# CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram

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**Answer the next 2 questions based on the information given below:**

In a class of 40 students, 20 like cricket and 25 like football.

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum number of students who like both the sports.

Answer: 20

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the least number of students who like both the sports.

Answer: 5

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**Answer the next 3 questions based on the information given below.**

In a group of 130 students, 60 like Cricket, 50 like Football, 45 like TT and 90 like exactly one of the three games.

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum possible number of students who like at least two of the three games?

- (a)
26

- (b)
32

- (c)
34

- (d)
48

Answer: Option B

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum possible number of students who like none of the games?

- (a)
40

- (b)
32

- (c)
18

- (d)
8

Answer: Option C

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum possible number of students who like Football but like neither Cricket nor TT?

- (a)
29

- (b)
39

- (c)
49

- (d)
50

Answer: Option C

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

Of the students who like TT, the number of students who like football is 5 more than those who like Cricket. What is the difference between the number of students who like only Cricket and those who like only Football?

- (a)
5

- (b)
15

- (c)
25

- (d)
39

Answer: Option B

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**Answer the next 2 questions based on the information given below.**

According to a survey conducted among 1000 people in a multiplex on a binge watching weekend, 400 participants bought tickets for Avengers, 500 participants bought tickets for Interstellar and 600 participants bought tickets for Eat Pray Love. Each person had purchased tickets for at least one movie.

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the minimum number of people who bought tickets for all the three movies?

- (a)
400

- (b)
500

- (c)
600

- (d)
None of these

Answer: Option D

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum number of people who bought tickets for all the three movies?

- (a)
250

- (b)
600

- (c)
400

- (d)
None of these

Answer: Option A

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**Answer the next 2 questions based on the information given below.**

According to a survey, at least 70% participants like apples, at least 75% participants like bananas and at least 80% participants like cherries.

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the minimum percentage of people who like all the three fruits?

- (a)
25

- (b)
70

- (c)
41

- (d)
Cannot be determined

Answer: Option A

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum percentage of people who like all the three fruits?

- (a)
80

- (b)
70

- (c)
41

- (d)
100

Answer: Option D

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**Answer the next 2 questions based on the information given below.**

A survey was conducted among a group of 50000 people about their preferred newspapers. 90% liked Times of India, 85% liked Economic Times, 80% liked Hindustan Times, 82% liked Mumbai Mirror, 75% liked Daily News and Analysis and 4000 did not like any of these newspapers.

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the minimum number of people who liked all the five newspapers?

- (a)
44

- (b)
37500

- (c)
22000

- (d)
75

Answer: Option C

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum percentage of people who liked three out of the five newspapers?

- (a)
24

- (b)
12000

- (c)
34000

- (d)
68

Answer: Option A

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**Answer the next 5 questions based on the information given below:**

In a group of 100 people 65 can speak Hindi, 55 can speak Tamil and 60 can speak English.

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the minimum number of people who can speak exactly one language?

Answer: 20

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the minimum number of people who can speak at least one language?

Answer: 65

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Workspace:

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum number of people who can speak exactly one language?

Answer: 60

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**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the minimum number of people who can speak exactly two languages?

Answer: 0

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Workspace:

**CRE 4 - Venn Diagram based Optimization | LR - Venn Diagram**

What is the maximum number of people who can speak exactly two languages?

Answer: 90

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