Your reasoning is correct answer should be C, not E.

Is triangle ABC an isosceles?


(1) AB/BC = 2 --> \(AB\neq{BC}\). Not sufficient on its own.
(2) x≠y --> \(AB\neq{AC}\). Not sufficient on its own.

(1)+(2) Since \(AB\neq{BC}\) and \(AB\neq{AC}\), then the only way ABC to be isosceles is when \(AC=BC\). But in this case as given that AB=2BC then AB=BC+BC=BC+AC which is not possible because the length of any side of a triangle must be smaller than the sum of the other two sides. So, \(AC\neq{BC}\), which means that ABC is not isosceles. Sufficient.

Answer: C.
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Initially tricked upon thinking it is E. Thanks Bunuel for the explanation.

When considering the statements together the red scenario is not possible. If x=z then it would mean that AC=BC. But in this case as given that AB=2BC then AB=BC+BC=BC+AC which is not possible because the length of any side of a triangle must be smaller than the sum of the other two sides.
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can side AB=AC from 1st statement by making x=y?

Hi,

Basis Statement 1 alone: Given ratio of two sides of a triangle AB:BC as 2:1 and Triangle Inequality, how is it possible to create an isoslece triangle?

Please advice.

St 1

This statement just tells us that angle A = 2Y however we don't know for certain whether this is an isosceles because

2(50) + 50 + x =180
x =30

Or you could have an isosceles

2(45) + 45 +45 =180

But we can't make that decision unless we have more info

Insuff

St 2

Not necessarily

St 1 and St 2

If x cannot equal y then we cannot have an equilateral

C