kullayappayenugula wrote: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

Saw the solution in OG but looking for better explanation.

Let the 1997 rent = 100.
Increase in 1998 = (x/100)*100 = x.
Rent in 1998 = 100+x.
Decrease in 1999 = y/100*(100+x) = y + xy/100
Total percent change = increase - decrease = x - (y + xy/100) = x - y - xy/100.

For the rent in 1999 to be higher than the rent in 1997, the total percent change must be POSITIVE.
Question rephrased: Is x - y - xy/100 > 0?

Statement 1: x > y
If x=20 and y=10, then x - y - xy/100 = 20 - 10 - (20*10)/100 = 8.
In this case, the percent change is POSITIVE.
If x=200 and y=100, then x - y - xy/100 = 200 - 100 - (200*100)/100 = -100.
In this case, the percent change is NEGATIVE.
INSUFFICIENT.

Statement 2: x-y > xy/100
Thus, x - y - xy/100 > 0.
SUFFICIENT.

The correct answer is B.

It can be helpful to know the following formulas for repeated percent change:

If a value increases by x% and then by another y%, the total percent change = x + y + xy/100.
If a value increases by x% and then decreases by y%, the total percent change = x - y - xy/100.

Thanks for the explanation