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Caslet DI with Venn Diagram:

We need to understand the concept of the Venn Diagram with the help of the diagrams.

Venn diagram in case of two elements. Suppose the two elements are A and B

C = Number that is only A

D = Number that is only B

M = Number that belongs to both A and B

N = Number that belongs to none of A and B

Example 1:

In a college 200 students are randomly selected 150 students like Mathematics. 130 like science and 100 live both mathematics and science now.

(1) How many students like only mathematics?

(2) How many students like only science?

(3) How many students like neither Science nor mathematics?

(4) How many students like only one of mathematics and science?

(5) How many students like at least one of the subjects?

Solution:

T = 200

1. Students like only mathematics = 50

2. Students like only science = 30

3. Total students like mathematics and science = 50 +30 + 100 = 180

So, students like nor mathematics = (200 - 180) = 20

4. Students like only one of the mathematics and science = 50 + 30 = 80

5. Students like at least one of the subjects = (50 + 30 + 100) = 180

Venn Diagram is a case of three elements

Let us assume three elements are A, B, and C

Let us take an example

There is a total of 1000 students in a coaching center who are preparing for one or more government exams among bank PO., Bank Clerk, and SSC. 5% of students are preparing for all three given exams. 36% of students are preparing for only two exams. 10% of students are preparing for only SSC. 25% of students are preparing for only bank PO. 20% of students are preparing for both bank PO and bank Clerk but not SSC and 10% of students are preparing for both bank clerk and SSC but not for bank PO.

Q.1. What is the ratio of the total number of students who are preparing for the SSC exam to the total number of students who are preparing for the bank PO exam

(a) 23 : 31

(b) 56 : 31

(c) 31 : 56

(d) 47 : 29

(e) None of these

Q.2. How many students are not preparing for the bank clerk exam?

(a) 390 

(b) 410

(c) 590

(d) 420

(e) None of these

Q.3. The total number of students who are preparing for only one exam is what percent of total students?

(a) 59%

(b) 41%

(c) 50%

(d) 42%

(e) None of these

Q.4. What is the total number of students who are preparing for SSC exams?

(a) 170

(b) 310

(c) 530

(d) 690

(e) None of these

Q.5. How many students are preparing for only the bank PO exam?

(a) 620

(b) 430

(c) 580

(d) 560

(e) None of these

Solution:

To answer this question we need to draw the Venn diagram with all data.

Total students = 1000

So, a + b + c + d + e + f + g = 1000

g = 5% of 1000 = 50

d + e + f = 36%of 1000 = 360

c = 10% of 1000 = 100

b = 25% of 1000 = 250

e = 20% of 1000 = 200

f = 10% of 1000 = 100

So, e + f = 200 + 100 = 300

So, d = 360 – 300 = 60

a = 1000 – (50 + 100 + 250 + 200 + 100 + 60) 

= 1000 – 760

= 240

(1)

Total students preparing for SSC exams = (c + d + g + f) = (100 + 60 + 50 + 100) = 310 

Total Students preparing for bank PO exams = (b + d + e + g) 

= (250 + 60 + 200 + 50) = 560

So, ratio = 310 : 560 = 31 : 56

Option (c) is correct.

(2)

Students are not preparing for bank clerk exams = 1000 – (a + f + g + e)

= 1000 – (240 + 100 + 50 + 200)\

= 1000 – 590

= 410

Option (b) is correct.

(3)

Students preparing for only one exam is

a + b +c = 250 + 240 + 100 = 590

Option (a) is correct.

(4)

Total Number of students preparing for SSC exams = (c + d + f + g)

= (100 + 60 + 100 + 50)

= 310

Option (b) is correct.

(5)

Students preparing for only bank PO exams = b + d + g + e

= 250 + 60 + 50 + 200

= 560

Option (d) is correct.