msvmuthu wrote:Why shouldnt we simplify the above given equation?

for example, in the above question I simplified the equation to:
y<0

since the first choice is x>0,
and since we have derived y<0;
(x-y) / (x+y) => will be like (x+y) /(x-y)
there fore surely, this will be greater than 1.

There fore my choice was A.

Please some one throw more light on this!

There are two issues above- both are common mistakes, so important to understand:

First, you've 'simplified' the inequality to get y < 0, then used this as part of your solution. You can't do this: 'Is (x-y)/(x+y) > 1?' was the question; it's not a fact. If you assume that (x-y)/(x+y) > 1 is true, it shouldn't be surprising that you then discover that (x-y)/(x+y) > 1 is true; this is what's called 'begging the question' in logic. It can be a very good idea to simplify expressions like the one in the question above, but be clear about what you're doing: you are not deriving a fact; instead you are rephrasing the question.

Second, when you have an inequality, if you multiply both sides of the inequality by a negative, you must reverse the inequality. If, say, you know that

a/b > 1

you cannot multiply both sides by b and conclude that a > b, at least not without knowing something about b. It is certainly true that a > b if b is positive, but if b is negative, we would need to reverse the inequality; we would find that a < b. When you rewrote the inequality:

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

to get y < 0, you were assuming x+y is positive. If x+y is negative, you need to reverse the inequality; you would find that y > 0.