In a survey conducted to find out the readership of three Ne

This is the data given in the question:


The entire shaded area is given to be 85.
So x + y + z + 8 = 85 (people who read at least 2 newspapers)
or x + y + z = 77 (people who read exactly two newspapers)

The question asks us to minimize the area x (common to A and B but not to C)
There are 77 people in x + y + z so to give as few people as possible to x, we should try and give as many as possible to y and z.

But y + z + 8 + r <= 83 (because C is at most 83. We have a minimum value for C as well but let's not worry about it right now.)
So y + z + r <= 75
Now, even if r = 0, y + z can be 75 at the most. Since x + y + z = 77,
x has to be at least 2.
Answer (C).

Let's check if it is possible to satisfy all our conditions:
If y = 25, z = 50 (We took one of the many possible values for y)
Then A could lie between 20 - 40, B could lie between 50 - 70 and C is 83. All conditions satisfied and we got the minimum value of x.

@144144 - There is a maximum limit on C. I don't think you took that into account.

Second method: You may want to do it this way:

The entire shaded area is 85 (including the red one)
Now look at this:

In the diagram above, the entire shaded area is at most 83.
So the red shaded area has to be at least 85 - 83 = 2