(1) x not equal to y
--->Its obviously insufficient..as you dont know about 3rd angle.
(2) AB / BC = 2
-->Assume AB = AC , this could be a possible is a isosceles triangle .
-->Also a triangle where,lets say AB = 2 unit , BC = 1 unit and AC = 1.5 unit is also possible .
So 2 different possibilities , hence insifficient
Combining , lets try to consider any case for isosceles and see if it works
.
Isosceles cases could 2 only , as AB = BC is ruled out based on stmnt (2) as AB = 2 BC
a) BC = AC
b) AB = AC ( This case also you can drop as stmnt (1) tells you AB is not equal to AC )
Now case (a) , lets assume BC = AC = m and AB = 2m.
Is this triangle possible , no not all . The Reason is it violates the triangle property . The third side always got be less than sum of other 2 sides and is always greater than difference of other 2 sides
Here AB = sum of other 2 sides .is equal to sum of BC and AC..So this case doesnt hold true. Ruled out
Thus with 2 stmnts we know for sure its not a isosceles triangle
