23a2012 wrote:

Why the above question has the answer E while the below question has the answer D?Where I can understand the difference between option B in the both question from Bunuel clarification but I did not see any difference in the option A between both qouestion so why option A is incorrect in the above question while it is correct in the below question?

Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD

In the Kite as

Bunuel explained notice that only one diagonal is bisected while the other is not while in rhombus/square both diagonals are bisected(since, square is a special case of rhombus). So, (1) is sufficient. As far (2) is concerned it has to be rhombus any quadrilateral having equal sides is a rhombus & hence, (2) is sufficient as well.