Is v − w

Question

Is v − w < 0?

(1) v − 2w < 0

(2) 5w − v < 0

chetan2u · Answer

Is v−w<0? Or is vW If v is 4 and W is 7.....vv Insufficient Combined 2w>v>5w So 5w<2w...3w<0....w<0 and so v<2w means v

dvishal387 · Answer

Hi Chetan2u,

I could not get the last part. If we combine 1 and 2 should not the equation be  5w<v<2w 
=> w<0 . Although the answer would still be C.

chetan2u · Answer

Thanks Vishal .. it was a typo corrected it.

Mo2men · Answer

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

BrentGMATPrepNow · Answer

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

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