Difference between revisions of "2014 AMC 8 Problems/Problem 21"
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| + | Another solution is using the divisbility rule of 3. Just add the digits of each number together. | ||
Revision as of 12:30, 2 April 2019
Problem
The 
-digit numbers 
and 
are each multiples of 
. Which of the following could be the value of 
?
Solution
The sum of a number's digits 
is congruent to the number 
. 
must be congruent to 0, since it is divisible by 3. Therefore, 
is also congruent to 0. 
, so 
. As we know, 
, so 
, and therefore 
. We can substitute 2 for 
, so 
, and therefore 
. This means that C can be 1, 4, or 7, but the only one of those that is an answer choice is 
.
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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. 
Another solution is using the divisbility rule of 3. Just add the digits of each number together.
