Data Sufficiency

Max@Math Revolution wrote:(ex 20) (inequality) Is m/n>0?

1) m + n > 0
2) mn > 0

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: https://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: B

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