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​>1−100q​1​=100−q100​100p​>100−q100​−1=100−qq​p>100−q100q​.​