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

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:

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