Problem:
The smallest number greater than that leaves a remainder of when divided by , or lies between what numbers?
Answer Choices:
A. and
B. and
C. and
D. and
E. and
Solution:
Two less than the number must be divisible by , and . The least common multiple of these numbers is , so is the smallest number greater than to leave a remainder of when divided by , and . Therefore the number lies between and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions