Consider the Question and two Statements given below :
Question : Is x an integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3x is an integer.
Which one of the following is correct in respect of the Question and the Statements?

Correct Answer: (D) Both Statement-1 and Statement-2 are not sufficient to answer the Question

From Statement 1 ($x/3$ is not an integer), $x$ could be an integer (e.g., $x = 1$) or a non-integer (e.g., $x = 0.5$). From Statement 2 ($3x$ is an integer), $x$ could be an integer (e.g., $x = 1$, giving $3x = 3$) or a non-integer (e.g., $x = 1/3$, giving $3x = 1$). Combining both statements, $x$ can still be an integer (e.g., $x = 1$, where $x/3 = 1/3$ is non-integer and $3x = 3$ is integer) or a non-integer (e.g., $x = 1/3$, where $x/3 = 1/9$ is non-integer and $3x = 1$ is integer). Hence, both statements together are insufficient to determine if $x$ is an integer.