How To Solve Venn Diagrams Questions Quickly

How to solve Venn Diagram Quickly

Venn Diagram is the way to represent the differnt sets in a manner such that one can find all possible logical relations easily by just lookin at the Venn diagram.

How To Solve Venn Diagrams Questions:

  • Venn diagram is an illustration of common characteristics.
  • Maths logic a diagram in which mathematical sets or terms of categorical statement are represented by overlapping circles within a boundary representing the universal set, so that all possible combinations of the relevant properties are represented by various distinct areas in picture.
How to solve venn diagram questions quickly

How To Solve Quickly Venn Diagram

Question 1 How many numbers are there between 1 and 100 that are not divisible by 2, 3 and 5 ?


(a) 24                     (b) 20

(c) 25                     (d) 22

Solution:-  From the diagram it is clear that

(27+14+7+7+13+3+3 = 76 ) 76 numbers are divisible by either 2,3 or 5.

So 100 – 76 = 24 numbers are not divisible by 2,3 or 5.

Correct Option : (a)

Question 1
Question 2

Questions 2 How many students study only one of the three subjects?


(a) 21                     (b) 30

(c) 39                    (d) 42

Solution:-  From the above diagram, you can clearly see that 3 students study all three subjects.

Number of students who study only one subject = 18 + 9 +12 = 39.

Correct Option : (c)

How To Solve Questions on Venn Diagrams Quickly

Question 3 In the following diagram, triangle represents people who can sing, circle represents people who can paint. If the number of people who know to do exactly 2 of the above mentioned things is equal to the number of people who can paint is


(a) 23                      (b) 13

(c) 53                       (d) 63

Solution : 

Number of people who can do exactly 2 out of the 3 activities = 12 + 21 + 20 = 53.

Let the missing value be ‘x’.

Number of people who can do exactly one of the 3 activities = 23 + 7 + x = 30 + x.

It has been given that 30+x = 53

x = 23

Number of people who can paint = 12+8+20+23 = 63.

Therefore, option D is the right answer.

Correct Option: D

Question 3

Questions 4 In the following diagram, each geometric shape represents a movie


(a) 5                    (b) 14

(c) 13                   (d) 9

Solution :   The area common to the circle, trapezium and the hexagon but not common to the triangle represents the people who can sing, swim and paint but cannot dance.

From the diagram, we can see that the number of such people is 14. Therefore, option B is the right answer.

Correct Option: B