Let S = {x : x is a positive multiple of 3 less than 100} and P = {x : x is a prime number less than 20}. Then n(S) + n(P) is:

Correct option is B

Given:

S = multiples of 3 less than 100
P = prime numbers less than 20

Concept used:
n(S) = number of terms in arithmetic progression
3, 6, 9, …, 99

Solution:
For S:
a = 3, d = 3, last term = 99
n = (99 − 3)/3 + 1 = 96/3 + 1 = 32 + 1 = 33
=> n(S) = 33

For P:
Primes less than 20 → 2, 3, 5, 7, 11, 13, 17, 19
=> n(P) = 8

So,
n(S) + n(P) = 33 + 8 = 41

Correct answer is (b) 41.