Is m 0 ? (1) (m|n| - |mn|)/|m+n| 0

Question

Is  m > 0  ?

(1)  \frac{(m|n| - |mn|)}{|m+n|} < 0

(2)  |m + n| > 0

CrackverbalGMAT · Answer

We are trying to see if m is positive.

From statement I alone, we know that \(\frac{(m|n| - |mn|) }{ |m+n|}\) < 0.

|m+n| is always going to be positive since the output of a modulus is always positive. Because the denominator is positive and the overall fraction is negative, the numerator has to be negative.
-|mn| is negative since |mn| will be positive. If the entire numerator is negative, the other term i.e. m|n| should also be negative. This is only possible if m is negative since |n| is always positive.
From statement I alone, we can answer the question with a NO since m<0. Answer options B, C and E can be eliminated. Possible answer options at this stage are A or D.

From statement II alone, |m+n| > 0. This is clearly insufficient.
For example, if m = 10 and n= -5, |m+n| >0. In this case, m>0.
On the other hand, if m = -10 and n=5, |m+n|>0. In this case, m<0.
Since statement II alone is insufficient, answer option D can be eliminated.

The correct answer option is A.

In a question like this which involves absolute values, the fact that the output of a modulus is always positive, is something that you need to use extensively since the question is about positives and negatives.

Also note that a NO is as good as a YES in terms of an answer. So, do not try to prove a YES in a "YES-NO" DS question.

Hope that helps!

ajaygaur319 · Answer

Is m>0? Statement 1: (m|n|−|mn|) / |m+n|<0 ---(1) |m+n| is always positive, multiplying equation (1) with |m+n| both side: (m|n|−|mn|) < 0 By applying ( |mn| = |m||n| ) and taking |n| common: |n|(m - |m|) < 0 |n| is always positive (because it cannot be 0), hence m < |m| This can only happen if m is negative . Hence statement 1 - sufficient Statement 2 |m+n|>0 Here m can be positive, negative (Depending upon n) e.g. m = -4, n = 10 or m = 4, n = 10 Hence statement 2 is not sufficient Answer is (A)

hiranmay · Answer

Is m > 0 ? (1) \frac{(m|n| - |mn|)}{|m+n|} < 0 --> suff: (m|n| - |mn|)< 0 => |n|(m - |m|)< 0 => m < |m| => only possible if m <0 (2) |m + n| > 0 --> insuff: yes, if m=+1 & n=+2, but no, if if m=-1 & n=+2

MathRevolution · Answer

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. Visit https://www.mathrevolution.com/gmat/lesson for details. 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.

Is m > 0 ? (1) (m|n| - |mn|)/|m+n| < 0 (2) |m + n| > 0

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