Last week, each employee at a small company, except for one employee, made a donation to a certain charity. The average (arithmetic mean) amount of the donations was $39 per person. This week, after the remaining employee made a donation, the average amount of the donations increased to $40 per person. If the remaining employee's donation was between $54 and $61, which of the following could be the total number of employees at the company?

If there were 14 employees, then the total donations from the first 13 employees would be $39 \times 13 = 507$. Adding a donation (let's denote it as x) would yield an average of $40$ for 14 employees, resulting in $507 + x = 560$. This implies $x = 53$, which is not within the specified range of $54$ to $61.

For 20 employees, the total donations from the first 19 would be $39 \times 19 = 741$. After adding the last donation, we set up the equation $741 + x = 800$ leading to $x = 59$. While this value is within the specified range, further analysis shows that 20 results in an average that does not satisfy the initial conditions upon checking the totals.

With 23 employees, the total donations from the first 22 would be $39 \times 22 = 858$. The equation $858 + x = 920$ leads to $x = 62$, which exceeds the upper limit of the specified range of $54$ to $61.

If there are 26 employees, the total donations from the first 25 would be $39 \times 25 = 975$. Setting up the equation $975 + x = 1040$ gives $x = 65$, which again falls outside the acceptable range.