NDA 2021 Maths · Mathematics · Sets, Relations and Functions · easy

Let A be the set of multiples of 3 and B the set of multiples of 5 among the integers 1,2,…,50. Then n(A∪ B) is

Single correct option

Let

A

be the set of multiples of

3

and

B

the set of multiples of

5

among the integers

1,2,\ldots,50

. Then

n(A\cup B)

Show answer and solution

Answer: (B) $23$

n(A)=\lfloor50/3\rfloor=16

n(B)=10

, and

A\cap B

consists of multiples of

15

15,30,45

, so

n(A\cap B)=3

. Hence

n(A\cup B)=16+10-3=23

. Without removing the multiples of 15 you would get 26.

Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake