Question

How many two-digit numbers are divisible by 3?

• A. 30
• B. 35
• C. 40
• D. 45

Answer 1

The Correct Option is A

To solve the problem, we need to count how many two-digit numbers are divisible by 3.

1. Identifying the Range:
Two-digit numbers range from 10 to 99.

2. Finding the First and Last Two-Digit Numbers Divisible by 3:
First two-digit number divisible by 3 = 12
Last two-digit number divisible by 3 = 99

3. Applying the Arithmetic Progression (AP) Formula:
This forms an AP where:
First term, $a = 12$
Last term, $l = 99$
Common difference, $d = 3$

4. Using the AP formula:
The number of terms in an AP is given by:

$ n = \frac{l - a}{d} + 1 $

Substitute values:
$ n = \frac{99 - 12}{3} + 1 = \frac{87}{3} + 1 = 29 + 1 = 30 $

Final Answer:
The number of two-digit numbers divisible by 3 is 30.