Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the area of square ABCD?

(1) The diagonal of square ABCD is 5 √2

(2) The perimeter of square ABCD is 20

In the original condition, there is 1 variable(one side of square: x) for square, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. In fact, it is 99% that D is the answer.

For 1), from √2(x)=5√2, x=5, which is unique and sufficient.

For 2), from 4x=20, x=5, which is unique and sufficient.

Therefore, the answer is D.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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