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 Post subject: Re: if x does not equal -y
 Post Posted: Wed Jul 20, 2011 5:15 am 
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ManhattanGMAT Staff


Posts: 7146
vinnu.m558 wrote:
Hi,

Even after going through all comments on this particular question I still feel that B is the right choice.

The actual ques after rephrasing is :
IS x-y>x+y ??


no, you can't do this -- you can't multiply by a denominator whose sign you are unsure of.
i.e., to get to this “rephrase” you have to multiply by (x + y); that is a problem, because we don't know whether (x + y) is positive or negative.
if (x + y) is positive then you get to rephrase shown here, but, if it is negative, then it becomes "<".

PLEASE READ THE THREAD BEFORE YOU POST -- all of this has already been explained earlier on this same page:
post10355.html#p10355


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 Post subject: Re: if x does not equal -y
 Post Posted: Thu Jan 05, 2012 7:35 am 
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Posts: 3
If x is not equal to -y, is (x-y)/(x+y) > 1?

(1) x > 0
(2) y < 0

I performed a few steps to simplify the left side of the inequality
and obtain a certain sign for the denominator.

As one number, x+y multiplied or divided by itself is positive. So, I performed the following operation to only
the left side,

[(x-y)/(x+y)]*[(x+y)/(x+y)] =

(x^2-y^2)/(x^2+2xy+y^2)

The denominator is positive, because it has can be written as n^2. Multiply both sides of the inequality by it

(x-y)/(x+y) > 1.............?
(x^2-y^2)/(x^2+2xy+y^2) > 1
x^2-y^2 > x^2+2xy+y^2

and combine like variables.

0 > 2y^2+2xy.

With a bit more simplification, rephrase the original expression as

0 > y^2 + xy

Is y(y+x) < 0 ?

Viewed as a positive-negative product.
The answer is yes in two situations.
Note that each situation has four conditions.

y > 0, y+x < 0, x < 0 AND x < -y

y < 0, y+x > 0, x > 0 AND x > -y

(1) x > 0. Statement (1) does not allow one
to reach the further conclusions that y < 0 and x > -y.
(2) y < 0. Statement (2) provides no information
on the value of x or the signs of x and y.

We do not have further information that x > -y, as is necessary to conclude that (x-y)/(x+y) > 1.


Last edited by wxandr on Mon Feb 13, 2012 10:43 am, edited 8 times in total.

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 Post subject: Re: if x does not equal -y
 Post Posted: Sun Jan 15, 2012 3:57 pm 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
wxandr wrote:
Is 0 > y(y+x) ?

Now the inequality can be viewed as a positive-negative product.
If y > 0, y+x < 0, x < 0 and x < -y
If y < 0, y+x > 0, x > 0 and x > -y

(1) x > 0. This implies that y < 0, but it does not conclude that x > -y (x's positive pull is greater than y's negative pull).
(2) y < 0. This information is equivalent to (1).

We cannot conclude that x > -y, as is necessary to resolve whether (x-y)/(x+y) > 1.


your steps to manipulate this inequality are okay (i.e. the first line quoted above). the problem is everything after that. regardless of whether y is positive or negative (BTW notice that you haven't accounted for y being 0), we know nothing about x other than that it is not -y. you seem to be taking the question to be a true statement and comparing it against the statements, or reading too much into the relationship between x and y. either way, this analysis is incorrect..

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Tim Sanders
Manhattan GMAT Instructor


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 Post subject: Re: if x does not equal -y
 Post Posted: Mon Jan 23, 2012 2:16 pm 
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Course Students


Posts: 47
I did this problem with flow chart approach learned from advanced quant strategy book.

Basically, if I can rephrase the question starting with a condition:
that x+y is positive, then I can cross-multiply directly.

This condition thus leads to two possiblities, one in which:
x-y > x + y
so it becomes o>2y, thus y is negative

And one in which
x-y < x+y (pretending that the scenario is opposite and x+y is negative, then I had just flipped the sign by cross-multiplying, hence I'm compensating it by flipping the sign later.
then in this case, 0<2y, so y is positive

Therefore, we arrived at two different conclusions, based on whether x+y is positve or negative. And we need a statement that tells us that x+y is positve or negative to target one specific result. Yet, as you can see, given that x is positve and y is negative from combining both statements, there are still different possibilities. x+y can be either positive or negative. THUS E


Similar problems can be found in OG 11th:
question 143 and 145, both can be solved easily without picking numbers if you know the flow chart approach.


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 Post subject: Re: if x does not equal -y
 Post Posted: Tue Jan 24, 2012 11:11 pm 
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ManhattanGMAT Staff


Posts: 1857
rachel, you are doing great work here! Keep it up!

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Jamie Nelson
ManhattanGMAT Instructor


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