Problem:
Let and be numbers with . Which of the following is impossible?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because and , adding corresponding sides of the inequalities gives , so is impossible. To see that the other choices are possible, consider the following choices for , and :
and : , and ;
: , and ;
: , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions