Problems on Sets and Venn Diagrams: CAT Quantitative Aptitude

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].