The key thing here is being aware that a triangle inscribed in a circle and having as one of its sides the diameter of a circle is always a right triangle.
So triangle BCD is a right triangle.
Statement 1 gives us the ratio of the lengths of the hypotenuse and of one side of a right triangle. 2:1. From here we can use to Pythagorean theorem to figure out that 2² - 1² = 4 - 1 = 3. So the hypotenuse and two sides have lengths in the ratio 2:√3:1.
This we can recognize as a 30 - 60 - 90 triangle, and since the shorter side is opposed to angle x, then x = 30.
So the answer to the question is yes and Statement 1 is sufficient.
Statement 2 tells us that y = 60, which means that triangle BCD is a 30 - 60 - 90 triangle, with x = 30. So once again the answer to the question is clearly yes, and Statement 2 is sufficient.
So each statement alone is sufficient and the answer is D.
