Analyzing Integer Solutions in Modular Arithmetic

Very Hard Data Sufficiency Analyzing Information

Let $p$ be a positive integer. We are interested in finding whether the equation $p = 3k + 2$ has a solution where $k$ is a non-negative integer.

Statement (1): $p$ is an odd integer.

Statement (2): $p ext{ mod } 3 = 2$.

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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