Performance of Min and Max Sum of array in C#
Performance 
The current solution does two things:


Sort the inputs,   O(N log(N))
Sum the inputs,    O(N)


It is possible to calculate the result in a single pass O(N) by reading through the inputs, keeping track of the min, max and sum as we progress and then subtracting the min and max from the sum as we are currently doing.

Note: For the current code 

if(arr[i]&gt;=1 &amp;&amp; arr[i]&lt;=Math.Pow(10,9))
     sum += arr[i];                


does nothing useful, the problem definition says that the inputs are in the range [1,10^9] so the test will never fail.

Religious war trigger 
I would push for always using braces around a block, even single line blocks. I have seen too many cases of 

if(arr[i]&gt;=1 &amp;&amp; arr[i]&lt;=Math.Pow(10,9))
     sum += arr[i];                
     // do something else every time, not just when the test passes


The Hint 
The 64- bit integer hint means that the sum of the values may exceed the maximum value for a int, so use a long for the sum.