Michael picks three different digits from the set $\{1,2,3,4,5\}$ and forms a mixed number by placing the digits in the spaces of $\square$. The fractional part of the mixed number must be less than 1. (For example, $4 \frac{2}{3}$ ). What is the difference between the largest and smallest possible mixed number that can be formed?
(A) $4 \frac{3}{5}$
(B) $4 \frac{9}{20}$
(C) $4 \frac{3}{10}$
(D) $4 \frac{4}{15}$
(E) $4 \frac{7}{20}$
Michael picks three different digits from the set $\{1,2,3,4,5\}$ and forms a mixed number by placing the digits in the spaces of $\square$. The fractional part of the mixed number must be less than 1. (For example, $4 \frac{2}{3}$ ). What is the difference between the largest and smallest possible mixed number that can be formed?
(A) $4 \frac{3}{5}$
(B) $4 \frac{9}{20}$
(C) $4 \frac{3}{10}$
(D) $4 \frac{4}{15}$
(E) $4 \frac{7}{20}$

## Solution

The largest possible number that Michael can form is $5 \frac{3}{4}$ while the smallest is $1 \frac{2}{5}$.

The difference is $5 \frac{3}{4}-1 \frac{2}{5}=4 \frac{7}{20}$.

ANSWER: (E)