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why can't I divide by |y| ?

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why can't I divide by |y| ? [#permalink] New post 31 Oct 2011, 14:21
I don't understand why I can't divide by |y| here when rephrasing... can anyone help?

This is an MGMAT CAT question... They say this -->

"It is extremely tempting to divide both sides of this inequality by y or by the |y|, to come up with a rephrased question of “is x > y?” However, we do not know the sign of y, so this cannot be done. "

I thought you COULD divide y^2 by |y|, because |y| is positive?
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Re: why can't I divide by |y| ? [#permalink] New post 31 Oct 2011, 19:09
Expert's post
n2739178 wrote:
I don't understand why I can't divide by |y| here when rephrasing... can anyone help?

This is an MGMAT CAT question... They say this -->

"It is extremely tempting to divide both sides of this inequality by y or by the |y|, to come up with a rephrased question of “is x > y?” However, we do not know the sign of y, so this cannot be done. "

I thought you COULD divide y^2 by |y|, because |y| is positive?


Yes, you can divide by |y| since it is positive. I think all they are trying to say is that you cannot rephrase the question as "Is x > y"

If you divide by |y|, you will get "Is \(x > y*\frac{y}{|y|}\)?"
You have to keep in mind that y/|y| can be 1 or -1 depending on whether y is positive or negative.
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Re: why can't I divide by |y| ? [#permalink] New post 01 Nov 2011, 01:41
n2739178 wrote:
I don't understand why I can't divide by |y| here when rephrasing... can anyone help?

This is an MGMAT CAT question... They say this -->

"It is extremely tempting to divide both sides of this inequality by y or by the |y|, to come up with a rephrased question of “is x > y?” However, we do not know the sign of y, so this cannot be done. "

I thought you COULD divide y^2 by |y|, because |y| is positive?


|y| can be 0 as well. Division by 0 is undefined.
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Re: why can't I divide by |y| ? [#permalink] New post 01 Nov 2011, 03:05
Expert's post
fluke wrote:
|y| can be 0 as well. Division by 0 is undefined.


Yes, you are right. Division by 0 is undefined. But its relevance in this question is very limited since statement 2 states that y > 0. You know that the two statements never conflict so you don't really need to worry about y = 0.

Even if this condition were not mentioned, instead of wondering whether x*|y| > y^2, I would find it far easier to work with x > y*y/|y| since the variables are separated here. I can separately worry about the condition "y=0" if it is possible in a particular question.

My question will be: Is \(x > y*y/|y|\)?

I will think, "y/|y| can be 1 or -1 (assuming y is not 0)"
Statement 1 says x > y. Then can I say that x > -y too (in case y/|y| = -1)? Not necessarily. If y is negative, it may not hold.
e.g. x = 3, y = -4
y/|y| = -1
x is greater than y but x (=3) is not greater than y*y/|y| (=4)
I don't really need to worry about y = 0 here.

Statement 2 clarifies that y is positive. Now we know that y/|y| = 1
Since statement 1 says x > y, it is sufficient to say x > y*y/|y|.
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Joined: 11 May 2010
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Location: United Kingdom
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Re: why can't I divide by |y| ? [#permalink] New post 03 Nov 2011, 12:48
great thanks guys!
Re: why can't I divide by |y| ?   [#permalink] 03 Nov 2011, 12:48
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