Determine if a Positive Integer is a Perfect Square

Hard Data Sufficiency Analyzing Information

Let $x$ represent a positive integer. We want to determine whether $x$ is a perfect square.

Statement (1): The cube root of $x$ is a positive integer.

Statement (2): The square of the integer value obtained from the cube root of $x$ is equal to $x$.

Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but Statement (1) alone is not sufficient.

Both statements together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

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