Theory

➡ Average = Sum of all the Values / Total Number of Values
➡ Sum of All the values = Average * Total Number of Values
➡ Range = Highest Value - Lowest Value = Largest Value - Smallest Value

Set X consists of 11 different numbers

Let the Sum of these 11 numbers be S

The average (arithmetic mean) of the 10 smallest numbers is -1.6

Sum of 10 smallest numbers = Average * 10 = -1.6*10 = -16
Sum of 11 numbers = Sum of 10 smallest numbers + Largest Number
=> S = -16 + Largest Number
=> Largest Number = S + 16

The average of the 10 largest numbers is 5.2

Sum of 10 largest numbers = Average * 10 = 5.2*10 = 52
Sum of 11 numbers = Smallest number + Sum of 10 largest numbers
=> S = Smallest Number + 52
=> Smallest Number = S - 52

Range = Largest Number - Smallest Number = S + 16 - (S-52) = S-S + 16 + 52 = 68

So, Answer will be E.
Hope it helps!

Watch the following video to Learn the Basics of Statistics