Is rectangle ABCD a square?

Bunuel
The statement 2 will not hold in any case. If statement 2 is what it is given in the question, then the answer will be E.

But, I guess Statement 2 would be AC is perpendicular to BD rather than CD. That will be more logical and then the correct answer would be B because "if the diagonals of a rectangle are perpendicular to each other then it is a square."

Yes, it should have been BD. Edited. Thank you.

St.1 says that AB or BC are not diagonals. Further, we can make out that AC and BD are diagonals.
But all rectangles are not square. Therefore,

Insufficient

St.2 All squares are rectangles but all rectangles are not squares. A rectangle is also a square when the diagonals of the rectangle intersect each other at right angles (remember both diagonals of a rectangle are deemed to be congruent. So we don't need to prove this property of a square). This option says this.

Now here is the tricky part.

I am tempted to pick B for this as from the stem it is obvious that all the angles of ABCD are right. St 1 states something redundant (I agree with 14101992 on this one). The only thing that St 1 establishes (by a stretch of imagination) is the order of the points on the rectangle. But we can even make out from St 2 that AC and BD are perpendicular, for on a rectangle 2 sides, which are perpendicular, will be adjacent and will have a point common.

There are GMAT questions which have redundant/obvious statements.

Really? This is certainly a learning. In such a case should we be picking C then?

AmoyV
You should pick C or E only when both Statement 1 and Statement 2 alone are insufficient. In this question, Only statement 2 is sufficient. Hence, answer should be B.

RECTANGLE ABCD means all the angles are 90 degree, so we do not need option A. if a quadrilateral is both rhombus and rectangle then it has to be a square. now that we know ABCD is rectangle. choice B tells that diagonals are perpendicular. this means ABCD is a rhombus too. hence ABCD is square. option B is correct.