IMO the answer should be D
1- we have XYX=X - XY=X/X or 1 - sufficient
2- the same

are you sure in the official answer???

ershovici wrote:IMO the answer should be D
1- we have XYX=X - XY=X/X or 1 - sufficient
2- the same

are you sure in the official answer???

We cant do like this..
By your method we are ignoring a possible solution.
XYX - X=0
X(XY-1)=0
X=0 or XY=1
By your method, we are ignoring the solution X=0.... Hope this helps..

jimmiejaz wrote:Is XY=1?
1.) XYX=X
2.) YXY=Y

Please comment..

Jimmiejazz aptly points out the most common error people make in this situation - simply dividing both sides by a variable.

We need to be careful when dividing by variables, since by doing so we're assuming that the variable doesn't equal 0.

The safer way to solve is to get everything over to one side and then factor, just as you would when solving a quadratic. For example:

1) x^2*y = x

x^2*y - x = 0
x(xy - 1) = 0
x = 0 or xy = 1

2) y^2*x = y

y^2*x - y = 0
y(xy - 1) = 0
y = 0 or xy = 1

Now here's the tricky part - at first glance, it looks like the only solution that the statements have in common is xy=1. However, 0 is a tricksy number; if x=y=0 then we still satisfy both statments.

So, we could have:

xy = 1, a "yes" answer; or
x=y=0, a "no" answer.

Even together, we can get both a yes and a no answer: insufficient, choose E.

Stuart Kovinsky wrote: Now here's the tricky part - at first glance, it looks like the only solution that the statements have in common is xy=1. However, 0 is a tricksy number; if x=y=0 then we still satisfy both statments.

So, we could have:

xy = 1, a "yes" answer; or
x=y=0, a "no" answer.

Even together, we can get both a yes and a no answer: insufficient, choose E.

I would have picked C based on this. Statement 1 gives us either x=0 or xy=1, statement 2 gives us either y=0 or xy=1. Combine the statements and xy=1!

Stuart, how do we avoid this trap? I could easily see myself during test day, with the time pressure and all, picking C because both statements have xy=1... Are you saying to always double-check when the solution is zero?

Thanks for the explanation Stuart!!!

So The takeaway of this problem is Pls recheck the solution to a DS question where the answers contain 0 in both answer choices. Combined, they can provide a solution and therefore can change the correct answer choice.

Hope this helps.