We have to establish if the difference of the rents is positive or negative
1. x > y: not sufficient, e.g., check assuming the original rent as 80 units, x as 25% & y as 20%
2. xy/100 < x - y: because both x & y are positive, hence, xy/100 is positive
hence the this shows that x - y > 0
Now, tranform the data like this: Let the rents be R (in 1997) & R' in (1999) respectively, X = x/100 & Y = y/100; then:
R' = R [(100 + x)/100][(100 - y)/100]
R' = R[(1+X)(1-Y)]
R' = R (1 + X - Y - XY)
R' - R = R (X - Y - XY) ---------(1)
as given: xy/100 < x - y
change x, y to X, Y: XY < X - Y
i.e., X - Y - XY > 0; replace this in (1)
R' - R > 0
so 2 is sufficient, rent of 1999 is more than that of 1997
(I know its slightly long solution, please let me know the shortcut.)
