Explanation

Statement (1) Factoring x^{2} − 15x + 50 = 0 gives us (x − 10)(x − 5) = 0. Since x could be 5 or 10, and we don't know y, this statement alone is insufficient.

The correct answer could be B, C, or E.

Statement (2) Subtracting 5 from both sides and factoring gives us y(y − 10) = 0. Since y could be 0 or 10, and we don't know x, this statement alone is insufficient.

The correct answer must be C or E.

Statement (1 & 2) Taken together, we have x = 5 or 10 and y = 0 or 10. Since the possible values for xy are 0, 50, or 100, the statements together are insufficient.

The correct choice is E.

The correct answer could be B, C, or E.

Statement (2) Subtracting 5 from both sides and factoring gives us y(y − 10) = 0. Since y could be 0 or 10, and we don't know x, this statement alone is insufficient.

The correct answer must be C or E.

Statement (1 & 2) Taken together, we have x = 5 or 10 and y = 0 or 10. Since the possible values for xy are 0, 50, or 100, the statements together are insufficient.

The correct choice is E.