The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However,

[VJesus12]

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?

A. 1
B. 2
C. 3
D. 4
E. 5

Answer: B

Source: Manhattan GMAT

[Scott@TargetTestPrep]

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?

A. 1
B. 2
C. 3
D. 4
E. 5

Answer: B

Solution:

We can use the following formula:

Total = Group A + Group B + Group C - Both A and B - Both A and C - Both B and C + All three + Neither

In this problem, Total is 38, Group A (action) is 10, Group B (drama) is 20 and Group C (comedy) is 18. There are 5, 3 and 4 movies in the double overlaps, and Neither = 0. Let’s denote “All three” by n and fill in this information in the formula:

38 = 10 + 20 + 18 - 5 - 3 - 4 + n + 0

38 = 48 - 12 + n

n = 38 - 36 = 2

Answer: B