Consider the following statements:

1) The number $N$ is divisible by 2.
2) The number $N$ is divisible by 4.
3) The number $N$ is divisible by 12.
4) The number $N$ is divisible by 24.

Three of these statements are true and one is false. Which one is the false one?
Solution

Notice that the numbers in the set $\{2,4,12,24\}$ are all divisors of 24. Therefore, if the last statement is true, all the other three will also be true. Thus, the false statement is the last one. An example of a number that satisfies the first three conditions of the problem but not the last one is the number 36.

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