Difference between revisions of "2003 AMC 12B Problems/Problem 8"

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Let <math>a</math> and <math>b</math> be the digits of <math>x</math>,
 
Let <math>a</math> and <math>b</math> be the digits of <math>x</math>,
  
<cmath>\clubsuit(</cmath>\clubsuit(x)) = a + b = 3<math></math>
+
<cmath>\clubsuit(\clubsuit(x)) = a + b = 3</cmath>
  
 
Clearly the only two digit numbers whose digits sum to <math>3</math> are <math>12, 21,</math> and <math>30</math>, thus the answer is <math>3 \Rightarrow \text (A)</math>
 
Clearly the only two digit numbers whose digits sum to <math>3</math> are <math>12, 21,</math> and <math>30</math>, thus the answer is <math>3 \Rightarrow \text (A)</math>

Revision as of 23:24, 19 December 2012

Let $a$ and $b$ be the digits of $x$,

\[\clubsuit(\clubsuit(x)) = a + b = 3\]

Clearly the only two digit numbers whose digits sum to $3$ are $12, 21,$ and $30$, thus the answer is $3 \Rightarrow \text (A)$