Algebraic Inequality Comparison of Two Integers

Very Hard Problem Solving Algebra

Let x and y be two positive integers such that the following equation holds:

$$x^2 + y^2 = 100$$

Is it true that x is greater than y?

Statement (1): The value of x is 10.

Statement (2): The value of y is 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 (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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