gmatbusters' challenge questions

Explanation:

St1: x=4
As we know for any isosceles triangle, the third vertex C would lie on the perpendicular bisector of AB.
Hence x = (-2+8)/2 =3.
So it is sufficient to so that it is not an equilateral triangle.

St2: x and y are coprime. this means x and y are integers.
Now we know that " A triangle having all integral coordinates (even rational vertices) can never be an equilateral triangle"
So it is sufficient to so that it is not an equilateral triangle.

hence Answer is D

(PS: proof: A triangle having integral coordinates can never be an equilateral triangle : Using contradiction. At first take that we have a triangle with integral coordinates then find its area by the determinant method ,where you would get an rational solution. Then find the area by the formula of area of equilateral triangle(i.e.,area=(√3÷4)×a²). Here you would get an irrational solution. TNow, you get two different areas for the same triangle.proved by contradiction.)- this is only for those who are interested in proof.