<s>[INST] $xy=22$ and $yz=26$: What is $x+y+z $ equal to? Given the following: $$xy=22,\qquad yz=26,$$ where $x,y,z\in\mathbb{N}$. Which of the following is a possible value of $ x + y + z $? 
$ \textbf {(A) } 22 \qquad \textbf {(B) } 24 \qquad \textbf {(C) } 26 \qquad \textbf {(D) } 48 $ 
 [/INST] Shortcut. Since both given products are even, we can just assume that $y$ is even, so let it be $y=2$. Then, $x=11$ and $z=13$. Then, $$x+y+z=11+2+13=\boxed{\textbf{(C) } 26}.$$
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