Problem:
If p,q and M are positive numbers and q<100, then the number obtained by increasing M by p% and decreasing the result by q% exceeds M if and only if
Answer Choices:
A. p>q
B. p>100−qq
C. p>1−qq
D. p>100+q100q
E. p>100−q100q
Solution:
The following inequalities are equivalent to the inequality stated in words in the problem:
M(1+100p)(1−100q)>M(1+100p)(1−100q)>11+100p>1−100q1=100−q100100p>100−q100−1=100−qqp>100−q100q.