Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180

Statement 1: All sides can be equal in a rhombus as well as a square. This statement is insufficient. A square can be a special type of rhombus but vice versa is not true. With this given condition had the question asked if the quadrilateral is a rhombus, then the answer would have been "yes".

Statement 2: Sum of adjacent angles is equal to 180 degrees in a rectangle rhombus and square. Insufficient.

Together also, the quadrilateral can be either a square or rhombus. hence, insufficient. E.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

A quadrilateral has 5 variables by VA method.

Since we have 3 equations from the condition 1) and we have 1 equation from the condition 2), both conditions together are not sufficient.

E is the answer.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.

From (1) It can be a rhombus or square, hence NS (BCE can be the ans)
From (2) x+y=180 ( multiple values of x and y can satisfy this), hence NS (CE can be the ans)

From (1) & (2); we cannot conclude that any of the angle is a right angle, even when all sides are equal and hence E.

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