2016 AMC 8 Problems/Problem 11
Problem
Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is 
Solution 1
We can see that the original number can be written as 
, where 
represents the tens digit and 
represents the units digit. When this number is added to the number obtained by reversing its digits, which is 
, the sum would be 
. From this, we can construct the equation 
, which simplifies to 
. Since there are 7 pairs of such digits and , 
, the answer would be 
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See Also
| 2016 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
