What is a counterexample for the conjecture?
Conjecture: Any number that is divisible by 3 is also divisible by 6.
A: 12
B: 9
C: 26
D: 30
The counterexample for the conjecture is 26, which is not divisible by 6 but is divisible by 3. Therefore, the answer is C: 26.
To find a counterexample for the conjecture, we are looking for a number that is divisible by 3 but not divisible by 6.
A: 12 is divisible by both 3 and 6, so it is not a counterexample.
B: 9 is divisible by 3 but not by 6, so it is a counterexample.
C: 26 is not divisible by 3 or 6, so it is not a counterexample.
D: 30 is divisible by both 3 and 6, so it is not a counterexample.
Therefore, the counterexample for the conjecture is B: 9.
To find a counterexample for this conjecture, we need to look for a number that is divisible by 3, but not by 6.
A number is divisible by 3 if the sum of its digits is divisible by 3.
Let's consider the options given:
A: 12 - The sum of the digits of 12 is 1 + 2 = 3, which is divisible by 3. However, since 12 is also divisible by 2, it is divisible by 6 as well. So, this is not a counterexample.
B: 9 - The sum of the digits of 9 is 9, which is divisible by 3. However, since 9 is not divisible by 2, it is not divisible by 6. Therefore, 9 is a counterexample to the conjecture.
C: 26 - The sum of the digits of 26 is 2 + 6 = 8, which is not divisible by 3. 26 is also not divisible by 2, so it is not divisible by 6 either. However, it does not meet the first condition of being divisible by 3, so it is not a valid choice for a counterexample.
D: 30 - The sum of the digits of 30 is 3 + 0 = 3, which is divisible by 3. Additionally, since 30 is divisible by 2, it is also divisible by 6. So, this is not a counterexample.
Therefore, the counterexample for the conjecture is B: 9.