Ch.7 :- Logic Based Venn Diagrams :- Exercise 3

✦Directions for Q. No.1 to 3 :Fig below, depicts an area where people speak four different languages. The triangle depicts English speaking area, the square depicts Hindi speaking areas, the circle stands for Urdu speaking area and the rectangle for area where people speak Marathi. Each part is numbered. Your task is to study the figure and answer the questions that follow:

1. Which number depicts the area where, the three languages, English, Marathi and Urdu are spoken but Hindi is not spoken?
(a) 4     (b) 11     (c) 9     (d) 8     (e) None

Ans.(c)
Number 9 lies in the space, which is common to triangle, circle and rectangle but not the square.

2. Number 2 depicts
(a) English and Hindi speaking area.
(b) Only English speaking area.
(c) Hindi and Marathi speaking area.
(d) English and Marathi speaking area.

Ans.(a)
Number 2 lies in the space, which is common to triangle and square and hence represents English and Hindi speaking area.

3. Which number depicts Marathi, English and Hindi speaking area not the Urdu speaking area?
(a) 4     (b) 5     (c)  9     (d) 3     (e) None of these.

Ans.(d)
Number 3 lies in the space, which is common to triangle, square and rectangle but not to the circle.

✦ Directions for Q. No.4 to 8 : Read the following information carefully. In the diagram below the circle represents poor boys, the square represents educated boys, the triangle represents the boys who are employed somewhere and the rectangle represents those who help in the family business. Each section of the diagram is numbered. Now, answer the questions given below on the basis of the diagram.

4. Which number represents those poor boys who help in family business but are not educated or employed
elsewhere?

(a) 2     (b) 3     (c) 4     (d) 5     (e) 7

Ans.(d)
Number 5 represents those poor boys who are helping family business but are not educated or employed elsewhere because it occupies the space common to circle and rectangle only

5. Which number represents the group of educated poor boys who are employed somewhere but do not help in family business?
(a) 12     (b) 3     (c) 11     (d) 2     (e) None of these

Ans.(e)
No number occupies the space which is common to the figures circle, square and rectangle.

6. Which section does number 3 represent?
(a) Uneducated poor boys who do not help in family business.
(b) Educated poor boys employed in service.
(c) Uneducated boys who help in family business.
(d) Educated poor boys who help in family business.
(e) None of the above

Ans.(d)
Number is present in the space common to circle,square and rectangle, hence represents educated poor boys who help in family business.

7. Which number represents the section of poor boys who are neither educated nor are in any employment or have any family business?
(a) 4     (b)  5     (c) 1     (d) 11     (e) 1

Ans.(e)
Number 12 lies on that portion of the circle, which is not common to any other figure

8. Boys who by the number:
(a) 8     (b) 7     (c) 4     (d) 6     (e) 5

Ans.(b)
Number 7 represents the portion, which is common to triangle and rectangle only. Hence, it represents employed boys engaged in family business.

✦ Directions for Q. No.9 to 12 : Read the following information carefully and answer the questions based on them. In the Venn diagram given below, the square represents women, the triangle represents persons who are in govt.services, the circle represents educated persons, and the rectangle represents persons working in private sector. Each section of the diagram is numbered. Your task is to study the diagram and answer the questions that follow:

9. Which number represents educated women, who are in govt.jobs?
(a) 2     (b) 3     (e) 6     (d) 4     (e)None of these

Ans.(b)
Educated women in govt. jobs are represented by number 3 as it occupies the space common to circle,square and triangle.

10. Which number represents the uneducated women, who have govt. jobs as well as jobs in private sectors
(a) 6     (b) 4     (c) 12     (d) 9     (e) None of these

Ans.(d)
Number 9 represents uneducated women who have govt. jobs as well as jobs in private sectors because it lies in the space which is common to square, triangle and rectangle.

11. Number 10 represents
(a) Educated women in private jobs
(b) Uneducated men in govt. jobs
(c) Educated men working in private sectors
(d) Educated men having private as well as govt. jobs
(e) None of the above

Ans.(d)
Number 10 represents educated men having private jobs as well as govt. jobs.

12. Number 2 represents
(a) Educated women who neither have govt. jobs nor have a private job
(b) Uneducated women with no jobs
(c) Educated men with govt. jobs
(d) Uneducated men with govt. jobs
(e) None of the above

Ans.(a)
Number 2 occupies the space common to circle and square only and hence represents educated women who are neither in govt. jobs nor in private jobs.

13. Which numbered space in the Fig. below represents doctors who are players as well as artists?

(a) 2     (b) 3    (c) 6    ((d) 7    (e) None of these.

Ans.(d)
Since number 7 is present on that portion of the figure,which is common to square, circle and rectangle and hence represents doctors who are players as well as artists.

✦ Directions for Q. No. 14 to 18 : Study Fig.given below and answer the questions that follow.

14. Find out the number of families which have all the four things mentioned in the diagram above.
(a) 40     (b) 30     (c) 35     (d) 20     (e) None of these

Ans.(d)
Number 20 is common to all the four figures and hence it can be concluded that 20 families have all the four things.

15. Find out the number of families which have scooters.
(a)  145     (b) 100     (c) 188     (d) 240     (e) None of these

Ans.(c)
Numbers of families having scooters are represented by the square and total of all the numbers present in square is 188.

16. Find out the number of families which have VCR Rand TV both.
(a) 84     (b) 24     (c) 104    (d) 129    (e) None of these

Ans.(e)
100 families have both VCR and TV as it is the sum of the numbers present on the portion common to both the circles.

17. Find out the number of families which have only one thing, either VCR or TV or scooter or maruti.
(a) 160     (b) 184     (c) 225     (d) 254     (e) None of these

Ans.(c)
Sum of 110, 50, 40 and 25 will represent such families as all these numbers lie on the portion not common to other figures.

18. Find out the number of families which have TV and scooter both but have neither VCR nor maruti.
(a) 15    (b) 30     (c) 4     (d) 50     (e) None of these

Ans.(b)
Number 30 lies on the portion common to the figures representing families having TV and scooters only

✦ Directions for Q. No. 19 to 22 : The following questions are based on the diagram given below.

(i) The rectangle represents govt. employees
(ii) The triangle represents urban people
(iii) The circle represents graduates
(iv) The square represents clerks

19. Which of the following statements is true ?
(a) All govt. employees are clerks
(b) Some govt. employees are graduates as well as,clerks
(c) All govt. employees are graduates
(d) All clerks are govt. employees but not graduates

Ans.(b)
Because 6 represents the govt. employees, who are graduates as well as clerks.

20. Choose the correct statement:
(a) Some clerks are govt employees
(b) No clerk is from urban areas
(c) All graduates are from urban areas
(d) All graduates are govt. employees

Ans.(a)
Because number 7 and 6 represent clerks, who are govt.employees.

21. Which of the following numbers represents urban govt.employees, who are graduate but not clerk
(a) 9     (b) 4     (c) 10    (d) 5     (e) None of these