2016 AMC 8 Problems/Problem 11
Contents
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.
Video Solution
~savannahsolver
See Also
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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All AJHSME/AMC 8 Problems and Solutions |
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