Data Sufficiency

GMAT Prep

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

OA B

AAPL wrote:GMAT Prep

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

Let the 1997 rent = 100.
Increase in 1998 = (x/100)(100) = x.
Thus, rent in 1998 = 100+x.
Decrease in 1999 = (y/100)(100+x) = y + xy/100
For the rent to be greater in 1999 than in 1997, the increase in 1998 (x) must be greater than the decrease in 1999 (y + xy/100).
Question stem, rephrased:
Is x > y + xy/100?

Statement 1: x > y
If x=20 and y=10, then y + xy/100 = 10 + (20*10)/100 = 12.
Is 20 > 12?
YES.

If x=90 and y=80, then y + xy/100 = 80 + (90*80)/100 = 152.
Is 90 > 152?
NO.
Since the answer to the question stem is YES in the first case but NO in the second case, INSUFFICIENT.

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

The correct answer is B.

It is helpful to be able to recognize 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.