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.
Is |x + y| > |x - y| ?
(1) |x| > |y|
(2) |x - y| < |x|
First we need to modify the original condition and the question. Since an absolute value is always a positive number, we can square each side. Then, the original question, which asks if |x + y| > |x - y| is true, can be changed, and we can see how the question is asking if |x + y|^2 > |x - y|^2 is true. Squaring an absolute value and squaring just the value yield the same result. Therefore, we can further modify the question to (x + y)^2 > (x - y)^2? Then, we get x^2+2xy+y^2>x^2-2xy+y^2? We can simplify the question further to 4xy>0? So, we can see, essentially, the question is asking if xy>0 is true.
In the case of the condition 1), since it states |x|>|y|, it does not prove if xy>0.
In the case of the condition 2), we can see that |x-y|<|x|=|x-0|. This means that the absolute difference between x and y is less than that of between x and 0. In order to satisfy this condition, we need xy>0. The answer is ‘yes’ and the condition is sufficient. Therefore, the correct answer is B.
Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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