Problem:
The smallest positive integer greater than  that leaves a remainder of  when divided by , and  lies between which of the following pairs of numbers?
Answer Choices:
A.  and  
B.  and  
C.  and  
D.  and  
E.  and  
Solution:
The least common multiple of , and is . Numbers that leave a remainder of when divided by , and are more than a whole number multiple of . So the smallest positive number greater than that leaves a remainder of when divided by , and is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions