A question in GRE states:
In a survey of a town,it was found that 65% of the people surveyed watched the news on television,40% read newspaper, and 25% read a newspaper and watched the news on television. What percent of the people surveyed neither watched the news on television nor read a newspaper.
I am stuck .please
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Hint
What percentage of people watched the news on television and read a newspaper?
What percentage of people watched the news on television but did not read a newspaper?
What percentage of people did not watch the news on television but did read a newspaper?
What percentage of people neither watched the news on television nor read a newspaper?
On
I think that the easiest way to work through problems like these is to make a matrix. What I mean by this is creating a table with all the information you know and then using that info to find out the rest. With the information you have provided, we know this:
Now we can figure out the rest of the matrix pretty easily using the info we have. Each column and row need to add up to to total. For example, the percentage of people who watch tv and newspapers (25%), plus the percentage of people who watch tv, but don't watch newspapers (unknown) needs to add up to the total amount of people who watch TV. Thus your filled in matrix will look like this: 
And you know that the percentage of people who do neither is 20%
The number of people watching news on TV as well as reading newspaper already came under individual sections.
So you have to subtract that much number from the total tally of people surveyed watching TV and newspaper.
Suppose there are 100 people who got surveyed: Watching TV = 65% = 65 Reading Newspaper = 40% = 40
Doing both = 25% = 25
So, n(A union B) = n(A) + n(B) - n(A intersection B)
Remaining people is what you are looking for.
Thus percent of the people surveyed neither watching the news on television nor reading a newspaper = 100 - (65 + 40 - 25) = 100 - 80 = 20%