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
Solutions
Solution 1
We can write the two digit number in the form of ; reverse of is . The sum of those numbers is: We can use brute force to find order pairs such that . Since and are both digits, both and have to be integers less than . Thus our ordered pairs are or ordered pairs.
Solution 2 -SweetMango77
Since the numbers are “mirror images,” their average has to be . The highest possible value for the tens digit is because it is a two-digit number. , and , so our lowest tens digit is . The numbers between and inclusive is total possibilities.
See Also
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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