7. Four different positive integers are to be chosen so that they have a mean of 2017 . What is the smallest possible range of the chosen integers?
A 2
B 3
C 4
D 5
E 6
7. C The smallest possible range of four positive integers is 3 . Let these integers be $n$, $n+1, n+2, n+3$. For the mean of these four integers to equal 2017, we have $\frac{n+n+1+n+2+n+3}{4}=2017$, that is $n=2015 \frac{1}{2}$. So the smallest possible range is not 3. However, note that the integers 2015, 2016, 2018 and 2019 have mean 2017 and range 4 . So the smallest possible range of the integers is 4 .