Hi Anisha,

Best way to solve this question is using the venn-diagram and you should have good understanding of the venn – diagram.

Question is asking you to find the minimum number of people of watch atleast one of the three channels.

Lets first draw the venn-diagram,

If you look at in the above diagram,

we don’t know the all three intersection, if we know all three intersection then there is no point of finding the maximum or minimum intersection.

Let’s start analyzing this,

We need to minimize the number of people who watch atleast one of the show,

Lets take a simple example,

Lets say there are 100 students in the class, and lets say 50 opted Math and 70 opted science. If the question is what is the number of people who chose atleast one of the subject ? Answer would be 70. Why ?

Lets look at the below diagram. to minimize the number of people who chose atleast one we need to maximize the both intersection(students who chose both subjects).

Technically speaking the diagram should look like this,

Lets say suppose if the question is what is the maximum number of people who chose atleast one subject, then the answer would be 100. In this case we have to minimize the number of people of who chose both subjects. Minimum 20 people have to chose both subjects.

With the above thought process, let’s try to apply the same logic in our actual question,

Here we have three sets, so lets take two sets at a time and analyze it.

Bigger set is fox news which has the total as 120.

Look at the below diagram,

Clearly you can see that, this doesn’t help us because total number of people who watch fox is more than the number of people who watch both(Fox – ABC & Fox – Sky ).

Besides you can’t take all three intersection as zero because it contradicts the information given.

So, let’s move onto the next bigger set which is people who watch ABC = 90.

Now we need to have the minimum intersection as 35.

This makes the number of people who watch only ABC show as zero, which clearly help us to minimize the number of people who watch atleast one of the shows.

this gives the minimum number of people who watch atleast one of the three shows as 150. We can’t have further minimum than this.

NET – NET,

Remember, you need to minimize all three intersection to find the minimum number of people who watch atleast one show.

Similarly, you need to maximize all three intersection to find the maximum number of people who watch atleast one show.

This question you need to think little more logically to get to the answer quickly.

Hope this helps.