Question 601665
The sum of the students scores (sum) is an integer that divided buy the number (n) of students taking the exam is 55.15
{{{sum/n=55.15}}} --> {{{sum=55.15n=(5515/100)*n}}}
We can transform that fraction into one in lowest terms
{{{5515/100=1103/20}}} and write
{{{sum=(1103/20)*n}}}
Any n that is not a multiple of 20 would divide by 20 giving a quotient q and a remainder r<20, with
{{{n=20q+r}}} and {{{sum=(1103/20)*(20q+r)=1103q+1103*r/20}}} would not be an integer.
If, and only if, n is a multiple of 20, will {{{sum=(1103/20)*n}}} be an integer.
The number of students taking the exam could have been 20, 40, 60, ..., 340, or 360.
The minimum number of students that could have taken the exam is {{{highlight (20)}}}, and the maximum number of students that could have taken the exam is {{{highlight(360)}}} .