inner-most)


10+20+18-(12+2X)=38 the 12 is the sum of the movies that are in two catogories(5+4+3=12)


10+20+18-(12+2X)=38

48-12-2X=38

36-2X=38

2X=-2

X=-1, which does not make sense.

Where am i going wrong? How is it possible that most often to find the inner most is the above approach correct but not for this question.
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Rebaz
Bunuel KarishmaB


What about the well known formula for the union of all three.

Let X be the number of movies in all three section (the inner-most)


10+20+18-(12+2X)=38 the 12 is the sum of the movies that are in two catogories(5+4+3=12)


10+20+18-(12+2X)=38

48-12-2X=38

36-2X=38

2X=-2

X=-1, which does not make sense.

Where am i going wrong? How is it possible that most often to find the inner most is the above approach correct but not for this question.

There are two formulae and you are using the wrong one. Check here: https://gmatclub.com/forum/the-38-movie ... 60697.html

Hope it helps.
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