What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 3 is also divisible by 6.
A 30
B 26
C 12
D 9
The counterexample for the conjecture "Any number that is divisible by 3 is also divisible by 6" is option B: 26.
26 is divisible by 3 since 26 divided by 3 equals 8 remainder 2. However, 26 is not divisible by 6 since 26 divided by 6 equals 4 remainder 2.
To find a counterexample for the conjecture that any number divisible by 3 is also divisible by 6, we need to find a number that is divisible by 3 but not by 6.
Option D, 9, is a counterexample to the conjecture. 9 is divisible by 3 because 9 divided by 3 equals 3. However, it is not divisible by 6 because 9 divided by 6 gives a remainder of 3.
Therefore, the correct answer is D) 9.
To find a counterexample for the conjecture, we need to find a number that is divisible by 3 but not divisible by 6. Let's go through the answer choices given:
A) 30: This number is divisible by both 3 and 6, so it does not serve as a counterexample.
B) 26: This number is not divisible by 3, so it does not serve as a counterexample.
C) 12: This number is divisible by both 3 and 6, so it does not serve as a counterexample.
D) 9: This number is divisible by 3 but not divisible by 6. Therefore, 9 serves as a counterexample to the conjecture.
The correct answer is D) 9. A number that is divisible by 3 may not necessarily be divisible by 6, which is why this conjecture is false.