SOLUTION: Suppose a class takes an exam and earns and average of 55.2. If all students earned integer scores from 0 to 100, is it possible to find four of the students whose average is 55.2?

Question 32203: Suppose a class takes an exam and earns and average of 55.2. If all students earned integer scores from 0 to 100, is it possible to find four of the students whose average is 55.2?
Found 2 solutions by stanbon, Fermat:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume there are four such integer scores: a,b,c,d
Then [a+b+c+d]/4 = 55.2
And [a+b+c+d]=224.8
Therefore not all a, b, c, d are integers.
Cheers,
Stan H.
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
The answer is NO!
If the average of four students is 55.2, then the sum total of their scores is 4*55.2 = 220.8.
But we are told that their scores are integer values. Therefore the sum total of any number of scores is also an integer.
Since 220.8 is not an integer, then it canot be the sum total of any number of scores.
Therefore we cannot have four students, with integer scores, whose average is 55.2.
It would work with 5 students though.
In fact, this means that the number of students in the class must be a multiple of 5, if the average is 55.2 (= 55 1/5)
Do you think you might get bonus marks if you mention this in your answer ? :)
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