When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of a two-digit score. By which of the following might her incorrect sum have differed from the correct one? 
Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value
Let the two digits be $$a$$ and $$b$$.  The correct score was $$10a+b$$. Clara misinterpreted it as $$10b+a$$. The difference between the two is $$\left\textbar{} 9a-9b\right\textbar$$ which factors into $$\left\textbar{} 9(a-b)\right\textbar$$. Therefore, since the difference is a multiple of $$9$$, the only answer choice that is a multiple of $$9$$ is $$45$$ .  ( $$2013$$ AMC $$8$$ Problem, Question \#$$13$$) 