What is a counterexample of the following conjecture?

Conjecture: Any number that is divisible by 3 is also divisible by 6

36
27
23
18

Is it C, 23? A little confused:p Please help? Thanks

no, because 23 is not divisible by 3!

You want B, because 27 is divisible by 3, but not divisible by 6.

Ah, ok, thanks Steve. I got confused to what exactly counterexample meant in this.

Hey there! Let's tackle this question with a little humor, shall we?

Well, to find a counterexample, we need to look for a number that is divisible by 3 but not by 6. We don't want to get into a mathematic mess, so let's keep it simple!

Out of the options given, the number 23 stands out like a clown in a library! Why? Well, 23 is indeed divisible by 3 (because 23 divided by 3 is 7 with a remainder of 2). However, it is not divisible by 6, as 23 divided by 6 equals 3 with a remainder of 5. So, 23 does the trick, making option C the correct answer!

Remember, math may not always be a barrel of laughs, but with a little humor, we can make it more fun! Hope that clears things up for you. Keep those questions coming!

To find a counterexample for the conjecture "Any number that is divisible by 3 is also divisible by 6," we need to identify a number that is divisible by 3 but not divisible by 6.

Out of the given numbers, let's check if any of them are divisible by 3 but not by 6:

- 36 is divisible by both 3 and 6, so it does not serve as a counterexample.
- 27 is divisible by 3, but it is also divisible by 3 twice, which means it is divisible by 6 as well. Therefore, it is not a counterexample.
- 23 is not divisible by 3, so it is not a counterexample.
- 18 is both divisible by 3 and 6, as 6 is a multiple of 3.

Since none of the given numbers are divisible by 3 but not by 6, there is no counterexample to this conjecture among the options you provided.

To find a counterexample for the given conjecture, we need to find a number that is divisible by 3 but not by 6.

One way to do this is to check if the number is divisible by 3 first, and then check if it is divisible by 6. If it is divisible by 3 but not by 6, then it is a valid counterexample.

Let's go through the options to determine which one is a counterexample:

Option A: 36
To check if 36 is divisible by 3, we divide it by 3. 36 ÷ 3 = 12. Since the quotient is a whole number, 36 is divisible by 3.
Now we divide 36 by 6. 36 ÷ 6 = 6. Again, the quotient is a whole number, so 36 is divisible by 6 as well. Therefore, 36 is not a counterexample.

Option B: 27
To check if 27 is divisible by 3, we divide it by 3. 27 ÷ 3 = 9. Since the quotient is a whole number, 27 is divisible by 3.
Now we divide 27 by 6. 27 ÷ 6 = 4.5. Since the quotient is not a whole number, 27 is not divisible by 6. Therefore, 27 is a counterexample.

Option C: 23
To check if 23 is divisible by 3, we divide it by 3. 23 ÷ 3 = 7.67. Since the quotient is not a whole number, 23 is not divisible by 3. Therefore, 23 is not a counterexample.

Option D: 18
To check if 18 is divisible by 3, we divide it by 3. 18 ÷ 3 = 6. Since the quotient is a whole number, 18 is divisible by 3.
Now we divide 18 by 6. 18 ÷ 6 = 3. Again, the quotient is a whole number, so 18 is divisible by 6 as well. Therefore, 18 is not a counterexample.

Finally, we see that option B, 27, is the counterexample. This number is divisible by 3 but not by 6, contradicting the conjecture that any number divisible by 3 is also divisible by 6.