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For a quadrilateral to be a square, all the four sides have to be equal and all the interior angles must be 90 degrees.

Statement (1): Can't be sure. The other two angles may both be 90 degrees or not.
INSUFFICIENT.
Statement (2): Can be any quadrilateral.
INSUFFICIENT.

Let's try to combine the two statements.
Draw a figure with AB=BC=CD and AB perpendicular to BC and BC perpendicular to CD.


You will notice that:
(i) AD is parallel to BC
(ii) AD = BC

That is, the fourth side has no choice but to be joined in a way so that ABCD forms a square.


(C) is the answer.

Let's modify the question a little bit?

modified Q1: (the modification is made bold)

Is ABCD Square?

I. Angle A and Angle C are right angles.

II. AB=BC=CD

modified Q2: (the modification is made bold)
Is ABCD Square?

I. Angle B and Angle C are right angles.

II. AB=CD

modified Q3: (the modification is made bold)
Is ABCD a Rectangle?

I. Angle B and Angle C are right angles.

II. AB=CD

Note: Keep making slight modifications to the problem and solving it. It's a great way to learn. You can seek the support of experts here in verifying your answers.

_________________
Aneesh Bangia
GMAT Math Coach
aneesh.bangia@gmail.com

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