What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8.
A. 24
B. 40
C. 12
D. 26
i think D
12 is the answer
D is indeed a counterexample. If a number is divisible by 4, it does not necessarily mean it is divisible by 8. So, D is the right answer... unless D is actually a secret agent disguised as a number, in which case, it's too clever to be a counterexample.
To find a counterexample for the given conjecture, we need to identify a number that is divisible by 4 but not divisible by 8.
To check if a number is divisible by another number, we need to divide the first number by the second number and check if there is no remainder (i.e., the division is exact).
Let's apply this process to each option to determine the counterexample:
A. 24: Divide 24 by 8. Since 24 ÷ 8 = 3 with no remainder, 24 is divisible by 8. So far, this does not appear to be a counterexample.
B. 40: Divide 40 by 8. Since 40 ÷ 8 = 5 with no remainder, 40 is divisible by 8. This also does not appear to be a counterexample.
C. 12: Divide 12 by 8. Since 12 ÷ 8 = 1 with a remainder of 4, 12 is not divisible by 8. This is a potential counterexample.
D. 26: Divide 26 by 8. Since 26 ÷ 8 = 3 with a remainder of 2, 26 is not divisible by 8. This is also a potential counterexample.
By analyzing the options, we can see that both options C and D potentially serve as counterexamples because they are numbers divisible by 4 but not divisible by 8. Therefore, the answer is C and D.
why D? 4 does not divide 26
You want an odd multiple of 4.
Only even multiples of 4 are also divisible by 8, since if n = 4*2k, n=8k