Problem:
A whole number larger than leaves a remainder of when divided by each of the numbers and . The smallest such number lies between which two numbers?
Answer Choices:
A. and
B. and
C. and
D. and
E. and
Solution:
The numbers that leave a remainder of when divided by and are and so on. Checking these numbers for a remainder of when divided by both and yields as the smallest.
The smallest whole number that is evenly divided by each of and is . So the smallest whole number greater than that leaves a remainder of when divided by each of and is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions