Is quadrilateral ABCD Square?

[bellcurve]

Q: Is quadrilateral ABCD Square?

I. Angle B and Angle C are right angles.

II. AB=BC=CD

Please provide and explanation!

[Bill@VeritasPrep]

To be a square, ABCD must have 4 right angles and 4 equal sides.

1. B and C are right angles, so it could be a square, but it could also be a rectangle. Insufficient.

2. ABCD has 3 equal sides, so it could be a square, it could also be a rhombus. Insufficient.

Combined, the only quadrilateral that meets both conditions is a square. Sufficient.

[bellcurve]

Why don't we have to conside self intersecting quadrilateral in this case (like the forth one in the pic)? If we draw a self intersecting quadrilateral, then we can have one that satisfies stmts I and II and still not a square.

[Bill@VeritasPrep]

I have never seen a GMAT question involving complex (self-intersecting) polygons, and in any event I don't you could draw one where we had three equal sides and two right angles formed by those three equal sides.

[bellcurve]

This is what I am talking about.

Isn't this picture satifies all the conditions?

[Bill@VeritasPrep]

It does, but again, I do not believe complex polygons are tested. What is the OA?

[bellcurve]

The OA is C and that is why I got confused. Unless you make the assumption that complex quadrilaterals are excluded from the picture, you have to go with E.

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The OA has to be a C. In the concepts, under the chapter Quadrilaterals, such complex quadrilaterals are not in the portion. I know that the GMAT is famous for breaking its own rules and asking questions out of syllabus, but it will not go so out of the box.