Data Sufficiency

Pazoki wrote:Hi all,

Does XY=X^2?

1)Y^2-XY=0

2)X^2-2XY+Y^2=0

For question stem I concluded as "is X=Y?"
and Item 1: Y^2-XY=0 ==> Y^2=XY which means X=Y Sufficient.

Am I right?

The problem is where you divided both sides by y, because it may be the case that y=0, in which case our conclusion that y = x may not be true.

Consider this example: (2)(0) = (3)(0)
Divide both sides by 0 to get: 2 = 3

The big takeaway is that it's okay to divide both sides by a variable as long as we are certain that the variable does not equal zero.

Cheers,
Brent

Hi Pazoki,

You have to be very careful about removing a variable by division; doing so might remove a potential solution or fundamentally change the question that is asked. In this case, if you 'divide out an X', then you eliminate the possible outcome that X could be 0 (and in that case, the answer to the question would be YES).

You can TEST VALUES to answer this question.

We're asked if XY = X^2. This is a YES/NO question.

1) Y^2 - XY = 0

IF...
X = 0
Y = 0
Then the answer to the question is YES.

IF...
X = 1
Y = 0
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT.

2) X^2 - 2XY + Y^2 = 0

This Fact can be rewritten as...
(X - Y)(X - Y) = 0

The only way for (X - Y) to equal 0 is when X = Y. Regardless of what values you use for X and Y (try TESTing a few), you'll end up with a YES answer to the given question.
Fact 2 is SUFFICIENT.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich