Target question: Is m/n > 0

Statement 1: m + n > 0
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of m and n that satisfy statement 1. Here are two:
Case a: m = 1 and n = 1, in which case m/n = 1/1 = 1 and 1 > 0. So, m/n > 0
Case b: m = -1 and n = 2, in which case m/n = (-1)/2 = -0.5 and -0.5 < 0. So, m/n < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: mn > 0
If mn is positive, then there are two possible scenarios:
Scenario #1: m and n are both POSITIVE
Scenario #2: m and n are both NEGATIVE
In scenario #1, m/n = POS/POS = POS.
In scenario #2, m/n = NEG/NEG = POS.
So, in both possible scenarios, m/n > 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

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Hi

One way would be to test values as Gmatprepnow has done...
The other way would be..

When can m/n be positive?
When both m and n are of same sign------ either both positive both negative..
If we can FIND the relative sign of m and n, we can answer the Q..
A) if same sign .. ans is YES
B) if opposite sign, ans is NO

Let's see the statements
1) m+n>0..
Both m and n van be positive.. 4+2>0
Both can be opposite sign.. 4 and -2.. 4+(-2)>0
So insuff as we cannot answer " are the signs same?"

2) mn>0..
Clearly both have to be same sign
Both positive 4*2>0..ans YES
Both negative (-4)*(-2)=8>0.. again YES
Suff

B
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==> If you change the original condition and problems, in the case of sign of inequality, squaring is the most important thing because squaring never changes the direction of the sign of inequality even if it’s divided or multiplied since any number squared is a positive number. Hence, if you multiply n^2 by both sides, you get n2(m/n)>n2*0? --> mn>0?. Therefore, the answer is B.
Answer: B
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evaluating the positive and negative number relationship
Statement 1
M+N>0 is m/n>0
if -m,n no
if m,-n no
if m,n yes
insufficient

Statement 2
MN>0 is m/n>0
if -m,-n Yes
if -m,n Not possible
if m,n Yes
if m,-n Not possible

Sufficient

Ans B

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