BPHASDEU wrote:
Is \((|x^{-1}y^{-1}|)^{-1}> xy\)?
(1) xy > 1
(2) x^2 > y^2
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
\((|x^{-1} y^{-1}|)^{-1} > xy\)
\(⇔ |1/(xy)|^{-1} = > xy\)
\(⇔ |xy| > xy\)
\(⇔ xy < 0\)
Condition 1) : \(xy > 1\)
Since \(xy > 1\), \(xy\) is positive. Thus \(xy < 0\) is false and the answer is "no".
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, the condition 1) is sufficient, when used together.
Condition 2) \(x^2 > y^2\)
If \(x = 2\), \(y = -1\), then \(xy < 0\). The answer is "yes"
If \(x = 2\), \(y = 1\), then \(xy > 0\). The answer is "no".
Since we don't have a unique solution, the condition 2) is not sufficient.
Therefore, A is the answer.
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