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Data Sufficiency : Does XY=X^2?

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by Brent@GMATPrepNow » Fri Jul 15, 2016 11:37 am
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.

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Brent
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by [email protected] » Fri Jul 15, 2016 12:59 pm
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

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by OptimusPrep » Sun Jul 17, 2016 8:57 pm
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?
Always remember in case of variables: take common out, never divide.
You can write statement 1 as
y(y - x)
Hence you will have two solutions, y = 0 or y = x
Hope this helps.
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by Matt@VeritasPrep » Fri Jul 22, 2016 1:53 am
One nice workaround when you want to divide by a variable in an equality is to try x = 0. If that gives a valid solution, great, x is one of your solutions; if it doesn't, great, x ISN'T one of your solutions.

After that, you can safely divide by x to find the other solutions, and you're set!
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