harsh,
This is a yes/no question
We have to answer the question wether (x-y)/(x+y) >1

Stmt.1) x>0
we have 2 cases:
Case 1. y>0
If y>x, No
If y<x, yes
Hence insuff.

Case2. y<0
if lyl > lxl, No
if lyl < lxl, Yes

Stmt.2)
y<0
we have 2 cases
Case 1. x>0
insuff. See Case 2 above for stmt.1
Case 2. x<0
if lxl > lyl, No
if lxl < lyl, Yes
Hence, insuff.

Combining, stmt. 1 and 2,
we still get 2 possible answers ( see case 1 above in stmt.2)
Hence, the answer for #19 is E

harsh001 wrote:#19

Let X = 1 and Y = 2 then equation = -1/3 < 1
Let X = 1 and Y = -2 then equation = -3/2 < 1
Let X =0 and Y = 1 then equation = 1 = 1
Let X = 0 and Y =-1 then equation = -1 < 1
Let X = -1 and Y = 2 then equation = -3 < 1
Let X =-1 and Y = -2 then equation = -1/3 < 1

therefore in all cases the equation in not greater than 1 if we take similar values of condition 2 we will see that each condition in its own answers the question therefore D is the answer!!

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

Note that x+ y > 0, we need to know whether x - y > x + y i.e. whether y < 0
However, if x + y < 0, we need to know whether x - y < x + y i.e. whether y >0

Athough (2) tells us that y < 0, we do not know, not even together with x < 0 from (1), whether x+ y is positive or negative.
Choose E