Absolute values(Data Sufficiency)

yeah its not an official one, its one from crack verbal class lectures.I think the answer should be B.
I solved it by picking nos. strategy-

Question- mn ≠ 0, is m/n>0?(the question is asking whether both M and N are positive or both M and N are negative)?
I. (m|n|-|mn|)/(|m+n|)<0

First I picked up nos. for M and N that would satisfy the above inequality and next I tested whether M/N>0 or not?
If I pick M=-2 and N=3, the answer to- Is M/N>0?,would be No, but if I picked
M=-2 and N=-3, the answer to Is M/N>0?,would be YES.HENCE INSUFFICIENT.

II.|m+n|=|m|+|n|
Now analysing statement 2, we see in order to fulfil this statement, either M and N should both be positive or M and N should both be negative.
which means M/N will always be greater than 0.You can also check by picking Nos. for example (m=-2,n=-3, which gives M/N>0)or(m=2 and N=3, which also gives M/N>0).HENCE SUFFICIENT.

So the answer should be B.Please correct me if I am wrong?

Hello Shreya,

There's a specific concept about Absolute values being tested on this question. And that concept is,

|m+n| ≤ |m| + |n|. The two sides will be equal only when both m and n are of the same signs i.e. either both m and n are positive or both m and n are negative.

If you observe the question, that’s exactly what the question is asking you, by asking you if \(\frac{m}{n}\)>0. \(\frac{m}{n}\) can be more than 0 only when both m and n are of the same signs.

This much of analysis of the question stem helps us understand that statement II alone is clearly sufficient, since, as we discussed, |m+n| = |m| + |n| only when both m and n are of the same signs.

The possible answers are B or D. Answer options A, C and E can be ruled out.

With statement I alone, you need to analyse a bit more. The expression given in statement I is:

\(\frac{m|n|-|mn|}{|m+n|}\)<0. This says that the expression on the LHS is negative. The denominator |m+n| will always be positive. This means that the numerator has to be negative so that the entire expression becomes negative.

In the numerator, -|mn| will be negative; m|n| should also be negative so that the entire numerator becomes the addition of two negative numbers, eventually resulting in a negative number. From this, we can only conclude that ‘m’ HAS TO BE negative.

However, ‘n’ can still be positive or negative. If n is positive, then \(\frac{m}{n}\)>0; but, if n is negative, \(\frac{m}{n}\) < 0. No unique YES or NO when we use statement I alone. Therefore, statement I alone is insufficient.
Since statement I alone is insufficient, answer option D can be eliminated. The correct answer option is B.

When you have a leading clue in statements, the question is actually pointing you to go in that direction. In this question, statement II was clearly a huge clue, but only if you knew your concepts well.

Else, you would end up trying values like you did. The problem with trying values in difficult Inequalities questions is that they can go both ways – they can lead you to the right answer sometimes, but can also end up confusing you if you have not taken the right set of numbers.

Hope this helps!