Is the triangle in the attached picture isosceles?

Question

If a data sufficiency question about triangles asks whether a triangle is isosceles and in one of its two provisions mentions that two sides are equal, should we assume that the third side is unequal to the first two? In other words, the question is framed as follows:

1. a = b
2. c <> b

My answer would be E because a = b does not preclude b = c and hence that the triangle is equilateral. Though I agree that all equilateral triangles are isosceles in a sense, I do not assume GMAT will accept that 'sense.

Regards
Rahul

fluke · Answer

retro:
Is this an official Data Sufficiency question?

If yes, "A" should be sufficient.

I believe an equilateral triangle is a special type of isosceles. I am not 100% sure though.

Also,
Square is special rectangle
Square is special rhombus.

There may be more such cases.

I get a feeling that this question is meant more for the main Math forum(Intellectual Discussion) than an official "Data Sufficiency" question.

What do you say?

retro · Answer

The question comes into this list because it is a DS question. The concept is mathematical.

I'd disagree with the answer being A because IT DOES NOT PRECLUDE the third side also being equal.

I agree with you that I should go with answer C. My initial post had a typo.
It is not from the OG. It is from Nova's guide.

Regards
Rahul

fluke · Answer

Let me move it to the Data Sufficiency sub-forum and wait for others to respond.

What's the "OA"?

IanStewart · Answer

In contemporary mathematics, an equilateral triangle is normally considered to also be isosceles, in the same way that a square is considered to be a rectangle and a parallelogram. Euclid and other classical geometers, however, defined an isosceles triangle to be one with two equal sides and one unequal side. So there's no universal agreement about whether to consider an equilateral triangle to be isosceles. The GMAT simply can never test you on something that mathematicians cannot even agree about: many test takers could legitimately dispute the correct answer. This is the kind of technicality you'll never need to worry about, and you won't see a question like the one in the original post above on the real test.

ravsg · Answer

It should be A.

This link calls equi. as a special case of isosceles
https://library.thinkquest.org/20991/geo/ietri.html

Retro - why did you rule out C i.e both together are sufficient. Point 1 gives a relationship between two sides and point 2 provides information for the other two
A=B
B<>C
implies A<>C, so it is an isosceles tri.

retro · Answer

I am not ruling out C. In fact, that was my first choice but for a typo in my first post.

Rgds
Rahul

fluke · Answer

Please take a look at this Real GMAT question from the past. isosceles-triangle-96685.html GMAT does consider a triangle with at least 2 equal sides as isosceles.

Is the triangle in the attached picture isosceles?

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GMAT Data Sufficiency (DS) Questions

Is the triangle in the attached picture isosceles?

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615 to 715 in 15 Days (Ria's Strategies)

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