Determine the Value of x + y Given Two Statements

Very Hard Problem Solving Arithmetic

Let $x$ and $y$ be two positive integers.

1. The sum of $x$ and $y$ is 30.

2. The product of $x$ and $y$ is 200.

What is the value of $x + y$?

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.

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