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(1) X does not equal Y --> angles at the side BC are not equal --> \(AB\neq{AC}\), but the third side, BC, can be equal to either of them. Not sufficient.

(2) AB/BC=2 --> AB=2BC --> \(AB\neq{BC}\), but AB can be equal to AC. Not sufficient.

(1)+(2) As \(AB\neq{AC}\) and \(AB\neq{BC}\) then the only way triangle ABC to be an isosceles is AC to be equal to BC, but in this case AB=2BC=2AC=BC+AC --> but the length of any side of a triangle must be smaller than the sum of the other two sides, so AB must be less than BC+AC, hence the case when AC=BC is not possible: triangle ABC is not isosceles. Sufficient.

(1) X does not equal Y --> angles at the side BC are not equal --> , but the third side, BC, can be equal to either of them. Not sufficient.

Tells us nothing. X ≠ Y but the third angle could equal x or y in which case the triangle would be isosceles or the third angle would = w in which case the triangle would not be isosceles. Insufficient.

(2) AB/BC=2

The length of AB is twice the length of BC but we don't know anything about side AC. Insufficient.

1+2) The only way for this triangle to be isosceles is if a.) AC = BC or b.) AB = AC. Neither of these outcomes are possible. If AC = AB then a triangle wouldn't be possible. In any triangle, the sum of two legs must be greater than the third. If AC = BC then the formula for the triangle would be 2BC = BC + BC which isn't possible. We also know that AC ≠ AB because the angles opposite them, x and y respectively, do not equal one another. Thus, AC cannot = AB and AC is a different length than AB. This triangle CANNOT be isosceles. SUFFICIENT.

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Bunuel Statement 2 says AB=2BC. Lets say BC=x then, AB=2x. Thus, the third side has to be less than x and greater than 3x. So the triangle can't be isosceles. Please clarify...

Bunuel Statement 2 says AB=2BC. Lets say BC=x then, AB=2x. Thus, the third side has to be less than x and greater than 3x. So the triangle can't be isosceles. Please clarify...

Why not? The third side can have the length of 2x. For example, you can have an isosceles triangle with sides 1, 2, and 2.
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Bunuel Statement 2 says AB=2BC. Lets say BC=x then, AB=2x. Thus, the third side has to be less than x and greater than 3x. So the triangle can't be isosceles. Please clarify...

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Thus, if the length of two sides are x and 2x, then:

Bunuel Statement 2 says AB=2BC. Lets say BC=x then, AB=2x. Thus, the third side has to be less than x and greater than 3x. So the triangle can't be isosceles. Please clarify...

Hi NehaBhargava

If BC = x and AB = 2x, the third side has to be LESS than 3x (the sum of two sides is greater than the 3rd side in a triangle) The third side can still be equal to 2x, so this statement is not sufficient.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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