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# if x is not equal to -y, is (x-y)/(x+y) > 1? 1) x>0 2)

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Director
Joined: 17 Oct 2005
Posts: 928
if x is not equal to -y, is (x-y)/(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 (x-y)/(x+y) > 1?

1) x>0
2) y < 0
Director
Joined: 17 Dec 2005
Posts: 547
Location: Germany

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18 Dec 2005, 14:45
Great questions joemama, where have you got them from?

But I can't estimate if they are hard or not.

(x-y)/(x+y) > 1?

x-y > 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

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18 Dec 2005, 18:14
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 (x-y)/(x+y) > 1

does not imply (x-y) > (x+y) because we do not know whether x+y is positive or negative. x-y > 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...

(x-y)/(x+y) ?> 1

write x-y as x+y-2y

hence, (x-y)/(x+y) = (x+y-2y)/(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

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19 Dec 2005, 00:33
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

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20 Dec 2005, 23:21
I got E as well.

srinivas: brilliant expln
allabout : wie geht sie - muenchen ist sehr gut.
20 Dec 2005, 23:21
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