Which of the following is a divisibility rule for 3?

• A. The last digit is 0
• B. The sum of digits is divisible by 3
• C. The number ends with 9
• D. The number is even

Answer: (B)

Divisibility by 3 is determined by the sum of the digits. In base 10, 10 ≡ 1 (mod 3), so a number N = d_k...d_1d_0 satisfies N ≡ sum of its digits (mod 3). Therefore, N is divisible by 3 exactly when the sum of its digits is divisible by 3. For example, 123 has digits 1, 2, and 3; their sum is 6, which is divisible by 3, so 123 is divisible by 3. Conversely, 109 has digit sum 1 + 0 + 9 = 10, which is not divisible by 3, so 109 is not divisible by 3. The other statements don't test divisibility by 3—they relate to divisibility by other numbers (such as 10 or 2).