J2S2019 wrote:
Is \(m > 0\) ?
(1) \(\frac{(m|n| - |mn|)}{|m+n|} < 0\)
(2) \(|m + n| > 0\)
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.
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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
Condition 1)
\(\frac{m|n| - |mn| }{ |m+n|} < 0\)
⇔ \(m|n| - |mn| < 0\) since \(|m+n|>0\)
⇔ \(m|n| - |m| \cdot |n| < 0\)
⇔ \(m|n| - |mn| < 0\)
⇔ \(|n|(m - |m|) < 0\)
⇔ \(m - |m| < 0\)
⇔ \(m < |m|\)
⇔ \(m < 0\)
The answer is 'no'.
Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, both conditions are sufficient, when used together.
Condition 2)
\(m = 2, n = 1\) and \(m = 2, n = -1\) are possible values of \(m\) and \(n\).
If \(m = 2, n = 1\), then we have \(m > 0\) and the answer is 'yes'.
If \(m = 2, n = -1\), then we have \(m < 0\) and the answer is 'no'.
Since condition 2) does not yield a unique solution, it is not sufficient.
Therefore, A is the answer.
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