There are 30 two-digit numbers divisible by 3.
This can be solved using an arithmetic progression (AP) approach. The smallest two-digit number divisible by 3 is 12, and the largest is 99. These numbers form an arithmetic sequence with a common difference of 3.
- First term (a): 12
- Common difference (d): 3
- Last term (l): 99
We can use the formula for the nth term of an AP: l = a + (n-1)d, where 'n' is the number of terms. Solving for 'n':
99 = 12 + (n-1)3
87 = (n-1)3
29 = n-1
n = 30
Therefore, there are 30 two-digit numbers divisible by 3. This is confirmed by multiple sources, including Byju's (https://byjus.com/question-answer/how-many-two-digit-numbers-are-divisible-by-3-10/), LearnAtNoon (https://www.learnatnoon.com/s/in/how-many-two-digits-numbers-are-divisible-by-3/61575/), and others cited in the references. These sources corroborate the use of arithmetic progressions to efficiently determine the count.
