Data Sufficiency

sud21 wrote:Is x-y>0? (Or x+y>0?)
1). x-y/x>0
2). x+y/x-y>0

Hi Sud21!

I would love to hear the source for this problem because there are issues with the 2 Statements. When you solve them, you end up with contradictory information - something the GMAT will never do. I'm going to answer the question "Is x-y>0?" (not the other) but only to show what I mean about contradictory information. WARNING: Only use this question and its suggested solutions as a means to practice working with inequalities and data sufficiency - DO NOT use this problem as a true representation of a GMAT question because this does not meet standard GMAC rules. Always avoid questions that do not have clearly noted and reputable sources.

Rephrase the Question:
It might be easier to understand if we separate the x and y... "Is x>y?"
Now, when I'm trying to figure out if one value is greater than another in the world of inequalities, I will likely be setting up cases. So let's see what that means...

Statement 1: x-y/x>0
To simplify this we will need to multiply both sides by x so that means we have 2 cases (one where x>0 and one where x<0).

If x>0 --> x-y>x --> -y>0 --> 0>y
So when x>0, y<0... so y<0<x --> y<x

If x<0 --> x-y<x --> -y<0 --> 0<y
So when x<0, y>0... so x<0<y --> x<y

These are 2 different answers, so NOT sufficient.


Statement 2: x+y/x-y>0
To simplify this we will need to multiply both sides by (x-y) so that means we have 2 cases (one where (x-y)>0 and one where (x-y)<0).

If x-y>0 or x>y --> x+y>x-y --> y>-y --> 2y>0 --> y>0
So if x>y and y>0, then x>y>0 --> x>y

If x-y<0 or x<y --> x+y<x-y --> y<-y --> 2y<0 --> y<0
So when x<y, y<0... so x<y<0 --> x<y

These are 2 different answers, so NOT sufficient.


Statement 1+2:
Now comes the issue...from statement (1) we basically find out that x and y have opposite signs...so if x is positive, y is negative and x is greater, but if x is negative, y would be positive and therefore greater.

From Statement (2) we actually learn the opposite...x and y have the SAME sign, so if x is negative, so is y, but x is more negative (or less). If x were positive, however, y would also be positive but less positive (so x would be greater in this case). There is still no consistent answer (not sufficient)...BUT

The big point - these 2 statements cannot be true at the same time - I cannot have rules that simultaneously require x and y to have the same signs AND different signs.

On its face the question feels fairly GMAT-like but whoever wrote it did not pay careful enough attention to the GMAT rules. Therefore you should ALWAYS AVOID questions without clear and reputable sources!


Whit