Final answer:
A dump truck with a GVWR of 27,000lbs towing a trailer with a GVWR of 11,000lbs would require a Class A Commercial Driver's License (CDL) because the combined GVWR exceeds 26,001lbs and the trailer exceeds 10,000lbs.
Step-by-step explanation:
If you are operating a dump truck with a GVWR of 27,000lbs and towing a trailer with a GVWR of 11,000lbs, the combined GVWR is 38,000lbs. In the United States, a Class A CDL (Commercial Driver's License) is required when the vehicle being towed has a GVWR of more than 10,000lbs and the combined GVWR of the towing vehicle and the trailer is more than 26,001lbs. Therefore, you would need a Class A CDL to drive this vehicle configuration legally.