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Director
Joined: 17 Oct 2005
Posts: 928

if x is not equal to y, is (xy)/(x+y) > 1? 1) x>0 2) [#permalink]
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18 Dec 2005, 13:46
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if x is not equal to y, is (xy)/(x+y) > 1?
1) x>0
2) y < 0



Director
Joined: 17 Dec 2005
Posts: 547
Location: Germany

Great questions joemama, where have you got them from?
But I can't estimate if they are hard or not.
(xy)/(x+y) > 1?
xy > x+y ?
x > x + 2y?
2) Is not sufficient, since we dont know whether x is positive or negative.
1) Is not sufficient, since we don't know if y is positive or negative.
Both together are sufficient, because x > x  2y, while x > 0
I think it is C



Director
Joined: 17 Oct 2005
Posts: 928

allabout, its mostly from gmatprep



Intern
Joined: 18 Nov 2005
Posts: 8

The above reasoning appears incorrect.. [#permalink]
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18 Dec 2005, 18:38
There are a couple of flaws in the above reasoning.
if (xy)/(x+y) > 1
does not imply (xy) > (x+y) because we do not know whether x+y is positive or negative. xy > x+y only if (x+y) is positive.
the inequality is reversed if (x+y) is less than zero.
Secondly, in, x > x +2y, can't you cancel x and say 0 > 2y and say the answer is B (not sure why you did not cancel x).
Anyway, the way I would proceed is...
(xy)/(x+y) ?> 1
write xy as x+y2y
hence, (xy)/(x+y) = (x+y2y)/(x+y)
= 1 (2y/(x+y))
hence, the problem boils down to whether 1(2y/(x+y)) > 1
now you can cancel out 1 and say whether 2y/(x+y) > 0
statement 1: x > 0, say x = 5, then y = 1 and y = 6 gives two different results, hence statement one is not sufficient.
statement 2: y < 0, now if y = 2 say, x = 3 or 3 gives two different results. hence statemet two is not sufficient.
even with both the statements combined together, you can have x = 5 and y = 1 and 6 will give two different results. Hence, in my opinion E is the answer.
Srinivas (mathguru).



Director
Joined: 17 Dec 2005
Posts: 547
Location: Germany

Hey srinivasssrk,
You're right.
The idea to transform (x  y) to (x+ y 2y) is the way we have to go, the basic math transformation, when dealing with such terms.
Good job.



Director
Joined: 26 Sep 2005
Posts: 572
Location: Munich,Germany

I got E as well.
srinivas: brilliant expln
allabout : wie geht sie  muenchen ist sehr gut.










