Sum of Two Positive Integers

Hard Problem Solving Algebra

Let $x$ and $y$ be two positive integers. We want to know if it is true that the sum of these two integers is less than 30: $$x + y < 30$$

Given the following statements:

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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