My answer is that the longest is between 70 and 134.
Assume the order is a1, a2, a3, a4, a5, a6, a7. We know a4 is 84. We also know a7=4*a1+14. The largest number a7 could have is when the other numbers are the possible lowest, which means a2, a3 = a1 and a5, a6 = 84. Same reason, the smallest number a7 could have is when the other numbers are the possible biggest, which means a2, a3 = 84 and a5, a6 = a7. Since we know mean is 68, so the sum is 476. We can get following equations.
1. 3*a1 + 84*3 + a7 = 476 for biggest number
2. a1 + 84*3 + 3*a7 = 476 for smallest number
3. a7 = 4*a1 + 14 (this is we already know)
from above we can calculate that the a7 is between 70 and 134.
