Bunuel wrote:
enigma123 wrote:
If xy < 5, is x < 1 ?
(1) \(|y| > 5\)
(2) \(\frac{x}{y}> 0\)
I got the answer is C which is correct but it was a guess work. So here is how I did this question:
Statement 1
|y| > 5 i.e. y > 5 and y > -5 or y > 5 and y < -5.
As this statement doesn't say anything about x, its clearly insufficient.
Statement 2
x/y> 0 --> This statement only tells that x and y have the same sign. Therefore insufficient.
After this I struggled to complete the question, and guessed answer C as correct answer. Can someone please help?
|y| > 5 means that y<-5 or y>5.
If xy < 5, is x < 1 ?(1) \(|y| > 5\) --> if \(y=10\) and \(x=0\) then the answer is YES but if \(y=-10\) and \(x=2\) then the answer is NO. Not sufficient.
(2) \(\frac{x}{y}>0\) --> \(x\) and \(y\) have the same sign. Still insufficient: if \(y=-2\) and \(x=-1\) then the answer is YES but if \(y=2\) and \(x=2\) then the answer is NO. Not sufficient.
(1)+(2) From (2) \(x\) and \(y\) have the same sign. Now, if from (1) \(y>5\) then \(0<x<1\) (in order \(xy<5\) to hold true) and if from (1) \(y<-5\) then \(-1<x<0\) (again in order \(xy<5\) to hold true). So in both cases \(x<1\). Sufficient.
Answer: C.
May not be the easiest solution, but I find it interesting that these inequalities can be rigorously solved using graphical visualisation.
Given : xy<5 is the area between the hyperbola.
1) |y| > 5: When y>5, x can only be less than 1. When y<-5, x can only be greater than -1. Thus not sufficient.
2) Same sign, so not sufficient.
Combining.
When y>5, x can only be less 1 BUT greater than 0. So x<1? YES
When y<-5, x can only be greater than -1 BUT less than 0. So, x<1? YES
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