Data Sufficiency: Positive Variables and Their Sums

Very Hard Data Sufficiency Determining Sufficiency

Let $x$, $y$, and $z$ be real numbers. We want to determine whether the equation $x + y + z = 30$ can be satisfied for positive values of $x$, $y$, and $z$.

Statement (1): $x + y = 10$.

Statement (2): $yz = 200$.

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 (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

Hint

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