set 4 q 29

[radhika1306]

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?
(1) x > y
(2) xy/100 < x – y

[Bharat]

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.)

[ri2007]

Hi Radhika can you pls confirm the answer
thanks