Both the conditions are not sufficient to answer the question.

1st will give a+c =120
2nd will give a+c =2b

hence b=60
which does not tell whether triangle is isosceles or not.

Is the triangle depicted above isosceles? (Figure not necessarily drawn to scale.)

According to the OG an isosceles triangle has at least two sides of the same length.

a + b + c =180°

(1) 180° − (a + c) = 60° --> a + c =120° --> b = 60°. Now, if a = b = c = 60°, then the triangle is isosceles (equilateral) but if a = 100°, b = 60° and c = 20°, then the triangle is NOT isosceles. Not sufficient.

(2) a = 2b − c --> a + c =2b --> 2b + b = 180° --> b = 60°. The same as above. Not sufficient.

(1)+(2) Both statements provide with the same infor. Not sufficient.

Answer: E.

Notice that if we define an isosceles triangle as a triangle with exactly two equal sides (not the case for the GMAT) then the answer will be D.
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Why would the answer be D in that case Bunuel? None of the statements would be able to tell us the exact values for C or A. we would just know their sum to be 180....please point out the problem in my assumptions....

Ask yourself: do we need the angles to answer YES or NO to the question.
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I am sorry but I seem to miss something here.....to identify a triangle as an isosceles one, we either need to prove two sides equal or the opposite angles equal.....if yes then we do need the measure of individual angles

If we define an isosceles triangle as a triangle with exactly two equal sides (not the case for the GMAT) then the answer will be D, because from a + c =120° (b = 60°) we cannot have only two angles equal to each other, so the answer is NO the triangle is NOT isosceles.
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Right: The possibilities are either that 1) all the angles are 60 degrees, in which case the triangle is equilateral (which, according to the GMAT is also isosceles), or 2) all the angles are different, which is definitely not isosceles. With the GMAT definition, the OA should be E, but if we use the definition that isosceles triangles have EXACTLY TWO congruent sides, then either answer is sufficient to say NO.

Both the statements point towards saying that a+ 120 and b=60 hence no knowledge about whether a and b are isosceles.

This is an underrated post. Thanks Bunuel...I have always been under the impression that isosceles is EXACTLY two.
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