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Venn Diagram Questions and Shortcuts

Published on Thursday, June 26, 2014
Venn diagrams is one of the most chapter for Bank exams. Generally there is a 5 questions set from this chapter. Today I am going to use Venn Diagrams in various other chapters.

Ques 1
- How many numbers are there between 1 and 100 that are not divisible by 2, 3 and 5 ?
Solution - We can solve this question by drawing a Venn diagram.

Venn diagram in number system

From the above 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.

Ques 2 - In a class,7 students like to play Basketball and 8 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
Solution - Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
7 +8 - 3 = 12

Ques 3-4 - A college has 63 students studying Political Science, Chemistry and Botany. 33 students study Political Science, 25 Chemistry and 26 Botany. 10 study Political Science and Chemistry, 9 study Botany and Chemistry while 8 study both Political Science and Botany. Same number of students study all three subjects as those who learn none of the three. 

3) How many students study all the three subjects?
a) 2
b) 3
c) 5
d) 7

4) How many students study only one of the three subjects?
a) 21
b) 30
c) 39
d) 42

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 

I will post the solution of practice questions soon

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