NandishSS wrote:
Quote:
Is (x + 1)/(x - 3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0
HI
GMATGuruNY,
MentorTutoring ,
GMATBusters,
Can you please help me with my understanding?
\((x + 1)/(x - 3) < 0\) ? ==> Multiple by \((x-3)\) on both side ==> \((x + 1)(x - 3) < 0\)
Does it not mean Either \(x<-1 \) or \( x<3 \)?
Hello,
NandishSS. Pardon the delay in my response, but today was my busiest day, and this is the first time I have found in which I can adequately reply. I approached the problem a little differently, namely by reinterpreting the question. Rather than manipulate anything in the original inequality, which would lead to problems, I questioned what it
would take for the expression to be negative. There were only two ways:
1) negative/positive
2) positive/negative
With this in mind, I jumped straight into the statements, starting with (1). Looking at the lower extreme, if "x" were -0.999 or some similar value, then we would meet condition 2) above:
(-0.999 + 1)/(-0.999 - 3) = positive/negative
What about the other extreme, though? If "x" were, say, 0.999, then we would meet condition 2) again:
(0.999 + 1)/(0.999 - 3) = positive/negative
Consistency leads to a SUFFICIENT answer. Thus, the answer was down to (A) or (D). Looking at statement (2), I considered that whether I moved 4 to the other side of the inequality or left it where it was, "x" had to be between -2 and 2 for the inequality to hold. I repeated the same process as before, ignoring the exact values of the expressions but just paying attention to the general tendency of positive/negative:
(-1.999 + 1)/(-1.999 - 3) = negative/negative
(1.999 + 1)/(1.999 - 3) = positive/negative
Conflicting information is the opposite of what we want, so I wrote (2) off as NOT SUFFICIENT, leaving only (A) as the answer. I hope that helps. If you have further questions, please ask.
- Andrew
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