Which number can be used as a counter example to, "Any number that is divisible by 3 is divisible by 9"?
a)9, b)18, c)30, d)40
Can you explain me the answer how do you get it? because I don't understand about counter examples. Thanks
Study this site for an explanation of counter example.
http://www.icoachmath.com/math_dictionary/Counter_Example.html
Now, looking at your answer choices.
9 is divisible by both 3 and 9
18 is divisible by both 3 and 9
30 is divisible by 3 -- but NOT by 9
To find a counterexample to the statement "Any number that is divisible by 3 is divisible by 9," we need to find a number that is divisible by 3 but not by 9.
We can use the answer choices (9, 18, 30, 40) to test each number and see if it meets the criteria.
Starting with choice a) 9, we know that 9 is divisible by 3. However, to determine if it is divisible by 9, we divide 9 by 9 and check for a remainder. If there is no remainder, then 9 is divisible by 9. In this case, 9 divided by 9 equals 1 with no remainder, so 9 is indeed divisible by 9.
Next, let's try choice b) 18. Similar to the previous step, we divide 18 by 9. If there is no remainder, then 18 is divisible by 9. When we calculate 18 divided by 9, we find that it equals 2 with no remainder. This means 18 is divisible by 9.
Moving on to choice c) 30, we follow the same process and divide 30 by 9. After performing the division, we get 30 divided by 9 equals 3 with a remainder of 3. Since there is a remainder, this tells us that 30 is not divisible by 9.
Finally, let's check choice d) 40. Dividing 40 by 9 gives us 40 divided by 9 equals 4 with a remainder of 4. Once again, we see that there is a remainder, indicating that 40 is not divisible by 9.
Based on these calculations, choice c) 30 is the number that is divisible by 3 but not by 9. Therefore, it serves as the counterexample to the statement.