Problem:
Suppose x and y are inversely proportional and positive. If x increases by p%, then y decreases by
Answer Choices:
A. p%
B. 1+pp%
C. p100%
D. 100+pp%
E. 100+p100p%
Solution:
To say that x and y are inversely proportional is to say that if x is multiplied by k, then y is divided by k. Let x′ and y′ be the new values after x increases by p%. Then
x′=(1+100p)x and y′=(1+100p)y=100+p100y
By definition, the percentage decrease in y is
100(yy−y′)=100(1−100+p100)=100+p100p
Note. It is a common error to think that the correct answer to this question is (A). For instance, this error appeared a few years ago in the president's annual report from a famous American university!