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The above reasoning appears incorrect.. [#permalink]
18 Dec 2005, 17:38

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.