# MBA Logical Reasoning Questions & Answers – Venn Diagrams Set-I

The Venn Diagrams from the logical reasoning section would enhance your rational thinking skills. Take the practice test at jagranjosh.com to prepare for various entrances such as CAT, CMAT, MAT, XAT, IIFT, SNAP etc

Updated: May 12, 2016 15:49 IST

Directions (1 - 2): The figure given below is the finding of a survey conducted in an organisation for measuring the behavior of its employees in terms of four characteristics - Adventurous, Humble, Active and Original. Circle A represents Adventurous, circle B represents Humble, circle C represents Active, and circle D represents Original.

1. Which region represents the people who are Humble, Original and Active but not Adventurous?

a) 6

b) 8

c) 7

d) 11

2. Which region represents the people who are Adventurous, Original and Active but not Humble?

a) 7

b) 8

c) 6

d) 11

Directions (3 - 4): In a survey of 200 working women, it was found that 96 read Reader’s Digest, 78 read Woman’s Era and 88 read Savvy magazine. It was also found that 34 read both Reader’s Digest and Woman’s Era, 36 read both Woman’s Era and Savvy; and 44 read both Reader’s Digest and Savvy and the balance 40 read none of these 3 magazines.

3. The number of women who read all the three magazines are:

a) 8

b) 12

c) 16

d) 20

4. The number of women who read exactly one magazine are:

a) 66

b) 68

c) 70

d) 72

Directions (5 - 6): In a dance academy there are 240 dancers. All the dancers are numbered 1 to 120. All even numbered dancers learn Salsa. Dancers whose numbers are divisible by 5 learns Ballet and those whose numbers are divisible by 7 learns Hip Hop.

5. How many learns none of the three dance forms?

a) 38

b) 82

c) 42

d) 114

6. How many learn all of the three dance forms?

a) 1

b) 2

c) 3

d) 4

7. There are 60 children admitted to a Music Academy. Some children can play only Guitar and some can play only Sitar. 15 children can play both Guitar and Sitar. If the number of children who can play Guitar is 27, then how many children can play Sitar? Also, how many can play only Sitar and how many can play only Guitar?

a) 12, 33 and 48 respectively

b) 33, 48 and 12 respectively

c) 33, 27 and 12 respectively

d) 48, 33 and 12 respectively

8. In a school competition, there are three activities for students to participate: Musical Drama, Group Dance and Story Telling. Students must participate in at least one, and may participate in two or even in all three. There are total 240 students in the school. The total numbers of students participating in different activities are: 140 students in Musical Drama, 146 in the Group Dance, and 90 in the Story Telling. Furthermore, 74 students are in both the Musical Drama and Group Dance, 40 are in both Musical Drama and Story Telling, and 16 students are in all three groups. 50 students are just in the Group Dance and not in anything else. How many students participate in only the Story Telling?

a) 28

b) 30

c) 32

d) 27

9. Out of total 200 players in a Sports Club, 5% plays all the three games – Cricket, Hockey and Football. It so happens that the number of players who plays any two and only two of the above games is 50. The number of players who plays Cricket only is 60. What is the total number of players who plays Hockey alone or Football alone?

a) 100

b) 80

c) 70

d) 90

10. A coaching institute has total 200 students studying Mathematics, Accountancy, both or neither. There are just as many students who can study both subjects as the ones who study neither of them. One quarter of those students who study Accountancy also study Mathematics. The total number of students who study Mathematics is 10 fewer than those who study Accountancy only. How many students study Mathematics only?

a) 30

b) 70

c) 50

d) 80

In this section, we will provide you the solutions to the above questions along with their explanation.

 Ques 1 Ques 2 Ques 3 Ques 4 Ques 5 Ques 6 Ques 7 Ques 8 Ques 9 Ques 10 a b b c b c d a b c

Explanation

Explanation (1-2):

Not Adventurous = 4 + 5 + 3 + 2 + 1 + 6

Not Adventurous but Original = 5 + 3 + 2 + 6

Not Adventurous but Original and Humble = 2 + 6

Not Adventurous but Original, Humble and Active = 6

Similarly,

Not Humble but Original, Adventurous and Active = 8

Explanation (3 - 4):

Explanation (5 - 6):

Explanation (7):

15 children can play both Guitar and Sitar

27 children can play Guitar

So, 27 – 15 = 12 children can only play Guitar

60 – 12 = 48 children can play Sitar

48 – 15 = 33 can play only Sitar

Explanation (8) :

Explanation (9) :

Number of players who plays all the three games

Number of players who plays Hockey alone or Football alone

= Total Number of players – (Number of players who plays any and only two games + Number of players who plays Cricket + Number of players who plays all the three games)

= 200 – (50 + 60 + 10) = 80

Explanation (10) :

Let x be the number of students studying both the subjects, which means it is also the number of students studying neither of the two subjects. 1/4 th of the students who study Accountancy, also studies Mathematics. If the Accountancy students who also studies Mathematics are x, then all Accountancy students are 4x, and those who do not study Mathematics are 3x. Also, let y be the number of students who study Mathematics but not Accountancy. The total number of students who studies Mathematics is 10 fewer than those who study Accountancy only.

x + y = 3x – 10

10 = 2x – y

Total students = 200

3x + x + y + x = 200

5x + y = 200

We have two equations with two unknowns. Add the equations (2x – y = 10) and (5x + y = 200), and we get

7x = 210, x = 30 and y = 50

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