If $x$ and $y$ are each chosen from the set $\{1,2,3,5,10\}$, the largest possible value of $\frac{x}{y}+\frac{y}{x}$ is
(A) 2
(B) $12 \frac{1}{2}$
(C) $10 \frac{1}{10}$
(D) $2 \frac{1}{2}$
(E) 20

## Part B: Each question is worth 6 credits.
If $x$ and $y$ are each chosen from the set $\{1,2,3,5,10\}$, the largest possible value of $\frac{x}{y}+\frac{y}{x}$ is
(A) 2
(B) $12 \frac{1}{2}$
(C) $10 \frac{1}{10}$
(D) $2 \frac{1}{2}$
(E) 20

## Solution

The best strategy is to choose the largest value and the smallest so that, $\frac{x}{y}>1$, is as large as possible.

When we consider the reciprocal, $\frac{y}{x}$, this will always produce a number less than 1 and will be of little consequence in our final consideration. The best choices, then, are $x=10$ and $y=1$ and $\frac{x}{y}+\frac{y}{x}$ becomes $\frac{10}{1}+\frac{1}{10}=10 \frac{1}{10}$.

ANSWER: (C)

## Part B