# Venn Diagram Problems and Solutions for CAT PDF

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Venn diagrams questions that will be asked in CAT are basically 3 or 4 circle type. The questions will be generally asked to find out the minimum or maximum value that can be attained in the missing data. Here we have provided one solved set of venn diagrams from previous CAT papers.

Venn Diagram Problems and Solutions for CAT PDF:

Question 1:

Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e. either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?

a) 32
b) 24
c) 30
d) None of these

Question 2:

Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?

a) 4
b) 9
c) 10
d) 11

Instructions:

A survey of 200 people in a community who watched at least one of the three channels â€” BBC, CNN and DD â€” showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

Question 3:

What is the maximum percentage of people who can watch all the three channels?

a) 12.5%
b) 8.5%
c) 15%
d) Data insufficient

Question 4:

If 5% of people watched DD and CNN, 10% watched DD and BBC, then what percentage of people watched BBC and CNN only?

a) 2%
b) 5%
c) 8.5%
d) Cannot be determined

Question 5:

Referring to the previous question, what percentage of people watched all the three channels?

a) 3.5%
b) 0%
c) 8.5%
d) Cannot be determined

Answers and Solutions for Venn Diagram Problems and Solutions for CAT PDF:

Let the number of days in the vacation be x
They played tennis for x-14 days
They did yoga for x-24 days
So, they did yoga or played tennis for x-14+x-24 = 2x-38 days
2x – 38 = 22
=> x = 30

Number of people owning exactly 2 articles = 9
Number of people owning exactly 3 articles = 1
Applying AUBUC formula, we get
AUBUC = 22+15+14 – 9 -2*(1)=40
Number of people who do not own any article = 50-40 = 10

Let a be the number who watch only one channel, b be the number who watch only 2 channels and c be the number who watch all channels.
a+b+c = 100
a+2b+3c = 80+22+15 =117
Subtracting both equations,
b+2c = 117-100 = 17
Maximum c occurs when b = 0
2c = 17
c = 8.5

Applying AUBUC formula
Let x be the number who watch BBC and CNN and y be the number who watch all three channels.
100 = 80+22+15-(10+5+x)+y
x-y = 2
Hence only 2% people watch BBC and CNN only.