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Which of the following statements is false?

1. There exists a natural number which when divided by 3 leaves remainder 1 and which when divided by 4 leaves remainder 0
2. There exists a natural number which when divided by 6 leaves remainder 2 and when divided by 9 leaves remainder 1
3. There exists a natural number which when divided by 7 leaves remainder 1 and when divided by 11 leaves remainder 3
4. There exists a natural number which when divided by 12 leaves remainder 7 and when divided by 8 leaves remainder 3

A. One such number is $4$.
C. $36$ satisfies those conditions.
D. Smallest such number is $19$.

Option B is not possible.

$6 = 3 \times 2\\9 = 3 \times 3$

So, if a number $n$ is divisible by $9$, then it is either divisible by $6$, or leaves a remainder of $3$ when divided by $6$.

Hence, option B is our answer.

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