Problem:
What is the sum of all integer solutions to ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If , then the given inequality is equivalent to , or . The integer solutions in this case are , and . If , then the given inequality is equivalent to , or . The integer solutions in this case are , and . The sum of all integer solutions is .
The given inequality is equivalent to . The solution set consists of all numbers whose distance from on the number line is strictly between and . Because only integer solutions are sought, this set is . The required sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions