Statement-1 Alone: If $x/3$ is not an integer, it means that $x$ is not divisible by 3. This information tells us that x is not a multiple of 3, but it doesn’t indicate whether x itself is an integer. For example, x could be a fraction like $5/2$, which is not divisible by 3, or an integer like 5, which is also not divisible by 3. Conclusion: Statement-1 alone is insufficient to determine if x is an integer.

Statement-2 Alone: If $3x$ is an integer, this means x could either be an integer or a fraction with a denominator that divides 3 (like $x = 1/3$). Conclusion: Statement-2 alone is also insufficient to determine if x is an integer.

Using Both Statements Together: x could be $5/2$, satisfying both statements since $(5/2)/3$ is not an integer (Statement-1), and $3 \times (5/2) = 15/2$, which is not an integer (Statement-2). Alternatively, x could be 5, which is an integer, also satisfying both statements. Conclusion: Even with both statements combined, we cannot determine if x is definitively an integer.