DI Venn Diagrams

7/29/2019 DI Venn Diagrams

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Venn

Diagrams

An Approach

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Venn Diagrams

In a class 70 students have passed in

English and 80 students have

passed in Mathematics. Totallythere are 120 students in the class.

How many passed in only one

subject and how many passed in

both the subjects?

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Venn Diagrams

Given a + x = 70

b + x = 80

a + x + b + x = 150 a + b + 2x = 150

a + b + x + y = 120

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a x b

y


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Venn Diagrams

a + x + b + x = 150 a + b + 2x = 150

a + b + x + y = 120

x - y = 30

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Variable Min Max

a + b 80 90

Variable Max MinX 70 30

Y 40 0


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Venn Diagrams

Given a + x = 70 and b + x = 80

a + x + b + x = 150 Q1 + 2 Q2 = 150

Q1 + Q2 = 120 Q1 represents exactly only one quality & Q2

represents exactly 2 qualities.

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a x b

y


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Venn Diagrams

In a certain institute, out of every sevenstudents taking Accountancy, three takeEconomics as well. For every student taking

at least one of the two courses, there arethree students who take up neither. If 10%of the students take only Accountancy, thepercentage of students who take only

Economics is

(1) 17 % (2) 23 % (3) 7 % (4) 21 %

(5) Cannot be determined

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Venn Diagrams

Let no of people who take accountancy be 7 k

Then no of people who take accountancy &

Economics is 4 k Then no of people who take neither

accountancy nor Economics is 21 k + 3 b

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4k 3k b


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Venn Diagrams

Given 4k = 10%

28 k + 4 b =100%

70 % + 4 b = 100%

4 b = 30%

b = 7 %

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Venn Diagrams In a group of 100 students, each student has to opt

for one or more of the three subjects among

Physics, Chemistry and Mathematics. The number

of students who opted for Mathematics is more than

the number of students who opted for Physics,which, in turn, is more than the number of students

who opted for Chemistry, which, in turn, is more than

the number of students who opted for exactly two of

the three subjects, which, in turn, is more than thenumber of students who opted for all the three

subjects. It is also known that at least one student

opted for all the three subjects.

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Venn Diagrams

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Chemistry

gf

e

d

mp

c

M = m + d + e + g

P = p + d + f + g C = c + e + f + g Q2 = d +e + f Q3 =g

M > P > C > Q2 > Q3 1


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Venn Diagrams What is the maximum number of students

who opted for Chemistry?

(1) 72 (2) 79 (3) 80 (4) 81

(5) None of these

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Chemistry

M > P > C > Q2 > Q3 1If C has to be Maximum,

then Q2 has to be

Maximum & in turn Q3

has to be MaximumM = 84 B = 83 C = 82

Q2 = 51 Q3 = 49

C= 82

49

17

18

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Venn DiagramsWhat is the minimum number of students whoopted for Mathematics?

(1) 38 (2) 37 (3) 36 (4) 35 (5) 34

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Chemistry

M > P > C > Q2 > Q3 1 If M has to be

Minimum , then Q3

has to be Minimum

Q2 = 2 Q3 = 1 Remaining 97 can be

distributed.

M=36

1

2

32

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