shinbhu wrote:
Solving the modulus gives us two solutions x<2 and x>-2, with two other solutions that are invalid.
1. x<0. Unsuff since x>2 according to the stem.
2. x is between -2 and 2. Clearly, the stem shows exactly that.
B.
I completely agree with Ian here. Neither statement is needed to answer the question, stem is enough to do so. So technically the answer to this question is D. Though you'll never see such a question on real a test. Having said that I've seen one DS question from GMAT Prep where also only stem was enough to answer the question, though I think that it was just a flawed question (
if-zy-xy-0-is-x-z-x-z-101210.html#p783615).
To elaborate more on the given problem:Is |x-2|+|x+2|<4?We have two check points -2 for |x+2| and 2 for |x-2| (check points - the value of x for which the expression in || equals to zero). Thus we have 3 ranges to check:
--------{-2}--------{2}--------A. \(x<-2\) --> as for this range \(x-2=negative\) and \(x+2=negative\) then we'll have: \(-(x-2)-(x+2)=-2x\). Now, as we are considering the range where \(x<-2\) then \(-2x>4\) and the answer to the question "is \(|x-2|+|x+2|<4\)" is NO;
B. \(-2\leq{x}\leq{2}\) --> as for this range \(x-2=negative\) and \(x+2=positive\) then we'll have: \(-(x-2)+(x+2)=4\). Again, the answer to the question "is \(|x-2|+|x+2|<4\)?" is NO;
C. \(x>2\) --> as for this range \(x-2=positive\) and \(x+2=positive\) then we'll have: \((x-2)+(x+2)=2x\). The same here, as we are considering the range where \(x>2\) then \(2x>4\) and the answer to the question "is \(|x-2|+|x+2|<4\)" is NO.
So we can see that in ALL 3 ranges the answer to the question is NO: \(|x-2|+|x+2|\geq{4}\) (the minimum possible value of the given expression is 4 when \(-2\leq{x}\leq{2}\)). Therefore even if statement (1) were "Roses are red" and statement (2) were "Violets are blue" we could still answer definite NO to the question based on the stem alone and thus would have D as an answer.
Again as Ian noted if the question were: "is \(|x-2|+|x+2|\leq{4}\)" then yes, the answer to the question would be B, as the question in this case can be rephrased as "is \(-2\leq{x}\leq{2}\)?".
Hope it's clear.
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