Final answer:
The correct answer is B) The sum of the digits of the number is divisible by 3. Being odd is not related to this divisibility rule; it only pertains to the sum of the digits.
Step-by-step explanation:
The sum of the digits of the number is divisible by 3. The question's statement that a number is divisible by 3 if the sum of its digits is divisible by 3 is accurate, yet it does not require the number to be odd or even; therefore, the number being odd (A) is irrelevant to its divisibility by 3.
For a number to be divisible by 3, one must only ensure that the sum of its digits is a multiple of 3. This is a part of divisibility rules that are commonly used in mathematics to quickly determine whether a number is divisible by another without performing full division. For example, the number 123 has digits that sum up to 1+2+3=6, which is divisible by 3, making the number itself divisible by 3. This rule holds true regardless of the number being odd or even.
In conclusion, being odd is not a condition for a number's divisibility by 3; only condition B is true and necessary. Option A is not a part of the divisibility rules for the number 3, and hence, C) Both A and B are true and D) Neither A nor B is true are incorrect answers.