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matteomasciotti
- Junior | Next Rank: 30 Posts
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Hi guys,
I came across this easy DS problem on the Official Gmat Quant. Review, #80.
it states the following:
if xy>0 is (x-1)(y-1)=1?
1)x+y=xy
2)x=y
I'am not going to go through the first statement,but rather, I would like to draw your attention towards statement number 2.
if x=y , then the expression (x-1)(y-1)=1 can be written in this way:
xy-y-x+1=1
substituing x with y we get:
y^2-2y=0 (which is the same result showed at the end of the book)
Now, the solution at the back tells us that, since y^2-2y=0 has not gotten only one solution we can't tell whether (x-1)(y-1) is equal to 1. but ...are we really sure?
If we solve for y the equation y^2-2y=0 we can have two solutions, either y is 0 or y is 2.
Fine..but the initial statement tells us that XY>0 which means that y could not be 0, and therefore, in my humple opinion, y can only be 2, hence, if y=2 then (x-1)(y-1) is actually equal to 1.
But ..unfortunately this is not the case...why is my assumption flawed?
I came across this easy DS problem on the Official Gmat Quant. Review, #80.
it states the following:
if xy>0 is (x-1)(y-1)=1?
1)x+y=xy
2)x=y
I'am not going to go through the first statement,but rather, I would like to draw your attention towards statement number 2.
if x=y , then the expression (x-1)(y-1)=1 can be written in this way:
xy-y-x+1=1
substituing x with y we get:
y^2-2y=0 (which is the same result showed at the end of the book)
Now, the solution at the back tells us that, since y^2-2y=0 has not gotten only one solution we can't tell whether (x-1)(y-1) is equal to 1. but ...are we really sure?
If we solve for y the equation y^2-2y=0 we can have two solutions, either y is 0 or y is 2.
Fine..but the initial statement tells us that XY>0 which means that y could not be 0, and therefore, in my humple opinion, y can only be 2, hence, if y=2 then (x-1)(y-1) is actually equal to 1.
But ..unfortunately this is not the case...why is my assumption flawed?
