Overlapping Method

[2011mbaspirant]

Can some one please help me understand the following type of questions.

In the Kan film festival, 50 movies were presented. 3/5 are action and 4/5 are science fiction. How many movies were science fiction action movies?
a) 10
b) 15
c) 20
d) 30
e) 35

Per the manual the correct answer is C.

I am finding such problem difficult to crack.
Thanks for your time and help.

[papgust]

It's a simple venn diagram problem.

Total movies = 50

Action movies = 3/5 * 50 = 30
Science fiction = 4/5 * 50 = 40
Both Action and science fiction = 'x'

Total movies = Action movies + Science fiction - Both
50 = 30+40-x
[spoiler]x = 20[/spoiler]

[dtweah]

Here is one intuitive way. Draw your ven diagram of A and S and put X at the intersection.
Now if 3/5 are action movies, then 2/5 are NOT action movie or are ONLY Science moivies. PUt 2/5 in in the only Science portion. ( This area is the complement of A).

But u are told All of S is 4/5.

So total S is

X + 2/5 = 4/5

X = 2/5

2/5 x 50 = 20.