Difference between revisions of "2018 AMC 8 Problems/Problem 7"
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The <math>5</math>-digit number <math>\underline{2}</math> <math>\underline{0}</math> <math>\underline{1}</math> <math>\underline{8}</math> <math>\underline{U}</math> is divisible by <math>9</math>. What is the remainder when this number is divided by <math>8</math>? | The <math>5</math>-digit number <math>\underline{2}</math> <math>\underline{0}</math> <math>\underline{1}</math> <math>\underline{8}</math> <math>\underline{U}</math> is divisible by <math>9</math>. What is the remainder when this number is divided by <math>8</math>? | ||
Revision as of 12:51, 18 January 2021
Contents
Problem
The 
-digit number 
is divisible by 
. What is the remainder when this number is divided by 
?
Video Solution
https://youtu.be/6xNkyDgIhEE?t=2341
Solution
We use the property that the digits of a number must sum to a multiple of if it are divisible by . This means 
must be divisible by . The only possible value for 
then must be 
. Since we are looking for the remainder when divided by , we can ignore the thousands. The remainder when 
is divided by is 
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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. 
