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
Plug in 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
The problem asks whether the increase is greater than the decrease. Thus, the question can be rewritten as:
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 can be both yes and no, insufficient.
Statement 2: x-y > xy/100
If x-y > xy/100, then 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.Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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