Total units = 540 units
The 540 units comprise 1-person, 2-person, and 4-person capacity.
Question: How many people stayed in the motel's 4-person units yesterday?

Statement 1: At this motel, 1/3 of the units are 4-person units.
Total 4-person units = 1/3 * 540 = 180
There are 180 4-person units in the motel and the total no. of occupied units is unknown and the question does not state that all 540 units were occupied. So, the target question cannot be answered and statement 1 is NOT SUFFICIENT.

Statement 2: Yesterday, 80 percent of the 4-person units in the motel were filled to capacity, and the rest of the 4-person units were empty.
80% of 4-person unit was occupied and 20% of 4-person unit was empty but total no. of 4-person unit among all the 540 units are unknown. So target, 4 questions cannot be answered and statement 2 is NOT SUFFICIENT.

Combining both statement:
Total 4-person units = 180, and 80% of 4-person units were occupied yesterday.
Therefore, a total of 4-person units occupied = 80% of 180
= 80% * 180
= 144 4-person units
Logically, 4 people are supposed to fill 4-person unit.

Therefore, for 144 4-person unit => 144 * 4 = 576 people were in the motel's 4-person unit yesterday, both statements together ARE SUFFICIENT.

ANSWER = OPTION C