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Basic Algebra

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by gmatusa2010 » Mon Nov 29, 2010 4:19 am
2x^2=4xy what is X/Y?

I know you normally can't divide by a variable unless you know its not ZERO but in this case the question is asking for a ratio of X/Y or a re-arrangement of the expression. Is it ok to divide XY on both side? (You can solve it both ways and its the same answer.) Just wonder about the fundamentals.
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by rishab1988 » Mon Nov 29, 2010 5:05 am
2x^2-4xy=0
x(2x-4y)=0

x=0 or x=2y

x/y =2 [ x cannot be 0 for its a ratio]

This is like question giving you a quadratic equation involving distance and speed.Let x =distance and y=speed and asking you the time.Speed =0 means you never traveled [infinite here means that he will never complete the travel].

Tho I doubt that this is a GMAT question.Unless this is a P.S,I wont do this.On DS it would produce 2 answers.one answer would say it never moved[the object].The other would say it did.

More appropriately GMAT would test +ve and -ves in such questions.
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by jaymw » Mon Nov 29, 2010 8:00 am
Im just as curious as rishab1988 about where you got that question from.

There really are two answers to this problem.

First, assume x is not zero.

You want to know the value for x/y so solve for x/y and not for anything else.

2x^2=4xy |divide by x (you can do it here under the above assumption)
2x=4y | divide by 2y (y cannot be zero here, because the question probably wouldn't ask for the value of an undefined fraction)
2x/2y=2
x/y=2

So your first solution for the fraction x/y is 2.

However, assume x = 0.

2(0)^2=4*0*y will always be true

Therefore, if x is zero, x/y will also be zero!

Again, please tell me where you found this question!
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