Modulus question Quant

Question

Hi Sir,

I tried solving this question but did not get proper reason to eliminate. Could you please help me.

ArunSharma12 · Answer

I know this question is meant for some one else, just trying out my hand at this question.
let me know whether the logic below makes sense.

Given: m,n ≠ 0
m/n >0?
basically we need to find the sign of m and n.
if m & n have the same sign then m/n will be positive.

statement 1:
fraction is negative implies that numerator and denominator are of opposite signs.
denominator will always be positive as it is under mod, which will make numerator negative.
m|n|-|mn|<0
m|n|<|mn|
m|n|<0
m has to be negative but n can be positive or negative.
not sufficient

statement 2:
|m+n|= |m|+|n|
this is a property that states condition will always hold, if m & n have the same sign or at least one of them is 0.
we know m,n ≠ 0 thus m & n have same sign. could be (+,+) or (-,-) doesn't matter because the fraction will be positive in both cases.
sufficient

Ans: B

BijayKru · Answer

In statement 1

m |n| < |mn| —-> understood

But how you came to Know m|n| < 0. (Doubt) .

Posted from my mobile device

ArunSharma12 · Answer

That is a valid doubt. It is not very clear why |mn| will become 0 when it is given m,n ≠ 0. If you look at LHS and RHS, its the same numbers. only way LHS will be less than RHS is LHS becomes negative and RHS stays positive. This explains the negative sign of m|n| < 0. we can even try plugging some values to come to the same conclusion. img.png

CrackverbalGMAT · Answer

Hello Bijay,

ArunSharma12  has already done an exceptional job at explaining this question. I’ll try my best to not repeat things that he has already mentioned.

I want you to recall what we discussed when we took up this question in class. Question data says that neither m nor n can be zero. The question asks us whether m/n>0; in other words, it asks whether both m and n have the same signs.

Remember that I told you to test statement II alone first since that helps you eliminate certain answer options. 
Statement II alone is an identity on Modulus. As per statement II, m and n HAVE to be of the same signs to satisfy the equation |m+n| = |m| + |n|. 
Because statement II alone is sufficient, answer options A, C and E can be eliminated.

From statement I alone, m|n| - |mn| / |m+n| < 0. 
|m+n| is always positive since it’s a modulus. Because the denominator is positive, the numerator has to be negative.

The numerator has 2 components i.e. -|mn| and m|n|. 
-|mn| will definitely be negative. If the entire numerator has to be negative, m|n| also has to be negative. This can only happen when m is negative. Not sure?

Think about it – you are using the same values for m and n, you have the same product (of m and n) in both terms and the second term has a negative symbol – IF m is positive, the two terms will cancel out each other and numerator will become 0. If the numerator is 0, it invalidates the data given in statement I, isn’t it?

m HAS to be negative. However, we do not know anything about the sign of n.

Therefore, statement I alone is insufficient to determine if m and n are of the same signs. Answer option D can be eliminated. 
 The correct answer option is B .

Hope that helps!

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