There are 30 two-digit numbers divisible by 3.
This can be determined in several ways:
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Arithmetic Progression: The two-digit numbers divisible by 3 form an arithmetic progression: 12, 15, 18, ..., 99. The first term (a) is 12, the common difference (d) is 3, and the last term (l) is 99. Using the formula for the nth term of an arithmetic progression, l = a + (n-1)d, we can solve for n (the number of terms): 99 = 12 + (n-1)3. Solving this equation gives n = 30.
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Direct Calculation: Starting from 12 and incrementing by 3, we can count the numbers up to 99. This method is straightforward but can be time-consuming for larger ranges.
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Using Divisibility Rules: A number is divisible by 3 if the sum of its digits is divisible by 3. While this rule doesn't directly give the count, it provides a quick way to check if any given two-digit number is divisible by 3. Many online resources confirm this count. (Byjus.com, LearnAtNoon.com, Unacademy) These sources explicitly state that there are 30 two-digit numbers divisible by 3.
Several sources (Byjus.com, LearnAtNoon.com, Unacademy) independently confirm the answer of 30 two-digit numbers divisible by 3. The provided Stack Overflow link (stackoverflow.com) and other references discuss divisibility rules for 3, further supporting the methodology used to arrive at the answer.
