There are 3000 four-digit numbers divisible by 3.
Understanding the Solution
This problem can be solved using a simple arithmetic approach. There are 9000 four-digit numbers (from 1000 to 9999). Every third number is divisible by 3. Therefore, the number of four-digit numbers divisible by 3 is 9000 divided by 3.
- Calculation: 9000 / 3 = 3000
Further Insights from References
Multiple sources confirm this solution. For instance, the Quora answer (https://www.quora.com/How-many-4-digit-numbers-are-divisible-by-3) directly states that "Every 3rd number is divisible by 3, and since there are 9000 4 digit numbers, there must be 9000/3 = 3000 numbers divisible by 3." Other references, while addressing related problems like finding four-digit numbers divisible by 3 and ending in 23 (https://artofproblemsolving.com/wiki/index.php/2003_AMC_10B_Problems/Problem_25), or focusing on palindromes divisible by 3 (https://math.stackexchange.com/questions/2670602/how-many-4-digit-palindromes-are-divisible-by-3), implicitly support the basic principle used to arrive at the answer.
Example
The first few four-digit numbers divisible by 3 are 1002, 1005, 1008, and so on.
