Difference between revisions of "2004 AMC 8 Problems/Problem 19"
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Latest revision as of 00:00, 5 July 2013
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?
Solution
The smallest number divisible by 
and , or their least common multiple, can be found to be 
. When is added to a multiple of number, its remainder when divided by that number is . The number we are looking for is therefore 
, and between 
.
See Also
| 2004 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
