2003 AMC 12B Problems/Problem 8: Difference between revisions

Revision as of 22:32, 19 December 2012

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

$\clubsuit(\clubsuit(x)) = a + b = 3$

Clearly $\\clubsuit(x)$ can only be $3, 12, 21,$ or $30$ and only $3$ and $30$ are possible to have two digits sum to.

If $\\clubsuit(x)$ is \Rightarrow \text (E)$

@@ Line 3: / Line 3: @@
 <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 <math>\\clubsuit(x)</math> can only be <math>3, 12, 21,</math> or <math>30</math> and only <math>3</math> and <math>30</math> are possible to have two digits sum to.
+If <math>\\clubsuit(x)</math> is \Rightarrow \text (E)$