1994 AHSME Problems/Problem 10

Problem

For distinct real numbers $x$ and $y$ , let $M(x,y)$ be the larger of $x$ and $y$ and let $m(x,y)$ be the smaller of $x$ and $y$ . If $a<b<c<d<e$ , then $M(M(a,m(b,c)),m(d,m(a,e)))=$ $\textbf{(A)}\ a \qquad\textbf{(B)}\ b \qquad\textbf{(C)}\ c \qquad\textbf{(D)}\ d \qquad\textbf{(E)}\ e$

Solution

We work thorough the equation step by step, simplifying as follows:

$\begin{align*}M(M(a,m(b,c)),m(d,m(a,e)))&=M(M(a,b),m(d,a))\\&=M(b,a)\\&=\boxed{\textbf{(B) }b}\end{align*}$

--Solution by TheMaskedMagician

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1994 AHSME Problems/Problem 10

Problem

Solution