The values A,B,C, and [(A/B)+C], are all integers which are divisible by 3. Then, which of the following statements must be true:
A is divisible by 9
B is divisible by 9
C is divisible by 9
A and B are both divisible by 9
A,B,and C are all divisible by 9
?????
To solve this problem, we need to use the given information that A, B, C, and [(A / B) + C] are all integers divisible by 3.
Let's analyze each option:
A is divisible by 9:
We cannot necessarily conclude this. Keep in mind that A only needs to be divisible by 3, but not necessarily by 9.
B is divisible by 9:
We cannot necessarily conclude this. Just like A, B only needs to be divisible by 3, not necessarily by 9.
C is divisible by 9:
We cannot necessarily conclude this. Similar to A and B, C only needs to be divisible by 3, not necessarily by 9.
A and B are both divisible by 9:
This statement cannot be true, as we do not have enough information to determine the relationship between A and B regarding divisibility by 9. We only know that they are divisible by 3.
A, B, and C are all divisible by 9:
This statement must be true. To see why, let's consider [(A / B) + C]. Since [(A / B) + C] is an integer divisible by 3, both (A / B) and C must be integers divisible by 3.
If (A / B) is an integer divisible by 3, then A must also be divisible by 3. Furthermore, if C is an integer divisible by 3, A, B, and C are all divisible by 3.
Therefore, the correct answer is: A, B, and C are all divisible by 9.