Isoceles vs. equilateral triangle

[metallicafan]

In ISOCELES triangle MNP, MN = MP, and NP = 6. Which of the following could be the length of side MN?
I. 2
II. 6
III. 12
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

OA is D.

I don't agree with II. How can an isoceles triangle can be an equilateral at the same time? Ok, both have two sides equal, but I remember that an isoceles triangle MUST have a side unequal in comparison to the other two sides. So, strictly, an equilateral cannot be an isoceles. That's why I don't agree with II. The answer must be B.

Please, confirm whether I am ok.

[Anurag@Gurome]

How can an isosceles triangle can be an equilateral at the same time? Ok, both have two sides equal, but I remember that an isosceles triangle MUST have a side unequal in comparison to the other two sides. So, strictly, an equilateral cannot be an isosceles.

That's not true.
By definition, an isosceles triangle is that triangle which has two equal sides regardless of the length of the third side. Hence, all equilateral triangles are are isosceles triangles.