Is v − w < 0? (1) v − 2w < 0 (2) 5w − v < 0

Thanks Vishal .. it was a typo corrected it.

I think you reversed the sign. According to statement 2: v>5w.

Target question: Is v − w < 0?
This is a good candidate for rephrasing the target question.
Take: v − w < 0
Add w to both sides to get: v < w
REPHRASED target question: Is v < w?

Statement 1: v − 2w < 0
Let's TEST some values.
There are several values of v and w that satisfy statement 1. Here are two:
Case a: v = 0 and w = 1. In this case, the answer to the REPHRASED target question is YES, it is true that v < w
Case b: v = 3 and w = 2. In this case, the answer to the REPHRASED target question is NO, it is NOT true that v < w
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: 5w − v < 0
Let's TEST some values.
There are several values of v and w that satisfy statement 2. Here are two:
Case a: v = -2 and w = -1. In this case, the answer to the REPHRASED target question is YES, it is true that v < w
Case b: v = 1 and w = 0. In this case, the answer to the REPHRASED target question is NO, it is NOT true that v < w
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that v − 2w < 0
Statement 2 tells us that 5w − v < 0
If we ADD the two inequalities, we get: 3w < 0, which means w is NEGATIVE

Also, if we can take v − 2w < 0 and add 2w to both sides, we get v < 2w
And, if we can take 5w − v < 0 and add v to both sides, we get 5w < v
So, we can combine the inequalities to get: 5w < v < 2w
Since, we already know that w is NEGATIVE, we know that 2w < w
So, we can add this to our existing inequality to get: 5w < v < 2w < w
At this point, we can see that within our inequality, it is certain that v < w
In other words, the answer to the REPHRASED target question is YES, it is true that v < w
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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