Is the range of a combined set (S,T) bigger than the sum of

The range of a set is the difference between the largest and smallest elements of a set.

\(range_t=t_{max}-t_{min}\);
\(range_s=s_{max}-s_{min}\);

Question: \(range_{t&s}>t_{max}-t_{min}+s_{max}-s_{min}\)?

(1) The largest element of T is bigger than the largest element of S --> \(t_{max}>s_{max}\), so the largest element of combined set is \(t_{max}\) but we still don't know which is the smallest element of combined set:

If it's \(t_{min}\) then the question becomes is \(t_{max}-t_{min}>t_{max}-t_{min}+s_{max}-s_{min}\) --> is \(0>s_{max}-s_{min}\) and the answer would be NO;
If it's \(s_{min}\) then the question becomes is \(t_{max}-s_{min}>t_{max}-t_{min}+s_{max}-s_{min}\) --> is \(t_{min}>s_{max}\) and the answer would be sometimes NO and sometimes YES.

Not sufficient.

(2) The smallest element of T is bigger than the largest element of S --> \(t_{min}>s_{max}\), so the largest of combined set is \(t_{max}\) and the smallest element of combined set is \(s_{min}\).

So the question becomes is \(t_{max}-s_{min}>t_{max}-t_{min}+s_{max}-s_{min}\) --> is \(t_{min}>s_{max}\) and the answer is YES.

Sufficient.

Answer: B.