Question

How many two-digit numbers are divisible by 3?

Class 10

Arithmetic Progressions

Answer 1

⇒ The first two-digit number divisible by 3 is 12.

⇒ The last two digit number divisible by 3 is 99.

Here,

⇒ First term a = 12.

⇒ Common difference d = 3.

⇒ Last term an = 99.

We know that nth term of an AP is an = a + (n - 1) * d

⇒ 99 = 12 + (n - 1) * 3

⇒ 99 = 12 + 3n - 3

⇒ 99 = 3n + 9

⇒ 90 = 3n

⇒ n = 30.

Therefore, the number of two-digit numbers divisible by 3 = 30.

Hope this helps!

Answer 2

Answer:

So the first two digit number divisible by 3 is 12. And the last two digit number divisible by 3 is 99. So we must find the number of terms in between these two numbers that are divisible by 3.

=> a = 12, d = 3, l = 99, n = ?

=> 99 = 12 + ( n - 1 ) 3

=> 99 - 12 = ( n - 1 ) 3

=> 87 = ( n - 1 ) 3

=> 87 / 3 = ( n - 1 )

=> 29 = ( n - 1 )

=> n = 29 + 1 = 30

Hence there are 30 two digit numbers divisible by 3.