Question

How many two-digits numbers are divisible by 3 ? (Topic : Arithmetic progressions)

Answer 1

Answer:

There are 30 two-digit numbers divisible by 3.

Step-by-step explanation:

All the two-digit numbers that are divisible by 3 is :

• 12, 15, 18, 21, 24, 27, 30, .., 99.

If we observe this carefully it resembles an A.P (Arithmetic progression).

So,

• First term (a) = 12
• Common difference (d) = 15 - 12 = 3

We know, general term of an A.P :

• Tₙ = a + (n - 1)d

Substituting :

• T₉₉ = a + (n - 1)d
• 99 = a + (n - 1)d
• 87 = (n - 1)3
• n - 1 = 87/3 = 29
• n = 30

∴ There are 30 two-digit numbers divisible by 3.

Answer 2

Please check in the attachment for the answer..