Determining if x is a Positive Integer

Very Hard Data Sufficiency Determining Sufficiency

Let x be a real number. We want to determine if x is a positive integer.

Statement (1): The square of x is equal to 25.

Statement (2): The sum of x and 3 is greater than 8.

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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