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Five positive integers have a mean if 5, a median of 5 and just one mode of 8. What is the difference between the largest and smallest integers??

 

The numbers will have to be          a, b, 5, 8, 8

 

where 

\(\frac{a+b+5+8+8}{5}=5\\ a+b+21=25\\ a+b=4\\\)

 

So the little numbers could be   1 and   3          OR   they could be   2 and 2

But there is only one mode so I guess the numbers have to be 1 and 3

 

So the smallest is 1 and the largest is 8     The range (difference between smallest and largest )  is   7