Question

Joe is given five tests that all have a maximum score of 100 points. The mean of his test scores is 90. If all his tests have a different grade and all the grades are whole numbers, what is the lowest grade he could have scored?

Answer 1

We know that he took 5 tests, mean is equal 90 so we know that following equations will be true if x will be sum of 5 scores:
$\frac{x}{5}=90$
$x=450$
Also we have to remember that max points that he could get is 100 so to find the lowest score he could get we have to do equation like this 
$\frac{100+y}{2}=90$
$100+y=180$
$y=80$

Answer 2

If the Mean = 90 for 5 test values
it means that there was a variation of values between maximum i-e 100 and minimum that may be any number not known.
The possible minimum value is when 4 tests result in 100 and the 5th is unknown
it means
Mean     = [(4X 100)+x] / 5
        90 = (400+x) / 5
400 + x  = 90 X 5
         x  = 450 -400 = 50

So the minimum possible test result is 50.