# Logical Venn Diagram Questions

Q:

In a town of 500 people, 285 read Hindu and 212 read Indian Express and 127 read Times of India, 20 read Hindu and Times of India and 29 read Hindu and Indian Express and 35 read Times of India and Indian express . 50 read no news paper . Then how many read only one paper ?

 A) 123 B) 231 C) 312 D) 321

Explanation:

No. of people who read Hindu = 285
No. of people who read TOI = 127
No. of people who read IE = 212
Now,
No. of people who read Hindu and TOI both is = 20
No. of people who read TOI and IE both is = 35
No. of people who read Hindu and IE both is = 29
Let No. of people who read Hindu , TOI and IE all is = x ;
So, only Hindu is = 285-20-29-x = 236-x ;
Only TOI is = 127-20-35-x = 72-x ;
Only IE is = 212-35-29-x = 148-x ;
Now, 236-x + 72-x + 148-x + 20 + 29 + 35 + x + 50 = 500 590 -2x = 500
So, x = 45 this is the value who read all the 3 dailies.
So, No. of people who read only one paper is = 236-45 + 72-45 + 148-45 = 191 + 27 + 103 = 321.

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Q:

In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group, none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group ?

 A) 21 B) 22 C) 23 D) 24

Explanation:

Let us assume the two persons who can speak two languages speak Hindi and Tamil. The third person then speaks all the three languages.

Tamil – Number of persons who can speak is 6. Only Tamil 6 – 2 – 1 = 3

Hindi - Number of persons who can speak is 15. Only Hindi 15 – 2 – 1 12

Gujarati – Number of persons who can speak is 6. Only Gujarati 6 – 1 = 5

Thus the number of persons who can speak only one language is 3 + 12 + 5 = 20

Number of persons who can speak two languages = 2

Number of person who an speak all the languages = 1

Total number of persons = 23.

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Q:

Which of the following Venn- diagram correctly illustrates the relation ship among the classes : Tennis fans, Cricket players, Students

 A) 1 B) 2 C) 3 D) 4

Explanation:

Some Students can be Cricket players. Some Cricket players can be Tennis fans. Some Students can be Tennis fans. So, the given items are partly related to each other.

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Q:

Which of the following Venn- diagram correctly illustrates the relation ship among the classes  :  Carrot, Food, Vegetables

 A) a B) b C) c D) d

Explanation:

All Carrots are Vegetables. All Vegetables are Foods.

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Q:

Out of 120 students in aschool, 5% can play all the three games Cricket, Chess and Carroms. If so happens that the number of players who can play any and only two games is 30. The number of students who can play the Cricket alone is 40. What is the total number of those who can play Chess alone or Carroms alone ?

 A) 45 B) 44 C) 46 D) 24

Explanation:

Given U=120

5% of 120 = 6

Therefore, Students who can play Chess alone or Carroms alone =  120 - (30+40+6)= 44

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Q:

Identify the diagram that best represents the relationship among the given classes.

Brother, Husband, Men

 A) 1 B) 2 C) 3 D) 4

Explanation:

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Q:

Main street high school has 10 members on its football team and 14 members on its science club. 5 members at the school belong to both the football and science teams. How many students belong to only science club team or football team?

 A) 9 B) 14 C) 24 D) 21

Explanation:

Given that,

Members in football team = n(f) = 10

Members in science club = n(s) = 14

Members in both football team and science club = n(f ^ s) = 5

Then, Members in only football team = n(F) = 10 - 5 = 5

Members in only science team = n(S) = 14 - 5 = 9

Hence, members in only football or science team = n(FUS) = n(F) + n(S) - n(f^s)

= 9 + 5 - 5

= 9.

Hence, many students belong to only science club team or football team = 9.

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Q:

In a dinner party both fish and meat were served. Some took only fish and some only meat. There were some vegetarians who did not accept either. The rest accepted both fish and meat. Which of the following Venn-diagrams correctly reflects this situation?

 A) 1 B) 2 C) 3 D) 4