Data Sufficiency

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 equations ensures a solution.


If x^2 + y^2 =1, is x + y =1?
(1) xy =0
(2) y = 0

Since we have 2 variables (x,y) in the original condition, and 1 equation (x^2+y^2=1), we need 1 more equation to match the number of variables and since both (1) and (2) have 1 equations, D is likely the answer. Using (1) and (2) respectively, (2) itself already guarantees (1) as well thus if y = 0, x = -1 or 1,then x+y = -1 or 1, meaning both yes and no coexist. This is NOT sufficient, therefore the best answer is E.


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