How many numbers lying between 20 and 200 are divisible by 4?

1. 43

2. 44

3. 45

4. 46

The numbers divisible by 4 lying between 20 and 200 form an Arithmetic Progression (A.P.).

24, 28, ….., 196.

a = 24

l = 196

d = 4

Let no. of terms be n.

We know that,

nth term of A.P. :

∴ T_n = a + (n - 1)d

⇒ 196 = 24 + (n - 1)4

⇒ 196 - 24 = (n - 1)4

⇒ 172 = (n - 1)4

⇒ $\dfrac{172}{4}$ = n - 1

⇒ 43 = n - 1

⇒ n = 43 + 1

⇒ n = 44.

Hence, option 2 is the correct option.