document.write( "Question 601665: In a class that has 375 students, the average on an exam was exactly 55.15. If all students earned integer scores from 0 to 100, what is the minimum number of students that could have taken the exam, and what is the maximum number of students that could have taken the exam? \n" ); document.write( "

Algebra.Com's Answer #379988 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The sum of the students scores (sum) is an integer that divided buy the number (n) of students taking the exam is 55.15
\n" ); document.write( " $\"sum%2Fn=55.15\"$ --> $\"sum=55.15n=%285515%2F100%29%2An\"$
\n" ); document.write( "We can transform that fraction into one in lowest terms
\n" ); document.write( " $\"5515%2F100=1103%2F20\"$ and write
\n" ); document.write( " $\"sum=%281103%2F20%29%2An\"$
\n" ); document.write( "Any n that is not a multiple of 20 would divide by 20 giving a quotient q and a remainder r<20, with
\n" ); document.write( " $\"n=20q%2Br\"$ and $\"sum=%281103%2F20%29%2A%2820q%2Br%29=1103q%2B1103%2Ar%2F20\"$ would not be an integer.
\n" ); document.write( "If, and only if, n is a multiple of 20, will $\"sum=%281103%2F20%29%2An\"$ be an integer.
\n" ); document.write( "The number of students taking the exam could have been 20, 40, 60, ..., 340, or 360.
\n" ); document.write( "The minimum number of students that could have taken the exam is $\"highlight+%2820%29\"$ , and the maximum number of students that could have taken the exam is $\"highlight%28360%29\"$ . \n" ); document.write( "

\n" );