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Problems on Sets and Venn Diagrams: CAT Quantitative Aptitude

May 28, 2012 16:36 IST

Let us jump straight to the problems to understand the solution methodology.

Example:

Let A = {0, 1, 3, 5}, B = {5, 6, 1, 3, 9} and C = {0, 1, 2, 3, 9, 13}.
Then, :

[1] {0, 1, 2, 3, 9, 13}

[2] {0, 1, 2, 3, 5, 9, 13}

[3] {0, 1, 3}

[4] {1, 3}

Solution:

Therefore, the correct option is [2].

Example:

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

[1] 26

[2] 36

[3] 40

[4] 68

Solution:

Let us draw a Venn Diagram with the information as provided above.

therefore numbers divisible by 2, 3 and 5 = 27 + 13 + 3 + 7 + 14 + 3 + 7 = 74

therefore numbers not divisible by 2, 3 and 5 = 100 – 74 = 26

Therefore, the correct option is [1].

Refer to the data below and answer the questions that follow.

A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology and Chemistry while 8 study both Physics and Biology. Equal numbers study all three subjects as those who learn none of the three.

Example:

How many study all the three subjects?

[1] 2

[2] 3

[3] 5

[4] 7

Solution:

Let us draw a Venn diagram.

From the diagram, 3 students study all the three subjects.

Therefore, the correct option is [2].

Example:

How many study only one of the three subjects?

[1] 21

[2] 30

[3] 39

[4] 42

Solution:

33 + 25 –(19 – x) + 9 – x +26 –(17 – x) = 63 – x
33 + 25 – 19 + x + 9 – x + 26 – 17 + x = 63 – x
57 + x = 63 – x

Now, we have18 + 9 + 12 = 39

Therefore, the correct option is [2].

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4 Comment

Selvaprabha Gopal,

bhavani ,

an advertising agency finds that,of its 170 clients,115 use television,110 use radio and 130 use magazines also 85 use television and magazines 75 use television and radio 95 use radio and magazines 70 use all the three

Anjela Joy Endino,

..sobrang helpful nito sa mga assignments kue..

vandan,

this page is good for students who do not know what sets is.

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